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Sample records for underlying mathematical formalism

  1. Digital Resource Developments for Mathematics Education Involving Homework across Formal, Non-Formal and Informal Settings

    Science.gov (United States)

    Radovic, Slaviša; Passey, Don

    2016-01-01

    The aim of this paper is to explore further an under-developed area--how drivers of curriculum, pedagogy and assessment conceptions and practices shape the creation and uses of technologically based resources to support mathematics learning across informal, non-formal and formal learning environments. The paper considers: the importance of…

  2. A Mathematical Formalization Proposal for Business Growth

    Directory of Open Access Journals (Sweden)

    Gheorghe BAILESTEANU

    2013-01-01

    Full Text Available Economic sciences have known a spectacular evolution in the last century; beginning to use axiomatic methods, applying mathematical instruments as a decision-making tool. The quest to formalization needs to be addressed from various different angles, reducing entry and operating formal costs, increasing the incentives for firms to operate formally, reducing obstacles to their growth, and searching for inexpensive approaches through which to enforce compliancy with government regulations. This paper proposes a formalized approach to business growth, based on mathematics and logics, taking into consideration the particularities of the economic sector.

  3. The Transition to Formal Thinking in Mathematics

    Science.gov (United States)

    Tall, David

    2008-01-01

    This paper focuses on the changes in thinking involved in the transition from school mathematics to formal proof in pure mathematics at university. School mathematics is seen as a combination of visual representations, including geometry and graphs, together with symbolic calculations and manipulations. Pure mathematics in university shifts…

  4. A Mathematical Account of the NEGF Formalism

    DEFF Research Database (Denmark)

    Cornean, Decebal Horia; Moldoveanu, Valeriu; Pillet, Claude-Alain

    2018-01-01

    The main goal of this paper is to put on solid mathematical grounds the so-called non-equilibrium Green’s function transport formalism for open systems. In particular, we derive the Jauho–Meir–Wingreen formula for the time-dependent current through an interacting sample coupled to non-interacting......The main goal of this paper is to put on solid mathematical grounds the so-called non-equilibrium Green’s function transport formalism for open systems. In particular, we derive the Jauho–Meir–Wingreen formula for the time-dependent current through an interacting sample coupled to non...

  5. Developing corpus-based translation methods between informal and formal mathematics : project description

    NARCIS (Netherlands)

    Kaliszyk, C.; Urban, J.; Vyskocil, J.; Geuvers, J.H.; Watt, S.M.; Davenport, J.H.; Sexton, A.P.; Sojka, P.; Urban, J.

    2014-01-01

    The goal of this project is to (i) accumulate annotated informal/formal mathematical corpora suitable for training semi-automated translation between informal and formal mathematics by statistical machine-translation methods, (ii) to develop such methods oriented at the formalization task, and in

  6. Problem posing as a didactic resource in formal mathematics courses to train future secondary school mathematics teachers

    Directory of Open Access Journals (Sweden)

    Lorena Salazar Solórzano

    2015-06-01

    Full Text Available Beginning university training programs must focus on different competencies for mathematics teachers, i.e., not only on solving problems, but also on posing them and analyzing the mathematical activity. This paper reports the results of an exploratory study conducted with future secondary school mathematics teachers on the introduction of problem-posing tasks in formal mathematics courses, specifically in abstract algebra and real analysis courses. Evidence was found that training which includes problem-posing tasks has a positive impact on the students’ understanding of definitions, theorems and exercises within formal mathematics, as well as on their competency in reflecting on the mathematical activity. 

  7. Measurements and mathematical formalism of quantum mechanics

    Science.gov (United States)

    Slavnov, D. A.

    2007-03-01

    A scheme for constructing quantum mechanics is given that does not have Hilbert space and linear operators as its basic elements. Instead, a version of algebraic approach is considered. Elements of a noncommutative algebra (observables) and functionals on this algebra (elementary states) associated with results of single measurements are used as primary components of the scheme. On the one hand, it is possible to use within the scheme the formalism of the standard (Kolmogorov) probability theory, and, on the other hand, it is possible to reproduce the mathematical formalism of standard quantum mechanics, and to study the limits of its applicability. A short outline is given of the necessary material from the theory of algebras and probability theory. It is described how the mathematical scheme of the paper agrees with the theory of quantum measurements, and avoids quantum paradoxes.

  8. Numerical approximation abilities correlate with and predict informal but not formal mathematics abilities.

    Science.gov (United States)

    Libertus, Melissa E; Feigenson, Lisa; Halberda, Justin

    2013-12-01

    Previous research has found a relationship between individual differences in children's precision when nonverbally approximating quantities and their school mathematics performance. School mathematics performance emerges from both informal (e.g., counting) and formal (e.g., knowledge of mathematics facts) abilities. It remains unknown whether approximation precision relates to both of these types of mathematics abilities. In the current study, we assessed the precision of numerical approximation in 85 3- to 7-year-old children four times over a span of 2years. In addition, at the final time point, we tested children's informal and formal mathematics abilities using the Test of Early Mathematics Ability (TEMA-3). We found that children's numerical approximation precision correlated with and predicted their informal, but not formal, mathematics abilities when controlling for age and IQ. These results add to our growing understanding of the relationship between an unlearned nonsymbolic system of quantity representation and the system of mathematics reasoning that children come to master through instruction. Copyright © 2013 Elsevier Inc. All rights reserved.

  9. Mathematic-Graphical Formalization of Switch Point Control Circuit Function

    Directory of Open Access Journals (Sweden)

    Juraj Zdansky

    2004-01-01

    Full Text Available This article describes authors designed method then enables mathematic – graphical formalization of system’s functional specification. The result of this method is algebraic system – finite automata that is written in transition table. This transition table is possible to overwrite to graphic form (state diagram or to mathematic form (transition and output function. This method is described by example of switch point control circuit.

  10. Formal Verification -26 ...

    Indian Academy of Sciences (India)

    by testing of the components and successful testing leads to the software being ... Formal verification is based on formal methods which are mathematically based ..... scenario under which a similar error could occur. There are various other ...

  11. Non-formal mechanisms in mathematical cognitive development: The case of arithmetic

    NARCIS (Netherlands)

    Braithwaite, D.W.; Goldstone, R.L.; van der Maas, H.L.J.; Landy, D.H.

    The idea that cognitive development involves a shift towards abstraction has a long history in psychology. One incarnation of this idea holds that development in the domain of mathematics involves a shift from non-formal mechanisms to formal rules and axioms. Contrary to this view, the present study

  12. Mathematical formalization of theories of motivation proposed by Maslow and Herzberg

    OpenAIRE

    Kotliarov,Ivan

    2008-01-01

    Maslow's theory is by far the most known theory of motivation, and the most common in the business and management practice. Herzberg's theory fits the observations and explains some aspects of human motivation left unexplained by Maslow. However, these theories have never been formalized on a strictly mathematical basis. The present article gives an outline of a mathematical model of theories of motivation proposed by Abraham Maslow and Frederick Herzberg. This model is built on a basis of sp...

  13. Understanding Informal and Formal Mathematical Abilities in Mainland Chinese and Chinese-American Children.

    Science.gov (United States)

    Zhou, Zheng; Cheng, Christine; Mottram, Lisa; Rosenblum, Stacey

    Informal and formal mathematical abilities were studied in the preschool, kindergarten, and first grade children in Beijing, China and Chinese-American children in New York City. Test of Early Mathematical Abilities-2nd Edition (TEMA-2) was administered to the three groups of children (children from Beijing, Chinese-American from lower-class, and…

  14. Thermodynamic formalism the mathematical structures of equilibrium statistical mechanics

    CERN Document Server

    Ruelle, David

    2004-01-01

    Reissued in the Cambridge Mathematical Library, this classic book outlines the theory of thermodynamic formalism which was developed to describe the properties of certain physical systems consisting of a large number of subunits. Background material on physics has been collected in appendices to help the reader. Supplementary work is provided in the form of exercises and problems that were "open" at the original time of writing.

  15. Formality theory from Poisson structures to deformation quantization

    CERN Document Server

    Esposito, Chiara

    2015-01-01

    This book is a survey of the theory of formal deformation quantization of Poisson manifolds, in the formalism developed by Kontsevich. It is intended as an educational introduction for mathematical physicists who are dealing with the subject for the first time. The main topics covered are the theory of Poisson manifolds, star products and their classification, deformations of associative algebras and the formality theorem. Readers will also be familiarized with the relevant physical motivations underlying the purely mathematical construction.

  16. Viewing Formal Mathematics from Yoruba Conception of the Sky

    OpenAIRE

    Segla, Aimé

    2016-01-01

    Yoruba Cosmology resembles a generative system at the foundation of concepts. The traditional thought, which derives from the reality of the identical pair incorporated from cosmology into real life, exemplifies all kind of existing knowledge, culture and practices.  Previous studies by the author show in some detail the scientific interests in Yoruba cosmology. The present paper aims to view formal mathematics through the interpretation of Yoruba sky knowledge. It attempts to demonstrate tha...

  17. Mathematical formalization of theories of motivation proposed by Maslow and Herzberg

    Directory of Open Access Journals (Sweden)

    Ivan Kotliarov

    2008-12-01

    Full Text Available Maslow's theory is by far the most known theory of motivation, and the most common in the business and management practice. Herzberg's theory fits the observations and explains some aspects of human motivation left unexplained by Maslow. However, these theories have never been formalized on a strictly mathematical basis. The present article gives an outline of a mathematical model of theories of motivation proposed by Abraham Maslow and Frederick Herzberg. This model is built on a basis of special non-continuous functions. This description may be a good basis for HR software and may be useful for business and management.

  18. On the Formal-Logical Analysis of the Foundations of Mathematics Applied to Problems in Physics

    Science.gov (United States)

    Kalanov, Temur Z.

    2016-03-01

    Analysis of the foundations of mathematics applied to problems in physics was proposed. The unity of formal logic and of rational dialectics is methodological basis of the analysis. It is shown that critical analysis of the concept of mathematical quantity - central concept of mathematics - leads to the following conclusion: (1) The concept of ``mathematical quantity'' is the result of the following mental operations: (a) abstraction of the ``quantitative determinacy of physical quantity'' from the ``physical quantity'' at that the ``quantitative determinacy of physical quantity'' is an independent object of thought; (b) abstraction of the ``amount (i.e., abstract number)'' from the ``quantitative determinacy of physical quantity'' at that the ``amount (i.e., abstract number)'' is an independent object of thought. In this case, unnamed, abstract numbers are the only sign of the ``mathematical quantity''. This sign is not an essential sign of the material objects. (2) The concept of mathematical quantity is meaningless, erroneous, and inadmissible concept in science because it represents the following formal-logical and dialectical-materialistic error: negation of the existence of the essential sign of the concept (i.e., negation of the existence of the essence of the concept) and negation of the existence of measure of material object.

  19. Discrete mathematics, formal methods, the Z schema and the software life cycle

    Science.gov (United States)

    Bown, Rodney L.

    1991-01-01

    The proper role and scope for the use of discrete mathematics and formal methods in support of engineering the security and integrity of components within deployed computer systems are discussed. It is proposed that the Z schema can be used as the specification language to capture the precise definition of system and component interfaces. This can be accomplished with an object oriented development paradigm.

  20. Formalization of hydrocarbon conversion scheme of catalytic cracking for mathematical model development

    Science.gov (United States)

    Nazarova, G.; Ivashkina, E.; Ivanchina, E.; Kiseleva, S.; Stebeneva, V.

    2015-11-01

    The issue of improving the energy and resource efficiency of advanced petroleum processing can be solved by the development of adequate mathematical model based on physical and chemical regularities of process reactions with a high predictive potential in the advanced petroleum refining. In this work, the development of formalized hydrocarbon conversion scheme of catalytic cracking was performed using thermodynamic parameters of reaction defined by the Density Functional Theory. The list of reaction was compiled according to the results of feedstock structural-group composition definition, which was done by the n-d-m-method, the Hazelvuda method, qualitative composition of feedstock defined by gas chromatography-mass spectrometry and individual composition of catalytic cracking gasoline fraction. Formalized hydrocarbon conversion scheme of catalytic cracking will become the basis for the development of the catalytic cracking kinetic model.

  1. Mathematical logic in the human brain: syntax.

    Directory of Open Access Journals (Sweden)

    Roland Friedrich

    Full Text Available Theory predicts a close structural relation of formal languages with natural languages. Both share the aspect of an underlying grammar which either generates (hierarchically structured expressions or allows us to decide whether a sentence is syntactically correct or not. The advantage of rule-based communication is commonly believed to be its efficiency and effectiveness. A particularly important class of formal languages are those underlying the mathematical syntax. Here we provide brain-imaging evidence that the syntactic processing of abstract mathematical formulae, written in a first order language, is, indeed efficient and effective as a rule-based generation and decision process. However, it is remarkable, that the neural network involved, consisting of intraparietal and prefrontal regions, only involves Broca's area in a surprisingly selective way. This seems to imply that despite structural analogies of common and current formal languages, at the neural level, mathematics and natural language are processed differently, in principal.

  2. Formalization of Database Systems -- and a Formal Definition of {IMS}

    DEFF Research Database (Denmark)

    Bjørner, Dines; Løvengreen, Hans Henrik

    1982-01-01

    Drawing upon an analogy between Programming Language Systems and Database Systems we outline the requirements that architectural specifications of database systems must futfitl, and argue that only formal, mathematical definitions may 6atisfy these. Then we illustrate home aspects and touch upon...... come ueee of formal definitions of data models and databaee management systems. A formal model of INS will carry this discussion. Finally we survey some of the exkting literature on formal definitions of database systems. The emphasis will be on constructive definitions in the denotationul semantics...... style of the VCM: Vienna Development Nethd. The role of formal definitions in international standardiaation efforts is briefly mentioned....

  3. Mathematical Formalism for Designing Wide-Field X-Ray Telescopes: Mirror Nodal Positions and Detector Tilts

    Science.gov (United States)

    Elsner, R. F.; O'Dell, S. L.; Ramsey, B. D.; Weisskopf, M. C.

    2011-01-01

    We provide a mathematical formalism for optimizing the mirror nodal positions along the optical axis and the tilt of a commonly employed detector configuration at the focus of a x-ray telescope consisting of nested mirror shells with known mirror surface prescriptions. We adopt the spatial resolution averaged over the field-of-view as the figure of merit M. A more complete description appears in our paper in these proceedings.

  4. Formalizing the concept of sound.

    Energy Technology Data Exchange (ETDEWEB)

    Kaper, H. G.; Tipei, S.

    1999-08-03

    The notion of formalized music implies that a musical composition can be described in mathematical terms. In this article we explore some formal aspects of music and propose a framework for an abstract approach.

  5. Formalizing Probabilistic Safety Claims

    Science.gov (United States)

    Herencia-Zapana, Heber; Hagen, George E.; Narkawicz, Anthony J.

    2011-01-01

    A safety claim for a system is a statement that the system, which is subject to hazardous conditions, satisfies a given set of properties. Following work by John Rushby and Bev Littlewood, this paper presents a mathematical framework that can be used to state and formally prove probabilistic safety claims. It also enables hazardous conditions, their uncertainties, and their interactions to be integrated into the safety claim. This framework provides a formal description of the probabilistic composition of an arbitrary number of hazardous conditions and their effects on system behavior. An example is given of a probabilistic safety claim for a conflict detection algorithm for aircraft in a 2D airspace. The motivation for developing this mathematical framework is that it can be used in an automated theorem prover to formally verify safety claims.

  6. Examining Fourth-Grade Mathematics Writing: Features of Organization, Mathematics Vocabulary, and Mathematical Representations

    Science.gov (United States)

    Hebert, Michael A.; Powell, Sarah R.

    2016-01-01

    Increasingly, students are expected to write about mathematics. Mathematics writing may be informal (e.g., journals, exit slips) or formal (e.g., writing prompts on high-stakes mathematics assessments). In order to develop an effective mathematics-writing intervention, research needs to be conducted on how students organize mathematics writing and…

  7. Discrete Mathematics

    DEFF Research Database (Denmark)

    Sørensen, John Aasted

    2011-01-01

    The objectives of Discrete Mathematics (IDISM2) are: The introduction of the mathematics needed for analysis, design and verification of discrete systems, including the application within programming languages for computer systems. Having passed the IDISM2 course, the student will be able...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics......; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...

  8. Transforming process models : executable rewrite rules versus a formalized Java program

    NARCIS (Netherlands)

    Van Gorp, P.M.E.; Eshuis, H.; Petriu, D.C.; Rouquette, N.

    2010-01-01

    In the business process management community, transformations for process models are usually programmed using imperative languages (such as Java). The underlying mapping rules tend to be documented using informal visual rules whereas they tend to be formalized using mathematical set constructs. In

  9. Transforming process models : executable rewrite rules versus a formalized Java program

    NARCIS (Netherlands)

    Van Gorp, P.M.E.; Eshuis, H.

    2010-01-01

    In the business process management community, transformations for process models are usually programmed using imperative languages. The underlying mapping rules tend to be documented using informal visual rules whereas they tend to be formalized using mathematical set constructs. In the Graph and

  10. Making Explicit the Formalism Underlying Evaluation in Music Information Retrieval Research

    DEFF Research Database (Denmark)

    Sturm, Bob L.

    2014-01-01

    We make explicit the formalism underlying evaluation in music information retrieval research. We define a ``system,'' what it means to ``analyze'' one, and make clear the aims, parts, design, execution, interpretation, assumptions and limitations of its ``evaluation.'' We apply this formalism...... to discuss the MIREX automatic mood classification task....

  11. Classical Mathematical Logic The Semantic Foundations of Logic

    CERN Document Server

    Epstein, Richard L

    2011-01-01

    In Classical Mathematical Logic, Richard L. Epstein relates the systems of mathematical logic to their original motivations to formalize reasoning in mathematics. The book also shows how mathematical logic can be used to formalize particular systems of mathematics. It sets out the formalization not only of arithmetic, but also of group theory, field theory, and linear orderings. These lead to the formalization of the real numbers and Euclidean plane geometry. The scope and limitations of modern logic are made clear in these formalizations. The book provides detailed explanations of all proo

  12. The Mathematical Formalism of a Particle in a Magnetic Field

    CERN Document Server

    Mantoiu, M

    2005-01-01

    In this review article we develop a basic part of the mathematical theory involved in the description of a particle (classical and quantal) placed in the Euclidean space $\\mathbb R^N$ under the influence of a magnetic field $B$, emphasising the structure of the family of observables.

  13. Methodological imperfection and formalizations in scientific activity

    International Nuclear Information System (INIS)

    Svetlichny, G.

    1987-01-01

    Any mathematical formalization of scientific activity allows for imperfections in the methodology that is formalized. These can be of three types, dirty, rotten, and dammed. Restricting mathematical attention to those methods that cannot be construed to be imperfect drastically reduces the class of objects that must be analyzed, and related all other objects to these more regular ones. Examples are drawn from empirical logic

  14. Mathematical psychology.

    Science.gov (United States)

    Batchelder, William H

    2010-09-01

    Mathematical psychology is a sub-field of psychology that started in the 1950s and has continued to grow as an important contributor to formal psychological theory, especially in the cognitive areas of psychology such as learning, memory, classification, choice response time, decision making, attention, and problem solving. In addition, there are several scientific sub-areas that were originated by mathematical psychologists such as the foundations of measurement, stochastic memory models, and psychologically motivated reformulations of expected utility theory. Mathematical psychology does not include all uses of mathematics and statistics in psychology, and indeed there is a long history of such uses especially in the areas of perception and psychometrics. What is most unique about mathematical psychology is its approach to theory construction. While accepting the behaviorist dictum that the data in psychology must be observable and replicable, mathematical models are specified in terms of unobservable formal constructs that can predict detailed aspects of data across multiple experimental and natural settings. By now almost all the substantive areas of cognitive and experimental psychology have formal mathematical models and theories, and many of these are due to researchers that identify with mathematical psychology. Copyright © 2010 John Wiley & Sons, Ltd. For further resources related to this article, please visit the WIREs website. Copyright © 2010 John Wiley & Sons, Ltd.

  15. Formal verification - Robust and efficient code: Introduction to Formal Verification

    CERN Multimedia

    CERN. Geneva

    2016-01-01

    In general, FV means "proving that certain properties hold for a given system using formal mathematics". This definition can certainly feel daunting, however, as we will learn, we can reap benefits from the paradigm without digging too deep into ...

  16. Discrete Mathematics

    DEFF Research Database (Denmark)

    Sørensen, John Aasted

    2011-01-01

    ; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics...... to new problems. Relations and functions: Define a product set; define and apply equivalence relations; construct and apply functions. Apply these concepts to new problems. Natural numbers and induction: Define the natural numbers; apply the principle of induction to verify a selection of properties...

  17. Problem-solving rubrics revisited: Attending to the blending of informal conceptual and formal mathematical reasoning

    Science.gov (United States)

    Hull, Michael M.; Kuo, Eric; Gupta, Ayush; Elby, Andrew

    2013-06-01

    Much research in engineering and physics education has focused on improving students’ problem-solving skills. This research has led to the development of step-by-step problem-solving strategies and grading rubrics to assess a student’s expertise in solving problems using these strategies. These rubrics value “communication” between the student’s qualitative description of the physical situation and the student’s formal mathematical descriptions (usually equations) at two points: when initially setting up the equations, and when evaluating the final mathematical answer for meaning and plausibility. We argue that (i) neither the rubrics nor the associated problem-solving strategies explicitly value this kind of communication during mathematical manipulations of the chosen equations, and (ii) such communication is an aspect of problem-solving expertise. To make this argument, we present a case study of two students, Alex and Pat, solving the same kinematics problem in clinical interviews. We argue that Pat’s solution, which connects manipulation of equations to their physical interpretation, is more expertlike than Alex’s solution, which uses equations more algorithmically. We then show that the types of problem-solving rubrics currently available do not discriminate between these two types of solutions. We conclude that problem-solving rubrics should be revised or repurposed to more accurately assess problem-solving expertise.

  18. Mathematical logic foundations for information science

    CERN Document Server

    Li, Wei

    2014-01-01

    Mathematical logic is a branch of mathematics that takes axiom systems and mathematical proofs as its objects of study. This book shows how it can also provide a foundation for the development of information science and technology. The first five chapters systematically present the core topics of classical mathematical logic, including the syntax and models of first-order languages, formal inference systems, computability and representability, and Gödel’s theorems. The last five chapters present extensions and developments of classical mathematical logic, particularly the concepts of version sequences of formal theories and their limits, the system of revision calculus, proschemes (formal descriptions of proof methods and strategies) and their properties, and the theory of inductive inference. All of these themes contribute to a formal theory of axiomatization and its application to the process of developing information technology and scientific theories. The book also describes the paradigm of three kinds...

  19. Mathematical logic foundations for information science

    CERN Document Server

    Li, Wei

    2010-01-01

    This book presents the basic principles and formal calculus of mathematical logic. It covers core contents, extensions and developments of classical mathematical logic, and it offers formal proofs and concrete examples for all theoretical results.

  20. Beware the tail that wags the dog: informal and formal models in biology.

    Science.gov (United States)

    Gunawardena, Jeremy

    2014-11-05

    Informal models have always been used in biology to guide thinking and devise experiments. In recent years, formal mathematical models have also been widely introduced. It is sometimes suggested that formal models are inherently superior to informal ones and that biology should develop along the lines of physics or economics by replacing the latter with the former. Here I suggest to the contrary that progress in biology requires a better integration of the formal with the informal. © 2014 Gunawardena. This article is distributed by The American Society for Cell Biology under license from the author(s). Two months after publication it is available to the public under an Attribution–Noncommercial–Share Alike 3.0 Unported Creative Commons License (http://creativecommons.org/licenses/by-nc-sa/3.0).

  1. Formal Methods for Life-Critical Software

    Science.gov (United States)

    Butler, Ricky W.; Johnson, Sally C.

    1993-01-01

    The use of computer software in life-critical applications, such as for civil air transports, demands the use of rigorous formal mathematical verification procedures. This paper demonstrates how to apply formal methods to the development and verification of software by leading the reader step-by-step through requirements analysis, design, implementation, and verification of an electronic phone book application. The current maturity and limitations of formal methods tools and techniques are then discussed, and a number of examples of the successful use of formal methods by industry are cited.

  2. PhiMSAMP: philosophy of mathematics: sociological aspects and mathematical practice

    NARCIS (Netherlands)

    Löwe, B.; Müller, T.

    2010-01-01

    Philosophy of mathematics is moving in a new direction: away from a foundationalism in terms of formal logic and traditional ontology, and towards a broader range of approaches that are united by a focus on mathematical practice. The scientific research network PhiMSAMP (Philosophy of Mathematics:

  3. Stroh formalism and Rayleigh waves

    CERN Document Server

    Tanuma, Kazumi

    2008-01-01

    Introduces a powerful and elegant mathematical method for the analysis of anisotropic elasticity equationsThe reader can grasp the essentials as quickly as possibleCan be used as a textbook, which presents compactly introduction and applications of the Stroh formalismAppeals to the people not only in mathematics but also in mechanics and engineering sciencePrerequisites are only basic linear algebra, calculus and fundamentals of differential equations

  4. Concepts of formal concept analysis

    Science.gov (United States)

    Žáček, Martin; Homola, Dan; Miarka, Rostislav

    2017-07-01

    The aim of this article is apply of Formal Concept Analysis on concept of world. Formal concept analysis (FCA) as a methodology of data analysis, information management and knowledge representation has potential to be applied to a verity of linguistic problems. FCA is mathematical theory for concepts and concept hierarchies that reflects an understanding of concept. Formal concept analysis explicitly formalizes extension and intension of a concept, their mutual relationships. A distinguishing feature of FCA is an inherent integration of three components of conceptual processing of data and knowledge, namely, the discovery and reasoning with concepts in data, discovery and reasoning with dependencies in data, and visualization of data, concepts, and dependencies with folding/unfolding capabilities.

  5. Formal methods for industrial critical systems a survey of applications

    CERN Document Server

    Margaria-Steffen, Tiziana

    2012-01-01

    "Today, formal methods are widely recognized as an essential step in the design process of industrial safety-critical systems. In its more general definition, the term formal methods encompasses all notations having a precise mathematical semantics, together with their associated analysis methods, that allow description and reasoning about the behavior of a system in a formal manner.Growing out of more than a decade of award-winning collaborative work within the European Research Consortium for Informatics and Mathematics, Formal Methods for Industrial Critical Systems: A Survey of Applications presents a number of mainstream formal methods currently used for designing industrial critical systems, with a focus on model checking. The purpose of the book is threefold: to reduce the effort required to learn formal methods, which has been a major drawback for their industrial dissemination; to help designers to adopt the formal methods which are most appropriate for their systems; and to offer a panel of state-of...

  6. Pluralism in mathematics a new position in philosophy of mathematics

    CERN Document Server

    Friend, Michèle

    2014-01-01

    This book is about philosophy, mathematics and logic, giving a philosophical account of Pluralism which is a family of positions in the philosophy of mathematics. There are four parts to this book, beginning with a look at motivations for Pluralism by way of Realism, Maddy's Naturalism, Shapiro's Structuralism and Formalism. In the second part of this book the author covers: the philosophical presentation of Pluralism; using a formal theory of logic metaphorically; rigour and proof for the Pluralist; and mathematical fixtures. In the third part the author goes on to focus on the transcendental presentation of Pluralism, and in part four looks at applications of Pluralism, such as a Pluralist approach to proof in mathematics and how Pluralism works in regard to together-inconsistent philosophies of mathematics. The book finishes with suggestions for further Pluralist enquiry. In this work the author takes a deeply radical approach in developing a new position that will either convert readers, or act as a stron...

  7. Formalizing Darwinism and inclusive fitness theory.

    Science.gov (United States)

    Grafen, Alan

    2009-11-12

    Inclusive fitness maximization is a basic building block for biological contributions to any theory of the evolution of society. There is a view in mathematical population genetics that nothing is caused to be maximized in the process of natural selection, but this is explained as arising from a misunderstanding about the meaning of fitness maximization. Current theoretical work on inclusive fitness is discussed, with emphasis on the author's 'formal Darwinism project'. Generally, favourable conclusions are drawn about the validity of assuming fitness maximization, but the need for continuing work is emphasized, along with the possibility that substantive exceptions may be uncovered. The formal Darwinism project aims more ambitiously to represent in a formal mathematical framework the central point of Darwin's Origin of Species, that the mechanical processes of inheritance and reproduction can give rise to the appearance of design, and it is a fitting ambition in Darwin's bicentenary year to capture his most profound discovery in the lingua franca of science.

  8. Representations of spacetime: Formalism and ontological commitment

    Science.gov (United States)

    Bain, Jonathan Stanley

    This dissertation consists of two parts. The first is on the relation between formalism and ontological commitment in the context of theories of spacetime, and the second is on scientific realism. The first part begins with a look at how the substantivalist/relationist debate over the ontological status of spacetime has been influenced by a particular mathematical formalism, that of tensor analysis on differential manifolds (TADM). This formalism has motivated the substantivalist position known as manifold substantivalism. Chapter 1 focuses on the hole argument which maintains that manifold substantivalism is incompatible with determinism. I claim that the realist motivations underlying manifold substantivalism can be upheld, and the hole argument avoided, by adopting structural realism with respect to spacetime. In this context, this is the claim that it is the structure that spacetime points enter into that warrants belief and not the points themselves. In Chapter 2, an elimination principle is defined by means of which a distinction can be made between surplus structure and essential structure with respect to formulations of a theory in two distinct mathematical formulations and some prior ontological commitments. This principle is then used to demonstrate that manifold points may be considered surplus structure in the formulation of field theories. This suggests that, if we are disposed to read field theories literally, then, at most, it should be the essential structure common to all alternative formulations of such theories that should be taken literally. I also investigate how the adoption of alternative formalisms informs other issues in the philosophy of spacetime. Chapter 3 offers a realist position which takes a semantic moral from the preceding investigation and an epistemic moral from work done on reliability. The semantic moral advises us to read only the essential structure of our theories literally. The epistemic moral shows us that such structure

  9. An Ontology for a TripTych Formal Software Development

    DEFF Research Database (Denmark)

    Bjørner, Dines

    2003-01-01

    An ontology, ie., a formalised set of strongly interrelated definitions, is given for an approach to software development that spans domain engineering, requirements engineering and software design - and which is otherwise based on a judicious use of both informal and formal, mathematics-based te......An ontology, ie., a formalised set of strongly interrelated definitions, is given for an approach to software development that spans domain engineering, requirements engineering and software design - and which is otherwise based on a judicious use of both informal and formal, mathematics...

  10. The Markov process admits a consistent steady-state thermodynamic formalism

    Science.gov (United States)

    Peng, Liangrong; Zhu, Yi; Hong, Liu

    2018-01-01

    The search for a unified formulation for describing various non-equilibrium processes is a central task of modern non-equilibrium thermodynamics. In this paper, a novel steady-state thermodynamic formalism was established for general Markov processes described by the Chapman-Kolmogorov equation. Furthermore, corresponding formalisms of steady-state thermodynamics for the master equation and Fokker-Planck equation could be rigorously derived in mathematics. To be concrete, we proved that (1) in the limit of continuous time, the steady-state thermodynamic formalism for the Chapman-Kolmogorov equation fully agrees with that for the master equation; (2) a similar one-to-one correspondence could be established rigorously between the master equation and Fokker-Planck equation in the limit of large system size; (3) when a Markov process is restrained to one-step jump, the steady-state thermodynamic formalism for the Fokker-Planck equation with discrete state variables also goes to that for master equations, as the discretization step gets smaller and smaller. Our analysis indicated that general Markov processes admit a unified and self-consistent non-equilibrium steady-state thermodynamic formalism, regardless of underlying detailed models.

  11. Thermodynamic and multifractal formalism and the Bowen-series map

    International Nuclear Information System (INIS)

    Rudolph, O.

    1994-07-01

    In the theory of quantum chaos one studies the semiclassical behaviour of quantum mechanical systems whose corresponding classical counterparts exhibit chaos. These systems are sometimes considered as model systems in the theory of quantum chaos since they are well understood from a mathematical point of view. In this work we study the multifractal formalism for the geodesic flow on surfaces with constant negative curvature. The multifractal analysis of measures has been developed in order to characterize the scaling behaviour of measures on attractors of classical chaotic dynamical systems globally. In order to relate the multifractal formalism with quantities usually considered in the study of the geodesic flow on Riemann surfaces with constant negative curvature, it is necessary to establish the assertions of the multifractal formalism in a mathematically rigorous way. This is achieved with the help of the thermodynamic formalism for hyperbolic dynamical systems developed by Ruelle, Bowen and others. (orig.)

  12. Gauge theory and gravitation: an approach to a fiber bundle formalism

    International Nuclear Information System (INIS)

    Mello, L.A. de.

    1986-01-01

    The thesis is composed of two different parts. A formal complete and rigorous mathematical part-of topics of differential manilfolds, exterior calculus, riemannian geometry, principal fiber bundle (p.f.) with connections and linear connections and a second part of application of this mathematical formalism concerning physical theories, particularly the Maxwell eletromagnetism (EM), gauge theory of Yang-Mills (Y-M), the GRT, and the gravitation theory of Einstein-Cartan. (E.C.) [pt

  13. Early Number Competencies of Children at the Start of Formal ...

    African Journals Online (AJOL)

    cce

    occupy a central position in the Primary Mathematics Curriculum in Ghana. ... The results of the study suggest that pupils possess varied abilities .... formal classroom instruction, to the use of memorised number facts and formal addition and.

  14. Working memory resources in young children with mathematical difficulties.

    Science.gov (United States)

    Kyttälä, Minna; Aunio, Pirjo; Hautamäki, Jarkko

    2010-02-01

    Working memory (WM) (Baddeley, 1986, 1997) is argued to be one of the most important cognitive resources underlying mathematical competence (Geary, 2004). Research has established close links between WM deficits and mathematical difficulties. This study investigated the possible deficits in WM, language and fluid intelligence that seem to characterize 4- to 6-year-old children with poor early mathematical skills before formal mathematics education. Children with early mathematical difficulties showed poor performance in both verbal and visuospatial WM tasks as well as on language tests and a fluid intelligence test indicating a thoroughly lower cognitive base. Poor WM performance was not moderated by fluid intelligence, but the extent of WM deficits was related to language skills. The educational implications are discussed.

  15. The argument of mathematics

    CERN Document Server

    Aberdein, Andrew

    2014-01-01

    This book presents a comprehensive investigation into the relationship between argumentation theory and the philosophy of mathematical practice. It offers large array of examples ranging from the history of mathematics to formal proof verification.

  16. Developing Non-Formal Education Competences as a Complement of Formal Education for STEM Lecturers

    Science.gov (United States)

    Terrazas-Marín, Roy Alonso

    2018-01-01

    This paper focuses on a current practice piece on professional development for university lecturers, transformative learning, dialogism and STEM (Science, Technology, Engineering and Mathematics) education. Its main goals are to identify the key characteristics that allow STEM educators to experiment with the usage of non-formal education…

  17. A formal theory of the selfish gene.

    Science.gov (United States)

    Gardner, A; Welch, J J

    2011-08-01

    Adaptation is conventionally regarded as occurring at the level of the individual organism. In contrast, the theory of the selfish gene proposes that it is more correct to view adaptation as occurring at the level of the gene. This view has received much popular attention, yet has enjoyed only limited uptake in the primary research literature. Indeed, the idea of ascribing goals and strategies to genes has been highly controversial. Here, we develop a formal theory of the selfish gene, using optimization theory to capture the analogy of 'gene as fitness-maximizing agent' in mathematical terms. We provide formal justification for this view of adaptation by deriving mathematical correspondences that translate the optimization formalism into dynamical population genetics. We show that in the context of social interactions between genes, it is the gene's inclusive fitness that provides the appropriate maximand. Hence, genic selection can drive the evolution of altruistic genes. Finally, we use the formalism to assess the various criticisms that have been levelled at the theory of the selfish gene, dispelling some and strengthening others. © 2011 The Authors. Journal of Evolutionary Biology © 2011 European Society For Evolutionary Biology.

  18. Introducing philosophy of mathematics

    CERN Document Server

    Friend, Michele

    2014-01-01

    What is mathematics about? Does the subject-matter of mathematics exist independently of the mind or are they mental constructions? How do we know mathematics? Is mathematical knowledge logical knowledge? And how is mathematics applied to the material world? In this introduction to the philosophy of mathematics, Michele Friend examines these and other ontological and epistemological problems raised by the content and practice of mathematics. Aimed at a readership with limited proficiency in mathematics but with some experience of formal logic it seeks to strike a balance between conceptual acc

  19. A Formal Valuation Framework for Emotions and Their Control.

    Science.gov (United States)

    Huys, Quentin J M; Renz, Daniel

    2017-09-15

    Computational psychiatry aims to apply mathematical and computational techniques to help improve psychiatric care. To achieve this, the phenomena under scrutiny should be within the scope of formal methods. As emotions play an important role across many psychiatric disorders, such computational methods must encompass emotions. Here, we consider formal valuation accounts of emotions. We focus on the fact that the flexibility of emotional responses and the nature of appraisals suggest the need for a model-based valuation framework for emotions. However, resource limitations make plain model-based valuation impossible and require metareasoning strategies to apportion cognitive resources adaptively. We argue that emotions may implement such metareasoning approximations by restricting the range of behaviors and states considered. We consider the processes that guide the deployment of the approximations, discerning between innate, model-free, heuristic, and model-based controllers. A formal valuation and metareasoning framework may thus provide a principled approach to examining emotions. Copyright © 2017 Society of Biological Psychiatry. Published by Elsevier Inc. All rights reserved.

  20. IDEF3 Formalization Report

    Science.gov (United States)

    1991-10-01

    SUBJECT TERMS 15. NUMBER OF PAGES engineering management information systems method formalization 60 information engineering process modeling 16 PRICE...CODE information systems requirements definition methods knowlede acquisition methods systems engineering 17. SECURITY CLASSIFICATION ji. SECURITY... Management , Inc., Santa Monica, California. CORYNEN, G. C., 1975, A Mathematical Theory of Modeling and Simula- tion. Ph.D. Dissertation, Department

  1. Proof and knowledge in mathematics

    CERN Document Server

    Detlefsen, Michael

    2005-01-01

    These questions arise from any attempt to discover an epistemology for mathematics. This collection of essays considers various questions concerning the nature of justification in mathematics and possible sources of that justification. Among these are the question of whether mathematical justification is a priori or a posteriori in character, whether logical and mathematical differ, and if formalization plays a significant role in mathematical justification,

  2. Formal specification is an experimental science

    Energy Technology Data Exchange (ETDEWEB)

    Bjorner, D. [Technical Univ., Lyngby (Denmark)

    1992-09-01

    Traditionally, abstract models of large, complex systems have been given in free-form mathematics, combining - often in ad-hoc, not formally supported ways - notions from the disciplines of partial differential equations, functional analysis, mathematical statistics, etc. Such models have been very useful for assimilation of information, analysis (investigation), and prediction (simulation). These models have, however, usually not been helpful in deriving computer representations of the modelled systems - for the purposes of computerized monitoring and control, Computing science, concerned with how to construct objects that can exist within the computer, offers ways of complementing, and in some cases, replacing or combining traditional mathematical models. Formal, model-, as well as property-oriented, specifications in the styles of denotational (respectively, algebraic semantics) represent major approaches to such modelling. In this expository, discursive paper we illustrate what we mean by model-oriented specifications of large, complex technological computing systems. The three modelling examples covers the introvert programming methodological subject of SDEs: software development environments, the distributed computing system subject of wfs`s: (transaction) work flow systems, and the extrovert subject of robots: robotics! the thesis is, just as for mathematical modelling, that we can derive much understanding, etc., from experimentally creating such formally specified models - on paper - and that we gain little in additionally building ad-hoc prototypes. Our models are expressed in a model-oriented style using the VDM specification language Meta-IV In this paper the models only reflect the {open_quotes}data modelling{close_quotes} aspects. We observe that such data models are more easily captured in the model-oriented siyle than in the algebraic semantics property-oriented style which originally was built of the abstraction of operations. 101 refs., 4 figs.

  3. Closing the gap between formalism and application

    DEFF Research Database (Denmark)

    Christensen, Ole Ravn

    2008-01-01

    A common problem in learning mathematics concerns the gap between, on the one hand, doing the formalisms and calculations of abstract mathematics and, on the other hand, applying these in a specific contextualized setting for example the engineering world. The skills acquired through problem......-based learning (PBL), in the special model used at Aalborg University, Denmark, may give us some idea of how to bridge this gap. Through an investigation of a series of examples of student projects concerning the application of mathematical subjects-such as matrices, differential equations, cluster analysis...

  4. Perspectives on mathematical practices bringing together philosophy of mathematics, sociology of mathematics, and mathematics education

    CERN Document Server

    van Kerkhove, Bart

    2007-01-01

    Philosophy of mathematics today has transformed into a very complex network of diverse ideas, viewpoints, and theories. Sometimes the emphasis is on the ""classical"" foundational work (often connected with the use of formal logical methods), sometimes on the sociological dimension of the mathematical research community and the ""products"" it produces, then again on the education of future mathematicians and the problem of how knowledge is or should be transmitted from one generation to the next. The editors of this book felt the urge, first of all, to bring together the widest variety of aut

  5. Mathematical Modeling in the Undergraduate Curriculum

    Science.gov (United States)

    Toews, Carl

    2012-01-01

    Mathematical modeling occupies an unusual space in the undergraduate mathematics curriculum: typically an "advanced" course, it nonetheless has little to do with formal proof, the usual hallmark of advanced mathematics. Mathematics departments are thus forced to decide what role they want the modeling course to play, both as a component of the…

  6. Thermodynamic and multifractal formalism and the Bowen-series map

    International Nuclear Information System (INIS)

    Rudolph, O.

    1995-01-01

    In the theory of quantum chaos one studies the semiclassical behaviour of quantum mechanical systems whose corresponding classical counterparts exhibit chaos. The geodesic motion of a free classical particle on closed Riemann surfaces with constant negative curvature is strongly chaotic. Selberg's theory relates the classical and the quantum mechanical systems. These systems are sometimes considered as model systems in the theory of quantum chaos since they are well understood from a mathematical point of view. In this work we study the multifractal formalism for the geodesic flow on surfaces with constant negative curvature. The multifractal analysis of measures has been developed in order to characterize the scaling behaviour of measures on attractors of classical chaotic dynamical systems globally. In order to relate the multifractal formalism with quantities usually considered in the study of the geodesic flow on Riemann surfaces with constant negative curvature, it is necessary to establish the assertions of the multifractal formalism in a mathematically rigorous way. This is achieved with the help of the thermodynamic formalism for hyperbolic dynamical systems developed by Ruelle, Bowen and others. (orig.)

  7. Towards a simple mathematical theory of citation distributions.

    Science.gov (United States)

    Katchanov, Yurij L

    2015-01-01

    The paper is written with the assumption that the purpose of a mathematical theory of citation is to explain bibliometric regularities at the level of mathematical formalism. A mathematical formalism is proposed for the appearance of power law distributions in social citation systems. The principal contributions of this paper are an axiomatic characterization of citation distributions in terms of the Ekeland variational principle and a mathematical exploration of the power law nature of citation distributions. Apart from its inherent value in providing a better understanding of the mathematical underpinnings of bibliometric models, such an approach can be used to derive a citation distribution from first principles.

  8. Critical Thinking Skills Of Junior High School Female Students With High Mathematical Skills In Solving Contextual And Formal Mathematical Problems

    Science.gov (United States)

    Ismail; Suwarsono, St.; Lukito, A.

    2018-01-01

    Critical thinking is one of the most important skills of the 21st century in addition to other learning skills such as creative thinking, communication skills and collaborative skills. This is what makes researchers feel the need to conduct research on critical thinking skills in junior high school students. The purpose of this study is to describe the critical thinking skills of junior high school female students with high mathematical skills in solving contextual and formal mathematical problems. To achieve this is used qualitative research. The subject of the study was a female student of eight grade junior high school. The students’ critical thinking skills are derived from in-depth problem-based interviews using interview guidelines. Interviews conducted in this study are problem-based interviews, which are done by the subject given a written assignment and given time to complete. The results show that critical thinking skills of female high school students with high math skills are as follows: In solving the problem at the stage of understanding the problem used interpretation skills with sub-indicators: categorization, decode, and clarify meaning. At the planning stage of the problem-solving strategy is used analytical skills with sub-indicators: idea checking, argument identification and argument analysis and evaluation skills with sub indicators: assessing the argument. In the implementation phase of problem solving, inference skills are used with subindicators: drawing conclusions, and problem solving and explanatory skills with sub-indicators: problem presentation, justification procedures, and argument articulation. At the re-checking stage all steps have been employed self-regulatory skills with sub-indicators: self-correction and selfstudy.

  9. Modeling Clinic for Industrial Mathematics: A Collaborative Project Under Erasmus+ Program

    DEFF Research Database (Denmark)

    Jurlewicz, Agnieszka; Nunes, Claudia; Russo, Giovanni

    2018-01-01

    Modeling Clinic for Industrial Mathematics (MODCLIM) is a Strategic Partnership for the Development of Training Workshops and Modeling Clinic for Industrial Mathematics, funded through the European Commission under the Erasmus Plus Program, Key Action 2: Cooperation for innovation and the exchang...

  10. What is mathematical logic?

    CERN Document Server

    Crossley, J N; Brickhill, CJ; Stillwell, JC

    2010-01-01

    Although mathematical logic can be a formidably abstruse topic, even for mathematicians, this concise book presents the subject in a lively and approachable fashion. It deals with the very important ideas in modern mathematical logic without the detailed mathematical work required of those with a professional interest in logic.The book begins with a historical survey of the development of mathematical logic from two parallel streams: formal deduction, which originated with Aristotle, Euclid, and others; and mathematical analysis, which dates back to Archimedes in the same era. The streams beg

  11. Towards formalization of inspection using petrinets

    International Nuclear Information System (INIS)

    Javed, M.; Naeem, M.; Bahadur, F.; Wahab, A.

    2014-01-01

    Achieving better quality software has always been a challenge for software developers. Inspection is one of the most efficient techniques, which ensure the quality of software during its development. To the best of our knowledge, current inspection techniques are not realized by any formal approach. In this paper, we propose an inspection technique, which is not only backed by the formal mathematical semantics of Petri nets, but also supports inspecting concurrent processes. We also use a case study of an agent based distributed processing system to demonstrate the inspection of concurrent processes. (author)

  12. Formalization of the classification pattern: survey of classification modeling in information systems engineering.

    Science.gov (United States)

    Partridge, Chris; de Cesare, Sergio; Mitchell, Andrew; Odell, James

    2018-01-01

    Formalization is becoming more common in all stages of the development of information systems, as a better understanding of its benefits emerges. Classification systems are ubiquitous, no more so than in domain modeling. The classification pattern that underlies these systems provides a good case study of the move toward formalization in part because it illustrates some of the barriers to formalization, including the formal complexity of the pattern and the ontological issues surrounding the "one and the many." Powersets are a way of characterizing the (complex) formal structure of the classification pattern, and their formalization has been extensively studied in mathematics since Cantor's work in the late nineteenth century. One can use this formalization to develop a useful benchmark. There are various communities within information systems engineering (ISE) that are gradually working toward a formalization of the classification pattern. However, for most of these communities, this work is incomplete, in that they have not yet arrived at a solution with the expressiveness of the powerset benchmark. This contrasts with the early smooth adoption of powerset by other information systems communities to, for example, formalize relations. One way of understanding the varying rates of adoption is recognizing that the different communities have different historical baggage. Many conceptual modeling communities emerged from work done on database design, and this creates hurdles to the adoption of the high level of expressiveness of powersets. Another relevant factor is that these communities also often feel, particularly in the case of domain modeling, a responsibility to explain the semantics of whatever formal structures they adopt. This paper aims to make sense of the formalization of the classification pattern in ISE and surveys its history through the literature, starting from the relevant theoretical works of the mathematical literature and gradually shifting focus

  13. Transforming PLC Programs into Formal Models for Verification Purposes

    CERN Document Server

    Darvas, D; Blanco, E

    2013-01-01

    Most of CERN’s industrial installations rely on PLC-based (Programmable Logic Controller) control systems developed using the UNICOS framework. This framework contains common, reusable program modules and their correctness is a high priority. Testing is already applied to find errors, but this method has limitations. In this work an approach is proposed to transform automatically PLC programs into formal models, with the goal of applying formal verification to ensure their correctness. We target model checking which is a precise, mathematical-based method to check formalized requirements automatically against the system.

  14. Under Threes' Mathematical Learning

    Science.gov (United States)

    Franzén, Karin

    2015-01-01

    The article focuses on mathematics for toddlers in preschool, with the aim of challenging a strong learning discourse that mainly focuses on cognitive learning. By devoting more attention to other perspectives on learning, the hope is to better promote children's early mathematical development. Sweden is one of few countries to have a curriculum…

  15. Mathematical sense-making in quantum mechanics: An initial peek

    Science.gov (United States)

    Dreyfus, Benjamin W.; Elby, Andrew; Gupta, Ayush; Sohr, Erin Ronayne

    2017-12-01

    Mathematical sense-making—looking for coherence between the structure of the mathematical formalism and causal or functional relations in the world—is a core component of physics expertise. Some physics education research studies have explored what mathematical sense-making looks like at the introductory physics level, while some historians and "science studies" have explored how expert physicists engage in it. What is largely missing, with a few exceptions, is theoretical and empirical work at the intermediate level—upper division physics students—especially when they are learning difficult new mathematical formalism. In this paper, we present analysis of a segment of video-recorded discussion between two students grappling with a quantum mechanics question to illustrate what mathematical sense-making can look like in quantum mechanics. We claim that mathematical sense-making is possible and productive for learning and problem solving in quantum mechanics. Mathematical sense-making in quantum mechanics is continuous in many ways with mathematical sense-making in introductory physics. However, in the context of quantum mechanics, the connections between formalism, intuitive conceptual schema, and the physical world become more compound (nested) and indirect. We illustrate these similarities and differences in part by proposing a new symbolic form, eigenvector eigenvalue, which is composed of multiple primitive symbolic forms.

  16. Formal methods in software development: A road less travelled

    Directory of Open Access Journals (Sweden)

    John A van der Poll

    2010-08-01

    Full Text Available An integration of traditional verification techniques and formal specifications in software engineering is presented. Advocates of such techniques claim that mathematical formalisms allow them to produce quality, verifiably correct, or at least highly dependable software and that the testing and maintenance phases are shortened. Critics on the other hand maintain that software formalisms are hard to master, tedious to use and not well suited for the fast turnaround times demanded by industry. In this paper some popular formalisms and the advantages of using these during the early phases of the software development life cycle are presented. Employing the Floyd-Hoare verification principles during the formal specification phase facilitates reasoning about the properties of a specification. Some observations that may help to alleviate the formal-methods controversy are established and a number of formal methods successes is presented. Possible conditions for an increased acceptance of formalisms in oftware development are discussed.

  17. Proof, rigour and informality : a virtue account of mathematical knowledge

    OpenAIRE

    Tanswell, Fenner Stanley

    2017-01-01

    This thesis is about the nature of proofs in mathematics as it is practiced, contrasting the informal proofs found in practice with formal proofs in formal systems. In the first chapter I present a new argument against the Formalist-Reductionist view that informal proofs are justified as rigorous and correct by corresponding to formal counterparts. The second chapter builds on this to reject arguments from Gödel's paradox and incompleteness theorems to the claim that mathematics is inherently...

  18. Towards a Formal Framework for Computational Trust

    DEFF Research Database (Denmark)

    Nielsen, Mogens; Krukow, Karl Kristian; Sassone, Vladimiro

    2006-01-01

    We define a mathematical measure for the quantitative comparison of probabilistic computational trust systems, and use it to compare a well-known class of algorithms based on the so-called beta model. The main novelty is that our approach is formal, rather than based on experimental simulation....

  19. Formal methods for discrete-time dynamical systems

    CERN Document Server

    Belta, Calin; Aydin Gol, Ebru

    2017-01-01

    This book bridges fundamental gaps between control theory and formal methods. Although it focuses on discrete-time linear and piecewise affine systems, it also provides general frameworks for abstraction, analysis, and control of more general models. The book is self-contained, and while some mathematical knowledge is necessary, readers are not expected to have a background in formal methods or control theory. It rigorously defines concepts from formal methods, such as transition systems, temporal logics, model checking and synthesis. It then links these to the infinite state dynamical systems through abstractions that are intuitive and only require basic convex-analysis and control-theory terminology, which is provided in the appendix. Several examples and illustrations help readers understand and visualize the concepts introduced throughout the book.

  20. Philosophy of mathematics set theory, measuring theories, and nominalism

    CERN Document Server

    Preyer, Gerhard

    2008-01-01

    One main interest of philosophy is to become clear about the assumptions, premisses and inconsistencies of our thoughts and theories. And even for a formal language like mathematics it is controversial if consistency is acheivable or necessary like the articles in the firt part of the publication show. Also the role of formal derivations, the role of the concept of apriority, and the intuitions of mathematical principles and properties need to be discussed. The second part is a contribution on nominalistic and platonistic views in mathematics, like the ""indispensability argument"" of W. v. O.

  1. Talking about teaching and learning mathematics in indigenous schools

    Directory of Open Access Journals (Sweden)

    Lucélida de Fátima Maia da Costa

    2012-09-01

    Full Text Available To teach and to learn mathematics are not always conjugated concomitantly, particularly in the context of formal indigenous schools. This article puts in discussion some facts about the role of schools in indigenous communities, often mistakenly called Indian schools, as well as questions about the meaning of teaching mathematics in those contexts. Based on the concepts of ethnomathematics, it shows that a dialogue is possible between the traditional mathematical knowledge of various ethnic groups of the Amazon and the knowledge disseminated by formal school teaching practice.

  2. Formalization of processes in the land relations of Ukraine

    Directory of Open Access Journals (Sweden)

    K.О. Meteshkin

    2017-12-01

    Full Text Available The work listed a number of problematic tasks in the sphere of land relations of Ukraine, among which: weak communications between laws, inconsistency interpretations laws and insufficient use of modern information technologies. The relevance of the work is the need to solve problem tasks land relations in Ukraine and absence, proposed in the work, mathematical apparatus for solving these tasks. Analyzed work of scientists, who work in the sphere of land relations and who work in the sphere of formalize of rights. The proposed decision of actual tasks with help create mathematical ensuring for develop decision support system in land relations. The basis of this mathematical ensuring constitute methods of category theory, which provide the formalization of complex tasks. Based on methods of category theory models of land relations are constructed using data Land code of Ukraine. They will become an element of ontology land relations, which will be the structural parts of the knowledge base decision support system in the land management of Ukraine. It should also be noted, what similar models can be used in other subject areas.

  3. Fuzzy and rough formal concept analysis: a survey

    NARCIS (Netherlands)

    Poelmans, J.; Ignatov, D.I.; Kuznetsov, S.O.; Dedene, G.

    2014-01-01

    Formal Concept Analysis (FCA) is a mathematical technique that has been extensively applied to Boolean data in knowledge discovery, information retrieval, web mining, etc. applications. During the past years, the research on extending FCA theory to cope with imprecise and incomplete information made

  4. Formal specifications for safety grade systems

    International Nuclear Information System (INIS)

    Chisholm, G.H.; Smith, B.T.; Wojcik, A.S.

    1992-01-01

    The authors describe the findings of a study into the application of formal methods to the specification of a safety system for an operating nuclear reactor. They developed a formal specification that is used to verify and validate that no unsafe condition will result from action or inaction of the system. For this reason, the specification must facilitate thinking about, talking about, and implementing the system. In fact, the specification must provide a bridge between people (designers, engineers, policy makers) and diverse implementations (hardware, software, sensors, power supplies) at all levels. For a specification to serve as an effective linkage, it must have the following properties: (1) completeness, (2) conciseness, (3) unambiguity, and (4) communicativeness. In this paper they describe the development of a specification that has three properties. This development is based on the use of formal methods, i.e., methods that add mathematical rigor to the development, analysis and operation of computer systems and to applications based thereon (Neumann). They demonstrate that a specification derived from a formal basis facilitates development of the design and its subsequent verification

  5. A comprehensive overview on the foundations of formal concept analysis

    Directory of Open Access Journals (Sweden)

    K. Sumangali

    2017-12-01

    Full Text Available The immersion of voluminous collection of data is inevitable almost everywhere. The invention of mathematical models to analyse the patterns and trends of the data is an emerging necessity to extract and predict useful information in any Knowledge Discovery from Data (KDD process. The Formal Concept Analysis (FCA is an efficient mathematical model used in the process of KDD which is specially designed to portray the structure of the data in a context and depict the underlying patterns and hierarchies in it. Due to the huge increase in the application of FCA in various fields, the number of research and review articles on FCA has raised to a large extent. This review differs from the existing ones in presenting the comprehensive survey on the fundamentals of FCA in a compact and crisp manner to benefit the beginners and its focuses on the scalability issues in FCA. Further, we present the generic anatomy of FCA apart from its origin and growth at a primary level.

  6. The motivation of lifelong mathematics learning

    Science.gov (United States)

    Hashim Ali, Siti Aishah

    2013-04-01

    As adults, we have always learned throughout our life, but this learning is informal. Now, more career-switchers and career-upgraders who are joining universities for further training are becoming the major group of adult learners. This current situation requires formal education in courses with controlled output. Hence, lifelong learning is seen as a necessity and an opportunity for these adult learners. One characteristic of adult education is that the learners tend to bring with them life experience from their past, especially when learning mathematics. Most of them associate mathematics with the school subjects and unable to recognize the mathematics in their daily practice as mathematics. They normally place a high value on learning mathematics because of its prominent role in their prospective careers, but their learning often requires overcoming personal experience and motivating themselves to learn mathematics again. This paper reports on the study conducted on a group of adult learners currently pursuing their study. The aim of this study is to explore (i) the motivation of the adult learners continuing their study; and (ii) the perception and motivation of these learners in learning mathematics. This paper will take this into account when we discuss learners' perception and motivation to learning mathematics, as interrelated phenomena. Finding from this study will provide helpful insights in understanding the learning process and adaption of adult learners to formal education.

  7. Understanding mathematical proof

    CERN Document Server

    Taylor, John

    2014-01-01

    Introduction The need for proof The language of mathematics Reasoning Deductive reasoning and truth Example proofs Logic and ReasoningIntroduction Propositions, connectives, and truth tables Logical equivalence and logical implication Predicates and quantification Logical reasoning Sets and Functions Introduction Sets and membership Operations on setsThe Cartesian product Functions and composite functions Properties of functions The Structure of Mathematical ProofsIntroduction Some proofs dissected An informal framework for proofs Direct proof A more formal framework Finding Proofs Direct proo

  8. Mathematical foundations of event trees

    International Nuclear Information System (INIS)

    Papazoglou, Ioannis A.

    1998-01-01

    A mathematical foundation from first principles of event trees is presented. The main objective of this formulation is to offer a formal basis for developing automated computer assisted construction techniques for event trees. The mathematical theory of event trees is based on the correspondence between the paths of the tree and the elements of the outcome space of a joint event. The concept of a basic cylinder set is introduced to describe joint event outcomes conditional on specific outcomes of basic events or unconditional on the outcome of basic events. The concept of outcome space partition is used to describe the minimum amount of information intended to be preserved by the event tree representation. These concepts form the basis for an algorithm for systematic search for and generation of the most compact (reduced) form of an event tree consistent with the minimum amount of information the tree should preserve. This mathematical foundation allows for the development of techniques for automated generation of event trees corresponding to joint events which are formally described through other types of graphical models. Such a technique has been developed for complex systems described by functional blocks and it is reported elsewhere. On the quantification issue of event trees, a formal definition of a probability space corresponding to the event tree outcomes is provided. Finally, a short discussion is offered on the relationship of the presented mathematical theory with the more general use of event trees in reliability analysis of dynamic systems

  9. Perceived mathematical ability under challenge: a longitudinal perspective on sex segregation among STEM degree fields.

    Science.gov (United States)

    Nix, Samantha; Perez-Felkner, Lara; Thomas, Kirby

    2015-01-01

    Students' perceptions of their mathematics ability vary by gender and seem to influence science, technology, engineering, and mathematics (STEM) degree choice. Related, students' perceptions during academic difficulty are increasingly studied in educational psychology, suggesting a link between such perceptions and task persistence. Despite interest in examining the gender disparities in STEM, these concepts have not been considered in tandem. In this manuscript, we investigate how perceived ability under challenge-in particular in mathematics domains-influences entry into the most sex-segregated and mathematics-intensive undergraduate degrees: physics, engineering, mathematics, and computer science (PEMC). Using nationally representative Education Longitudinal Study of 2002 (ELS) data, we estimate the influence of perceived ability under challenging conditions on advanced high school science course taking, selection of an intended STEM major, and specific major type 2 years after high school. Demonstrating the importance of specificity when discussing how gender influences STEM career pathways, the intersecting effects of gender and perceived ability under mathematics challenge were distinct for each scientific major category. Perceived ability under challenge in secondary school varied by gender, and was highly predictive of selecting PEMC and health sciences majors. Notably, women's 12th grade perceptions of their ability under mathematics challenge increased their probability of selecting PEMC majors over and above biology. In addition, gender moderated the effect of growth mindset on students' selection of health science majors. Perceptions of ability under challenge in general and verbal domains also influenced retention in and declaration of certain STEM majors. The implications of these results are discussed, with particular attention to access to advanced scientific coursework in high school and interventions aimed at enhancing young women's perceptions of

  10. Perceived mathematical ability under challenge: a longitudinal perspective on sex segregation among STEM degree fields

    Science.gov (United States)

    Nix, Samantha; Perez-Felkner, Lara; Thomas, Kirby

    2015-01-01

    Students' perceptions of their mathematics ability vary by gender and seem to influence science, technology, engineering, and mathematics (STEM) degree choice. Related, students' perceptions during academic difficulty are increasingly studied in educational psychology, suggesting a link between such perceptions and task persistence. Despite interest in examining the gender disparities in STEM, these concepts have not been considered in tandem. In this manuscript, we investigate how perceived ability under challenge—in particular in mathematics domains—influences entry into the most sex-segregated and mathematics-intensive undergraduate degrees: physics, engineering, mathematics, and computer science (PEMC). Using nationally representative Education Longitudinal Study of 2002 (ELS) data, we estimate the influence of perceived ability under challenging conditions on advanced high school science course taking, selection of an intended STEM major, and specific major type 2 years after high school. Demonstrating the importance of specificity when discussing how gender influences STEM career pathways, the intersecting effects of gender and perceived ability under mathematics challenge were distinct for each scientific major category. Perceived ability under challenge in secondary school varied by gender, and was highly predictive of selecting PEMC and health sciences majors. Notably, women's 12th grade perceptions of their ability under mathematics challenge increased their probability of selecting PEMC majors over and above biology. In addition, gender moderated the effect of growth mindset on students' selection of health science majors. Perceptions of ability under challenge in general and verbal domains also influenced retention in and declaration of certain STEM majors. The implications of these results are discussed, with particular attention to access to advanced scientific coursework in high school and interventions aimed at enhancing young women

  11. Mathematics and Computer Science: The Interplay

    OpenAIRE

    Madhavan, Veni CE

    2005-01-01

    Mathematics has been an important intellectual preoccupation of man for a long time. Computer science as a formal discipline is about seven decades young. However, one thing in common between all users and producers of mathematical thought is the almost involuntary use of computing. In this article, we bring to fore the many close connections and parallels between the two sciences of mathematics and computing. We show that, unlike in the other branches of human inquiry where mathematics is me...

  12. A formalization of the flutter shutter

    Science.gov (United States)

    Tendero, Yohann; Rougé, Bernard; Morel, Jean-Michel

    2012-09-01

    Acquiring good quality images of moving objects by a digital camera remains a valid question. If the velocity of the photographed object is not known, it is virtually impossible to tune an optimal exposure time. For this reason the recent Agrawal et al. flutter shutter apparatus has generated much interest. In this communication, we propose a mathematical formalization of a general flutter shutter method, also permitting non-binary shutter sequences. Thanks to this formalization, the question of the optimal flutter shutter code can be defined and solved. The method gives analytic formulas for the best attainable SNR for the restored image. It also gives a way to compute optimal flutter shutter codes.

  13. Mathematics

    International Nuclear Information System (INIS)

    Demazure, M.

    1988-01-01

    The 1988 progress report of the Mathematics center (Polytechnic School, France), is presented. The Center is composed of different research teams: analysis, Riemann geometry, group theory, formal calculus and algorithm geometry, dynamical systems, topology and singularity. For each team, the members, the research topics, the national and international cooperations, are given. The papers concerning the investigations carried out in 1988, are listed [fr

  14. Perturbation theory and collision probability formalism. Vol. 2

    Energy Technology Data Exchange (ETDEWEB)

    Nasr, M [National Center for Nuclear Safety and Radiation Control, Atomic Energy Authority, Cairo (Egypt)

    1996-03-01

    Perturbation theory is commonly used in evaluating the activity effects, particularly those resulting from small and localized perturbation in multiplying media., e.g. in small sample reactivity measurements. The Boltzmann integral transport equation is generally used for evaluating the direct and adjoint fluxes in the heterogenous lattice cells to be used in the perturbation equations. When applying perturbation theory in this formalism, a term involving the perturbation effects on the special transfer kernel arises. This term is difficult to evaluate correctly, since it involves an integration all over the entire system. The main advantage of the perturbation theory which is the limitation of the integration procedure on the perturbation region is found to be of no practical use in such cases. In the present work, the perturbation equation in the collision probability formalism is analyzed. A mathematical treatment of the term in question is performed. A new mathematical expression for this term is derived. The new expression which can be estimated easily is derived.

  15. Formal methods in design and verification of functional specifications

    International Nuclear Information System (INIS)

    Vaelisuo, H.

    1995-01-01

    It is claimed that formal methods should be applied already when specifying the functioning of the control/monitoring system, i.e. when planning how to implement the desired operation of the plant. Formal methods are seen as a way to mechanize and thus automate part of the planning. All mathematical methods which can be applied on related problem solving should be considered as formal methods. Because formal methods can only support the designer, not replace him/her, they must be integrated into a design support tool. Such a tool must also aid the designer in getting the correct conception of the plant and its behaviour. The use of a hypothetic design support tool is illustrated to clarify the requirements such a tool should fulfill. (author). 3 refs, 5 figs

  16. The normative structure of mathematization in systematic biology.

    Science.gov (United States)

    Sterner, Beckett; Lidgard, Scott

    2014-06-01

    We argue that the mathematization of science should be understood as a normative activity of advocating for a particular methodology with its own criteria for evaluating good research. As a case study, we examine the mathematization of taxonomic classification in systematic biology. We show how mathematization is a normative activity by contrasting its distinctive features in numerical taxonomy in the 1960s with an earlier reform advocated by Ernst Mayr starting in the 1940s. Both Mayr and the numerical taxonomists sought to formalize the work of classification, but Mayr introduced a qualitative formalism based on human judgment for determining the taxonomic rank of populations, while the numerical taxonomists introduced a quantitative formalism based on automated procedures for computing classifications. The key contrast between Mayr and the numerical taxonomists is how they conceptualized the temporal structure of the workflow of classification, specifically where they allowed meta-level discourse about difficulties in producing the classification. Copyright © 2014. Published by Elsevier Ltd.

  17. Some properties for integro-differential operator defined by a fractional formal.

    Science.gov (United States)

    Abdulnaby, Zainab E; Ibrahim, Rabha W; Kılıçman, Adem

    2016-01-01

    Recently, the study of the fractional formal (operators, polynomials and classes of special functions) has been increased. This study not only in mathematics but extended to another topics. In this effort, we investigate a generalized integro-differential operator [Formula: see text] defined by a fractional formal (fractional differential operator) and study some its geometric properties by employing it in new subclasses of analytic univalent functions.

  18. Mathematics Teaching as Problem Solving: A Framework for Studying Teacher Metacognition Underlying Instructional Practice in Mathematics.

    Science.gov (United States)

    Artzt, Alice F.; Armour-Thomas, Eleanor

    1998-01-01

    Uses a "teaching as problem solving" perspective to examine the components of metacognition underlying the instructional practice of seven experienced and seven beginning secondary-school mathematics teachers. Data analysis of observations, lesson plans, videotapes, and audiotapes of structured interviews suggests that the metacognition of…

  19. Modeling of requirement specification for safety critical real time computer system using formal mathematical specifications

    International Nuclear Information System (INIS)

    Sankar, Bindu; Sasidhar Rao, B.; Ilango Sambasivam, S.; Swaminathan, P.

    2002-01-01

    Full text: Real time computer systems are increasingly used for safety critical supervision and control of nuclear reactors. Typical application areas are supervision of reactor core against coolant flow blockage, supervision of clad hot spot, supervision of undesirable power excursion, power control and control logic for fuel handling systems. The most frequent cause of fault in safety critical real time computer system is traced to fuzziness in requirement specification. To ensure the specified safety, it is necessary to model the requirement specification of safety critical real time computer systems using formal mathematical methods. Modeling eliminates the fuzziness in the requirement specification and also helps to prepare the verification and validation schemes. Test data can be easily designed from the model of the requirement specification. Z and B are the popular languages used for modeling the requirement specification. A typical safety critical real time computer system for supervising the reactor core of prototype fast breeder reactor (PFBR) against flow blockage is taken as case study. Modeling techniques and the actual model are explained in detail. The advantages of modeling for ensuring the safety are summarized

  20. Psychologist in non-formal education

    OpenAIRE

    Pavićević Miljana S.

    2011-01-01

    Learning is not limited to school time. It starts at birth and continues throughout the entire life. Equally important as formal education there are also non-formal and informal education. Any kind of learning outside the traditional school can be called informal. However, it is not easy to define non-formal education because it is being described differently, for example as an education movement, process, system… Projects and programs implemented under the name of non-formal education are of...

  1. Improvement of Word Problem Solving and Basic Mathematics Competencies in Students with Attention Deficit/Hyperactivity Disorder and Mathematical Learning Difficulties

    Science.gov (United States)

    González-Castro, Paloma; Cueli, Marisol; Areces, Débora; Rodríguez, Celestino; Sideridis, Georgios

    2016-01-01

    Problem solving represents a salient deficit in students with mathematical learning difficulties (MLD) primarily caused by difficulties with informal and formal mathematical competencies. This study proposes a computerized intervention tool, the integrated dynamic representation (IDR), for enhancing the early learning of basic mathematical…

  2. Formalism and physical interpretation in Schroedinger

    International Nuclear Information System (INIS)

    Paty, M.

    1992-01-01

    The question of the relation between a formalism and its physical interpretation arises not only when theoretical and conceptual systems are reorganized, but in the theoretical elaboration as well. The Schroedinger's work and thought are examined in this paper with this double concern. His work on the mathematical formalism is constantly sustained by a proper physical thought which takes the form of a wave intuition that guarantees him intelligibility. Concerning his interpretation of quantum mechanics, his thought remains characterized, through its evolution, by a w ave image of the world . The way he deals with space-time structure in General Relativity and favours the possibility of a direct interpretation of space-time geometrical quantities, is also studied. (author). 75 refs

  3. Mathematical Sense-Making in Quantum Mechanics: An Initial Peek

    Science.gov (United States)

    Dreyfus, Benjamin W.; Elby, Andrew; Gupta, Ayush; Sohr, Erin Ronayne

    2017-01-01

    Mathematical sense-making--looking for coherence between the structure of the mathematical formalism and causal or functional relations in the world--is a core component of physics expertise. Some physics education research studies have explored what mathematical sense-making looks like at the introductory physics level, while some historians and…

  4. Weak Quantum Theory: Formal Framework and Selected Applications

    International Nuclear Information System (INIS)

    Atmanspacher, Harald; Filk, Thomas; Roemer, Hartmann

    2006-01-01

    Two key concepts of quantum theory, complementarity and entanglement, are considered with respect to their significance in and beyond physics. An axiomatically formalized, weak version of quantum theory, more general than the ordinary quantum theory of physical systems, is described. Its mathematical structure generalizes the algebraic approach to ordinary quantum theory. The crucial formal feature leading to complementarity and entanglement is the non-commutativity of observables.The ordinary Hilbert space quantum mechanics can be recovered by stepwise adding the necessary features. This provides a hierarchy of formal frameworks of decreasing generality and increasing specificity. Two concrete applications, more specific than weak quantum theory and more general than ordinary quantum theory, are discussed: (i) complementarity and entanglement in classical dynamical systems, and (ii) complementarity and entanglement in the bistable perception of ambiguous stimuli

  5. Perceived Mathematical Ability under Challenge: A Longitudinal Perspective on Sex Segregation among STEM Degree Fields

    Directory of Open Access Journals (Sweden)

    Samantha eNix

    2015-06-01

    Full Text Available Students’ perceptions of their mathematics ability vary by gender and seem to influence science, technology, engineering, and math (STEM degree choice. Related, students’ perceptions during academic difficulty are increasingly studied in educational psychology, suggesting a link between such perceptions and task persistence. Despite interest in examining the gender disparities in STEM, these concepts have not been considered in tandem. We investigate how perceived ability under challenge – in particular in mathematics domains – influences entry into the most sex-segregated and mathematics-intensive undergraduate degrees: physics, engineering, mathematics, and computer science (PEMC. Using nationally representative Education Longitudinal Study of 2002 (ELS data, we estimate the influence of perceived ability under challenging conditions on advanced high school science course taking, selection of an intended STEM major, and specific major type two years after high school. Demonstrating the importance of specificity when discussing how gender influences STEM career pathways, the intersecting effects of gender and perceived ability under mathematics challenge were distinct for each scientific major category. Perceived ability under challenge in secondary school varied by gender, and was highly predictive of selecting PEMC and health sciences majors. Notably, women’s 12th grade perceptions of their ability under mathematics challenge increased the probability that they would select PEMC majors, increasing women's probability of selecting PEMC over and above biology. In addition, gender moderated the effect of growth mindset on students’ selection of health science majors. The implications of these results are discussed, with particular attention to access to advanced scientific coursework in high school and interventions aimed at enhancing young women’s perceptions of their ability to facilitate their pathways to scientific degrees.

  6. Applications of Mathematical Logic in Philosophy and Linguistics, Papers of a Conference

    CERN Document Server

    Malzkom, Wolfgang; Räsch, Thoralf

    2003-01-01

    "Foundations of the Formal Sciences" (FotFS) is a series of interdisciplinary conferences in mathematics, philosophy, computer science and linguistics. The main goal is to reestablish the traditionally strong links between these areas of research that have been lost in the past decades. The second conference in the series had the subtitle "Applications of Mathematical Logic in Philosophy and Linguistics" and brought speakers from all parts of the Formal Sciences together to give a holistic view of how mathematical methods can improve our philosophical and technical understanding of language and scientific discourse, ranging from the theoretical level up to applications in language recognition software. Audience: This volume is of interest to all formal philosophers and theoretical linguists. In addition to that, logicians interested in the applications of their field and logic students in mathematics, computer science, philosophy and linguistics can use the volume to broaden their knowledge of applications of...

  7. Is neoclassical microeconomics formally valid? An approach based on an analogy with equilibrium thermodynamics

    Energy Technology Data Exchange (ETDEWEB)

    Sousa, Tania; Domingos, Tiago [Environment and Energy Section, DEM, Instituto Superior Tecnico, Avenida Rovisco Pais, 1, 1049-001 Lisboa (Portugal)

    2006-06-10

    The relation between Thermodynamics and Economics is a paramount issue in Ecological Economics. Two different levels can be distinguished when discussing it: formal and substantive. At the formal level, a mathematical framework is used to describe both thermodynamic and economic systems. At the substantive level, thermodynamic laws are applied to economic processes. In Ecological Economics, there is a widespread claim that neoclassical economics has the same mathematical formulation as classical mechanics and is therefore fundamentally flawed because: (1) utility does not obey a conservation law as energy does; (2) an equilibrium theory cannot be used to study irreversible processes. Here, we show that neoclassical economics is based on a wrong formulation of classical mechanics, being in fact formally analogous to equilibrium thermodynamics. The similarity between both formalisms, namely that they are both cases of constrained optimisation, is easily perceived when thermodynamics is looked upon using the Tisza-Callen axiomatisation. In this paper, we take the formal analogy between equilibrium thermodynamics and economic systems far enough to answer the formal criticisms, proving that the formalism of neoclassical economics has irreversibility embedded in it. However, the formal similarity between equilibrium thermodynamics and neoclassical microeconomics does not mean that economic models are in accordance with mass, energy and entropy balance equations. In fact, neoclassical theory suffers from flaws in the substantive integration with thermodynamic laws as has already been fully demonstrated by valuable work done by ecological economists in this field. (author)

  8. Formal and physical equivalence in two cases in contemporary quantum physics

    Science.gov (United States)

    Fraser, Doreen

    2017-08-01

    The application of analytic continuation in quantum field theory (QFT) is juxtaposed to T-duality and mirror symmetry in string theory. Analytic continuation-a mathematical transformation that takes the time variable t to negative imaginary time-it-was initially used as a mathematical technique for solving perturbative Feynman diagrams, and was subsequently the basis for the Euclidean approaches within mainstream QFT (e.g., Wilsonian renormalization group methods, lattice gauge theories) and the Euclidean field theory program for rigorously constructing non-perturbative models of interacting QFTs. A crucial difference between theories related by duality transformations and those related by analytic continuation is that the former are judged to be physically equivalent while the latter are regarded as physically inequivalent. There are other similarities between the two cases that make comparing and contrasting them a useful exercise for clarifying the type of argument that is needed to support the conclusion that dual theories are physically equivalent. In particular, T-duality and analytic continuation in QFT share the criterion for predictive equivalence that two theories agree on the complete set of expectation values and the mass spectra and the criterion for formal equivalence that there is a "translation manual" between the physically significant algebras of observables and sets of states in the two theories. The analytic continuation case study illustrates how predictive and formal equivalence are compatible with physical inequivalence, but not in the manner of standard underdetermination cases. Arguments for the physical equivalence of dual theories must cite considerations beyond predictive and formal equivalence. The analytic continuation case study is an instance of the strategy of developing a physical theory by extending the formal or mathematical equivalence with another physical theory as far as possible. That this strategy has resulted in

  9. The Use of GBL to Teach Mathematics in Higher Education

    Science.gov (United States)

    Naik, Nitin

    2017-01-01

    Innovation in learning and teaching is an everyday requirement in contemporary higher education (HE), especially in challenging subjects such as mathematics. Teaching mathematics to students with limited experience of formal mathematical instruction is a good example of a demanding pedagogical undertaking where innovatory practice can help HE…

  10. Giftedness and Aesthetics: Perspectives of Expert Mathematicians and Mathematically Gifted Students

    Science.gov (United States)

    Tjoe, Hartono

    2015-01-01

    Giftedness in mathematics has been characterized by exceptional attributes including strong mathematical memory, formalizing perception, generalization, curtailment, flexibility, and elegance. Focusing on the last attribute, this study examined the following: (a) the criteria which expert mathematicians and mathematically gifted students fleshed…

  11. Industrial applications of formal methods to model, design and analyze computer systems

    CERN Document Server

    Craigen, Dan

    1995-01-01

    Formal methods are mathematically-based techniques, often supported by reasoning tools, that can offer a rigorous and effective way to model, design and analyze computer systems. The purpose of this study is to evaluate international industrial experience in using formal methods. The cases selected are representative of industrial-grade projects and span a variety of application domains. The study had three main objectives: · To better inform deliberations within industry and government on standards and regulations; · To provide an authoritative record on the practical experience of formal m

  12. Preschoolers' precision of the approximate number system predicts later school mathematics performance.

    Science.gov (United States)

    Mazzocco, Michèle M M; Feigenson, Lisa; Halberda, Justin

    2011-01-01

    The Approximate Number System (ANS) is a primitive mental system of nonverbal representations that supports an intuitive sense of number in human adults, children, infants, and other animal species. The numerical approximations produced by the ANS are characteristically imprecise and, in humans, this precision gradually improves from infancy to adulthood. Throughout development, wide ranging individual differences in ANS precision are evident within age groups. These individual differences have been linked to formal mathematics outcomes, based on concurrent, retrospective, or short-term longitudinal correlations observed during the school age years. However, it remains unknown whether this approximate number sense actually serves as a foundation for these school mathematics abilities. Here we show that ANS precision measured at preschool, prior to formal instruction in mathematics, selectively predicts performance on school mathematics at 6 years of age. In contrast, ANS precision does not predict non-numerical cognitive abilities. To our knowledge, these results provide the first evidence for early ANS precision, measured before the onset of formal education, predicting later mathematical abilities.

  13. The formal Darwinism project: a mid-term report.

    Science.gov (United States)

    Grafen, A

    2007-07-01

    For 8 years I have been pursuing in print an ambitious and at times highly technical programme of work, the 'Formal Darwinism Project', whose essence is to underpin and formalize the fitness optimization ideas used by behavioural ecologists, using a new kind of argument linking the mathematics of motion and the mathematics of optimization. The value of the project is to give stronger support to current practices, and at the same time sharpening theoretical ideas and suggesting principled resolutions of some untidy areas, for example, how to define fitness. The aim is also to unify existing free-standing theoretical structures, such as inclusive fitness theory, Evolutionary Stable Strategy (ESS) theory and bet-hedging theory. The 40-year-old misunderstanding over the meaning of fitness optimization between mathematicians and biologists is explained. Most of the elements required for a general theory have now been implemented, but not together in the same framework, and 'general time' remains to be developed and integrated with the other elements to produce a final unified theory of neo-Darwinian natural selection.

  14. The formal de Rham complex

    Science.gov (United States)

    Zharinov, V. V.

    2013-02-01

    We propose a formal construction generalizing the classic de Rham complex to a wide class of models in mathematical physics and analysis. The presentation is divided into a sequence of definitions and elementary, easily verified statements; proofs are therefore given only in the key case. Linear operations are everywhere performed over a fixed number field {F} = {R},{C}. All linear spaces, algebras, and modules, although not stipulated explicitly, are by definition or by construction endowed with natural locally convex topologies, and their morphisms are continuous.

  15. Formal specification and animation of a water level monitoring system

    International Nuclear Information System (INIS)

    Jackson, P.S.; Stokes, P.A.

    1993-03-01

    This report describes the Vienna Development Method (VDM), which is a formal method for software specification and development. VDM evolved out of attempts to use mathematics in programming language specifications in order to avoid ambiguities in specifications written in natural language. This report also describes the use of VDM for a real-time application, where it is used to formally specify the requirements of a water level monitoring system. The procedures and techniques used to produce an executable form (animation) of the specification are covered. (Author)

  16. Skolem and pessimism about proof in mathematics.

    Science.gov (United States)

    Cohen, Paul J

    2005-10-15

    Attitudes towards formalization and proof have gone through large swings during the last 150 years. We sketch the development from Frege's first formalization, to the debates over intuitionism and other schools, through Hilbert's program and the decisive blow of the Gödel Incompleteness Theorem. A critical role is played by the Skolem-Lowenheim Theorem, which showed that no first-order axiom system can characterize a unique infinite model. Skolem himself regarded this as a body blow to the belief that mathematics can be reliably founded only on formal axiomatic systems. In a remarkably prescient paper, he even sketches the possibility of interesting new models for set theory itself, something later realized by the method of forcing. This is in contrast to Hilbert's belief that mathematics could resolve all its questions. We discuss the role of new axioms for set theory, questions in set theory itself, and their relevance for number theory. We then look in detail at what the methods of the predicate calculus, i.e. mathematical reasoning, really entail. The conclusion is that there is no reasonable basis for Hilbert's assumption. The vast majority of questions even in elementary number theory, of reasonable complexity, are beyond the reach of any such reasoning. Of course this cannot be proved and we present only plausibility arguments. The great success of mathematics comes from considering 'natural problems', those which are related to previous work and offer a good chance of being solved. The great glories of human reasoning, beginning with the Greek discovery of geometry, are in no way diminished by this pessimistic view. We end by wishing good health to present-day mathematics and the mathematics of many centuries to come.

  17. Two Project-Based Strategies in an Interdisciplinary Mathematical Modeling in Biology Course

    Science.gov (United States)

    Ludwig, Patrice; Tongen, Anthony; Walton, Brian

    2018-01-01

    James Madison University faculty team-teach an interdisciplinary mathematical modeling course for mathematics and biology students. We have used two different project-based approaches to emphasize the mathematical concepts taught in class, while also exposing students to new areas of mathematics not formally covered in class. The first method…

  18. Category Theory as a Formal Mathematical Foundation for Model-Based Systems Engineering

    KAUST Repository

    Mabrok, Mohamed

    2017-01-09

    In this paper, we introduce Category Theory as a formal foundation for model-based systems engineering. A generalised view of the system based on category theory is presented, where any system can be considered as a category. The objects of the category represent all the elements and components of the system and the arrows represent the relations between these components (objects). The relationship between these objects are the arrows or the morphisms in the category. The Olog is introduced as a formal language to describe a given real-world situation description and requirement writing. A simple example is provided.

  19. Introduction to the foundations of mathematics

    CERN Document Server

    Wilder, Raymond L

    2012-01-01

    This classic undergraduate text by an eminent educator acquaints students with the fundamental concepts and methods of mathematics. In addition to introducing many noteworthy historical figures from the eighteenth through the mid-twentieth centuries, the book examines the axiomatic method, set theory, infinite sets, the linear continuum and the real number system, and groups. Additional topics include the Frege-Russell thesis, intuitionism, formal systems, mathematical logic, and the cultural setting of mathematics. Students and teachers will find that this elegant treatment covers a vast amou

  20. Generation of gravitational waves. II. The postlinear formalism revisited

    International Nuclear Information System (INIS)

    Crowley, R.J.; Thorne, K.S.

    1977-01-01

    Two different versions of the Green's function for the scalar wave equation in weakly curved spacetime (one due to DeWitt and DeWitt, the other to Thorne and Kovacs) are compared and contrasted; and their mathematical equivalence is demonstrated. Then the DeWitt-DeWitt Green's function is used to construct several alternative versions of the Thorne-Kovacs postlinear formalism for gravitational-wave generation. Finally it is shown that, in calculations of gravitational bremsstrahlung radiation, some of our versions of the postlinear formalism allow one to treat the interacting bodies as point masses, while others do not

  1. Decision-Making under Criteria Uncertainty

    Science.gov (United States)

    Kureychik, V. M.; Safronenkova, I. B.

    2018-05-01

    Uncertainty is an essential part of a decision-making procedure. The paper deals with the problem of decision-making under criteria uncertainty. In this context, decision-making under uncertainty, types and conditions of uncertainty were examined. The decision-making problem under uncertainty was formalized. A modification of the mathematical decision support method under uncertainty via ontologies was proposed. A critical distinction of the developed method is ontology usage as its base elements. The goal of this work is a development of a decision-making method under criteria uncertainty with the use of ontologies in the area of multilayer board designing. This method is oriented to improvement of technical-economic values of the examined domain.

  2. Dissemination actions and the popularization of the Exact Sciences by virtual environments and non-formal spaces of education

    Directory of Open Access Journals (Sweden)

    Carlos Coimbra-Araujo

    2017-08-01

    Full Text Available For several reasons, the Exact Sciences have been shown as one of the areas of scientific knowledge that most demand actions in non-formal spaces of education. One of the main reasons lies in the fact that Mathematics, Physics, Chemistry and Astronomy are traditionally addressed, within the school environment and in the formal curriculum, unrelated to the student reality. Such subjects are often seen as a set of inflexible and incomprehensible principles. In this aspect, the present work reviews the main problems surrounding the teaching of the mentioned scientific areas, highlighting non-formal tools for the teaching of Mathematics, Physics, Chemistry, Astronomy and, in particular, the modern virtual environments of teaching modeled by Computing Science. Other historical difficulties that the formal education of Exact Sciences has suffered in Brazil are also presented, as well some of the main non-formal resources sought to complement the curriculum that is usually presented in the classroom.

  3. The origin of the logic of symbolic mathematics Edmund Husserl and Jacob Klein

    CERN Document Server

    Hopkins, Burt C

    2011-01-01

    Burt C. Hopkins presents the first in-depth study of the work of Edmund Husserl and Jacob Klein on the philosophical foundations of the logic of modern symbolic mathematics. Accounts of the philosophical origins of formalized concepts-especially mathematical concepts and the process of mathematical abstraction that generates them-have been paramount to the development of phenomenology. Both Husserl and Klein independently concluded that it is impossible to separate the historical origin of the thought that generates the basic concepts of mathematics from their philosophical meanings. Hopkins explores how Husserl and Klein arrived at their conclusion and its philosophical implications for the modern project of formalizing all knowledge.

  4. Digital system verification a combined formal methods and simulation framework

    CERN Document Server

    Li, Lun

    2010-01-01

    Integrated circuit capacity follows Moore's law, and chips are commonly produced at the time of this writing with over 70 million gates per device. Ensuring correct functional behavior of such large designs before fabrication poses an extremely challenging problem. Formal verification validates the correctness of the implementation of a design with respect to its specification through mathematical proof techniques. Formal techniques have been emerging as commercialized EDA tools in the past decade. Simulation remains a predominantly used tool to validate a design in industry. After more than 5

  5. Foundations and fundamental concepts of mathematics

    CERN Document Server

    Eves, Howard

    1997-01-01

    Third edition of popular undergraduate-level text offers historic overview, readable treatment of mathematics before Euclid, Euclid's Elements, non-Euclidean geometry, algebraic structure, formal axiomatics, sets, more. Problems, some with solutions. Bibliography.

  6. Formal languages, automata and numeration systems introduction to combinatorics on words

    CERN Document Server

    Rigo, Michel

    2014-01-01

    Formal Languages, Automaton and Numeration Systems presents readers with a review of research related to formal language theory, combinatorics on words or numeration systems, such as Words, DLT (Developments in Language Theory), ICALP, MFCS (Mathematical Foundation of Computer Science), Mons Theoretical Computer Science Days, Numeration, CANT (Combinatorics, Automata and Number Theory). Combinatorics on words deals with problems that can be stated in a non-commutative monoid, such as subword complexity of finite or infinite words, construction and properties of infinite words, unavoidabl

  7. Formalism and beyond on the nature of mathematical discourse

    CERN Document Server

    Link, Godehard

    2014-01-01

    The essays collected in this volume focus on the role of formalist aspects in mathematical theorizing and practice, examining issues such as infinity, finiteness, and proof procedures, as well as central historical figures in the field, including Frege, Russell, Hilbert and Wittgenstein. Using modern logico-philosophical tools and systematic conceptual and logical analyses, the volume provides a thorough, up-to-date account of the subject.

  8. Stochastic and Deterministic Models for the Metastatic Emission Process: Formalisms and Crosslinks.

    Science.gov (United States)

    Gomez, Christophe; Hartung, Niklas

    2018-01-01

    Although the detection of metastases radically changes prognosis of and treatment decisions for a cancer patient, clinically undetectable micrometastases hamper a consistent classification into localized or metastatic disease. This chapter discusses mathematical modeling efforts that could help to estimate the metastatic risk in such a situation. We focus on two approaches: (1) a stochastic framework describing metastatic emission events at random times, formalized via Poisson processes, and (2) a deterministic framework describing the micrometastatic state through a size-structured density function in a partial differential equation model. Three aspects are addressed in this chapter. First, a motivation for the Poisson process framework is presented and modeling hypotheses and mechanisms are introduced. Second, we extend the Poisson model to account for secondary metastatic emission. Third, we highlight an inherent crosslink between the stochastic and deterministic frameworks and discuss its implications. For increased accessibility the chapter is split into an informal presentation of the results using a minimum of mathematical formalism and a rigorous mathematical treatment for more theoretically interested readers.

  9. Formalizing structured file services for the data storage and retrieval subsystem of the data management system for Spacestation Freedom

    Science.gov (United States)

    Jamsek, Damir A.

    1993-01-01

    A brief example of the use of formal methods techniques in the specification of a software system is presented. The report is part of a larger effort targeted at defining a formal methods pilot project for NASA. One possible application domain that may be used to demonstrate the effective use of formal methods techniques within the NASA environment is presented. It is not intended to provide a tutorial on either formal methods techniques or the application being addressed. It should, however, provide an indication that the application being considered is suitable for a formal methods by showing how such a task may be started. The particular system being addressed is the Structured File Services (SFS), which is a part of the Data Storage and Retrieval Subsystem (DSAR), which in turn is part of the Data Management System (DMS) onboard Spacestation Freedom. This is a software system that is currently under development for NASA. An informal mathematical development is presented. Section 3 contains the same development using Penelope (23), an Ada specification and verification system. The complete text of the English version Software Requirements Specification (SRS) is reproduced in Appendix A.

  10. Implications of Informal Education Experiences for Mathematics Teachers' Ability to Make Connections beyond Formal Classroom

    Science.gov (United States)

    Popovic, Gorjana; Lederman, Judith S.

    2015-01-01

    The Common Core Standard for Mathematical Practice 4: Model with Mathematics specifies that mathematically proficient students are able to make connections between school mathematics and its applications to solving real-world problems. Hence, mathematics teachers are expected to incorporate connections between mathematical concepts they teach and…

  11. MATHEMATICS TEACHER: MOVING KNOWLEDGE UNDER FORMATION

    Directory of Open Access Journals (Sweden)

    Roselaine Machado Albernaz

    2010-07-01

    Full Text Available This essay approaches the Mathematics teacher forming process from his/her experiences in the school system and the set of knowledge that hashistorical, philosophical and politically constituted him/her. This set of knowledge not only comprises academic knowledge, but also involves the subjective effects of knowledge it incorporates. Starting from a tale, the character, called ‘researcher-teacher’, conducts the text throughout questions about the forming processes of teachers of such a particular subject as Mathematics. The character seems to have an “interrogative something” which is peculiar to us, teachers, concerned about our disciplinary field. Having the objective of problematize the formation and knowledge of our character, her ways of being, thinking and perceiving, we intend to question, with and through her, the new requirements that have been demanded towards Mathematics teachers and the set of knowledge that constitute her, the way she is, her way of acting and taking  position in the school universe. The proposed essay seeks for an articulation between the fields of Art, Philosophy, Science and Education. It speaks about the intriguing school world, but not least, the ways we think to treat the forming process of Mathematics teachers from a set of logical, subjective and sensitive knowledge.  Key words: Forming process of teachers; mathematics; aesthetic experience; philosophy of difference.

  12. A Formal Approach to User Interface Design using Hybrid System Theory, Phase I

    Data.gov (United States)

    National Aeronautics and Space Administration — Optimal Synthesis Inc.(OSI) proposes to develop an aiding tool for user interface design that is based on mathematical formalism of hybrid system theory. The...

  13. Under-Threes' Mathematical Learning--Teachers' Perspectives

    Science.gov (United States)

    Franzén, Karin

    2014-01-01

    This project highlights preschool teachers' views of toddlers' learning in mathematics. The Swedish national curriculum covers even the youngest children who are 1-3?years old. Interesting questions are thus: what should mathematics be for this age group and how should preschool teachers work with maths to achieve the curriculum objectives? Data…

  14. Putting Foundations Into Mathematics

    Science.gov (United States)

    Hubbard, G. L.

    1972-01-01

    For meaningful learning of mathematics, a learning set is required which demands that all things accepted as true should be demonstrable in terms of a paradigm appropriate to the child's cognitive development: preparatory, concrete-particular, concrete-general, formal-abstract. Future teachers should experience all paradigms to become aware that…

  15. Mathematics for quantum chemistry

    CERN Document Server

    Anderson, Jay Martin

    2005-01-01

    This concise volume offers undergraduates an introduction to mathematical formalism in problems of molecular structure and motion. The main topics cover the calculus of orthogonal functions, algebra of vector spaces, and Lagrangian and Hamiltonian formulation of classical mechanics and applications to molecular motion. Answers to problems. 1966 edition.

  16. Formal concept analysis applied to the prediction of additives for galvanizing process

    Directory of Open Access Journals (Sweden)

    J. Klimeš

    2010-04-01

    Full Text Available Formal concept analysis is a new mathematical approach to data analysis, data mining and to discavering patterns in data. The result of the application of the formal concept analysis method to the behavior of the galvanizing of rimmed steel is presented. Effects of additives in the galvanizing process have been correlated to the chemical element properties of the additives. This model may also help to design new alloys as additives in the galvanizing process.

  17. The generation of gravitational waves. 2. The post-linear formalism revisted

    International Nuclear Information System (INIS)

    Crowley, R.J.; Thorne, K.S.

    1976-04-01

    Different versions of the Green's function for the scalar wave equation in weakly curved space-time are compared and contrasted and their mathematical equivalence is demonstrated. Then the DeWitt--DeWitt Green's function is used to construct several alternative versions of the Thorne--Kovacs post-linear formalism for gravitational-wave generation. Finally, it is shown that, in calculations of gravitational bremsstrahlung radiation, some of the presented versions of the post-linear formalism allow one to treat the interacting bodies as point masses, while others do not

  18. Does Writing Have Any Effect on Mathematics Success?

    Science.gov (United States)

    Dündar, Sefa

    2016-01-01

    In this study, the relationship between mathematics success and the formal properties and contents of the notebooks in which students take notes during mathematics classes have been examined. The exploratory model, in which quantitative and qualitative data are used together, has been used in this study. This study consists of 176 students from 3…

  19. Oriented matroid theory as a mathematical framework for M-theory

    OpenAIRE

    Nieto, J. A.

    2006-01-01

    We claim that $M$(atroid) theory may provide a mathematical framework for an underlying description of $M$-theory. Duality is the key symmetry which motivates our proposal. The definition of an oriented matroid in terms of the Farkas property plays a central role in our formalism. We outline how this definition may be carried over $M$-theory. As a consequence of our analysis we find a new type of action for extended systems which combines dually the $p$-brane and its dual $p^{\\perp}$-brane.

  20. Mathematics is always invisible, Professor Dowling

    Science.gov (United States)

    Cable, John

    2015-09-01

    This article provides a critical evaluation of a technique of analysis, the Social Activity Method, recently offered by Dowling (2013) as a `gift' to mathematics education. The method is found to be inadequate, firstly, because it employs a dichotomy (between `expression' and `content') instead of a finer analysis (into symbols, concepts and setting or phenomena), and, secondly, because the distinction between `public' and `esoteric' mathematics, although interesting, is allowed to obscure the structure of the mathematics itself. There is also criticism of what Dowling calls the `myth of participation', which denies the intimate links between mathematics and the rest of the universe that lie at the heart of mathematical pedagogy. Behind all this lies Dowling's `essentially linguistic' conception of mathematics, which is criticised on the dual ground that it ignores the chastening experience of formalism in mathematical philosophy and that linguistics itself has taken a wrong turn and ignores lessons that might be learnt from mathematics education.

  1. Critical Analysis of the Mathematical Formalism of Theoretical Physics. II. Foundations of Vector Calculus

    Science.gov (United States)

    Kalanov, Temur Z.

    2014-03-01

    A critical analysis of the foundations of standard vector calculus is proposed. The methodological basis of the analysis is the unity of formal logic and of rational dialectics. It is proved that the vector calculus is incorrect theory because: (a) it is not based on a correct methodological basis - the unity of formal logic and of rational dialectics; (b) it does not contain the correct definitions of ``movement,'' ``direction'' and ``vector'' (c) it does not take into consideration the dimensions of physical quantities (i.e., number names, denominate numbers, concrete numbers), characterizing the concept of ''physical vector,'' and, therefore, it has no natural-scientific meaning; (d) operations on ``physical vectors'' and the vector calculus propositions relating to the ''physical vectors'' are contrary to formal logic.

  2. Using History to Teach Mathematics: The Case of Logarithms

    Science.gov (United States)

    Panagiotou, Evangelos N.

    2011-01-01

    Many authors have discussed the question why we should use the history of mathematics to mathematics education. For example, Fauvel (For Learn Math, 11(2): 3-6, 1991) mentions at least fifteen arguments for applying the history of mathematics in teaching and learning mathematics. Knowing how to introduce history into mathematics lessons is a more difficult step. We found, however, that only a limited number of articles contain instructions on how to use the material, as opposed to numerous general articles suggesting the use of the history of mathematics as a didactical tool. The present article focuses on converting the history of logarithms into material appropriate for teaching students of 11th grade, without any knowledge of calculus. History uncovers that logarithms were invented prior of the exponential function and shows that the logarithms are not an arbitrary product, as is the case when we leap straight in the definition given in all modern textbooks, but they are a response to a problem. We describe step by step the historical evolution of the concept, in a way appropriate for use in class, until the definition of the logarithm as area under the hyperbola. Next, we present the formal development of the theory and define the exponential function. The teaching sequence has been successfully undertaken in two high school classrooms.

  3. Formal methods in the design of Ada 1995

    Science.gov (United States)

    Guaspari, David

    1995-01-01

    Formal, mathematical methods are most useful when applied early in the design and implementation of a software system--that, at least, is the familiar refrain. I will report on a modest effort to apply formal methods at the earliest possible stage, namely, in the design of the Ada 95 programming language itself. This talk is an 'experience report' that provides brief case studies illustrating the kinds of problems we worked on, how we approached them, and the extent (if any) to which the results proved useful. It also derives some lessons and suggestions for those undertaking future projects of this kind. Ada 95 is the first revision of the standard for the Ada programming language. The revision began in 1988, when the Ada Joint Programming Office first asked the Ada Board to recommend a plan for revising the Ada standard. The first step in the revision was to solicit criticisms of Ada 83. A set of requirements for the new language standard, based on those criticisms, was published in 1990. A small design team, the Mapping Revision Team (MRT), became exclusively responsible for revising the language standard to satisfy those requirements. The MRT, from Intermetrics, is led by S. Tucker Taft. The work of the MRT was regularly subject to independent review and criticism by a committee of distinguished Reviewers and by several advisory teams--for example, the two User/Implementor teams, each consisting of an industrial user (attempting to make significant use of the new language on a realistic application) and a compiler vendor (undertaking, experimentally, to modify its current implementation in order to provide the necessary new features). One novel decision established the Language Precision Team (LPT), which investigated language proposals from a mathematical point of view. The LPT applied formal mathematical analysis to help improve the design of Ada 95 (e.g., by clarifying the language proposals) and to help promote its acceptance (e.g., by identifying a

  4. Computers as medium for mathematical writing

    DEFF Research Database (Denmark)

    Misfeldt, Morten

    2011-01-01

    The production of mathematical formalism on state of the art computers is quite different than by pen and paper.  In this paper I examine the question of how different media influence the writing of mathematical signs. The examination is based on an investigation of professional mathematicians' use...... of various media for their writing. A model for describing mathematical writing through turntakings is proposed. The model is applied to the ways mathematicians use computers for writing, and especially it is used to understand how interaction with the computer system LaTeX is different in the case...

  5. The Professional Learning Experiences of Non-Mathematics Subject Specialist Teachers: A Descriptive Study

    OpenAIRE

    Ho Younghusband, Alice Christine

    2017-01-01

    Certified teachers in British Columbia (BC) schools can be assigned to teach secondary mathematics without having a major, minor, or formal background in mathematics. This is known as out-of-field teaching. These non-mathematics subject specialist teachers (NMSSTs) must learn or relearn the subject matter of mathematics to teach secondary mathematics. This study investigates what professional learning activities NMSSTs participate in to gain subject matter content knowledge in mathematics, wh...

  6. Foundations of mathematical logic

    CERN Document Server

    Curry, Haskell B

    2010-01-01

    Written by a pioneer of mathematical logic, this comprehensive graduate-level text explores the constructive theory of first-order predicate calculus. It covers formal methods, including algorithms and epitheory, and offers a brief treatment of Markov's approach to algorithms, explains elementary facts about lattices and similar algebraic systems, and more. 1963 edition.

  7. 37 CFR 251.41 - Formal hearings.

    Science.gov (United States)

    2010-07-01

    ... ARBITRATION ROYALTY PANEL RULES AND PROCEDURES COPYRIGHT ARBITRATION ROYALTY PANEL RULES OF PROCEDURE Procedures of Copyright Arbitration Royalty Panels § 251.41 Formal hearings. (a) The formal hearings that will be conducted under the rules of this subpart are rate adjustment hearings and royalty fee...

  8. Formal Women-only Networks

    DEFF Research Database (Denmark)

    Villesèche, Florence; Josserand, Emmanuel

    2017-01-01

    /organisations and the wider social group of women in business. Research limitations/implications: The authors focus on the distinction between external and internal formal women-only networks while also acknowledging the broader diversity that can characterise such networks. Their review provides the reader with an insight...... member level, the authors suggest that such networks can be of value for organisations and the wider social group of women in management and leadership positions.......Purpose: The purpose of this paper is to review the emerging literature on formal women-only business networks and outline propositions to develop this under-theorised area of knowledge and stimulate future research. Design/methodology/approach: The authors review the existing literature on formal...

  9. Unity and disunity and other mathematical essays

    CERN Document Server

    Davis, Philip J

    2015-01-01

    This book is a mathematical potpourri. Its material originated in classroom presentations, formal lectures, sections of earlier books, book reviews, or just things written by the author for his own pleasure. Written in a nontechnical fashion, this book expresses the unique vision and attitude of the author towards the role of mathematics in society. It contains observations or incidental remarks on mathematics, its nature, its impacts on education and science and technology, its personalities and philosophies. The book is directed towards the math buffs of the world and, more generally, toward

  10. Formal Models of the Network Co-occurrence Underlying Mental Operations.

    Science.gov (United States)

    Bzdok, Danilo; Varoquaux, Gaël; Grisel, Olivier; Eickenberg, Michael; Poupon, Cyril; Thirion, Bertrand

    2016-06-01

    Systems neuroscience has identified a set of canonical large-scale networks in humans. These have predominantly been characterized by resting-state analyses of the task-unconstrained, mind-wandering brain. Their explicit relationship to defined task performance is largely unknown and remains challenging. The present work contributes a multivariate statistical learning approach that can extract the major brain networks and quantify their configuration during various psychological tasks. The method is validated in two extensive datasets (n = 500 and n = 81) by model-based generation of synthetic activity maps from recombination of shared network topographies. To study a use case, we formally revisited the poorly understood difference between neural activity underlying idling versus goal-directed behavior. We demonstrate that task-specific neural activity patterns can be explained by plausible combinations of resting-state networks. The possibility of decomposing a mental task into the relative contributions of major brain networks, the "network co-occurrence architecture" of a given task, opens an alternative access to the neural substrates of human cognition.

  11. The materiality of mathematics: presenting mathematics at the blackboard.

    Science.gov (United States)

    Greiffenhagen, Christian

    2014-09-01

    Sociology has been accused of neglecting the importance of material things in human life and the material aspects of social practices. Efforts to correct this have recently been made, with a growing concern to demonstrate the materiality of social organization, not least through attention to objects and the body. As a result, there have been a plethora of studies reporting the social construction and effects of a variety of material objects as well as studies that have explored the material dimensions of a diversity of practices. In different ways these studies have questioned the Cartesian dualism of a strict separation of 'mind' and 'body'. However, it could be argued that the idea of the mind as immaterial has not been entirely banished and lingers when it comes to discussing abstract thinking and reasoning. The aim of this article is to extend the material turn to abstract thought, using mathematics as a paradigmatic example. This paper explores how writing mathematics (on paper, blackboards, or even in the air) is indispensable for doing and thinking mathematics. The paper is based on video recordings of lectures in formal logic and investigates how mathematics is presented at the blackboard. The paper discusses the iconic character of blackboards in mathematics and describes in detail a number of inscription practices of presenting mathematics at the blackboard (such as the use of lines and boxes, the designation of particular regions for specific mathematical purposes, as well as creating an 'architecture' visualizing the overall structure of the proof). The paper argues that doing mathematics really is 'thinking with eyes and hands' (Latour 1986). Thinking in mathematics is inextricably interwoven with writing mathematics. © London School of Economics and Political Science 2014.

  12. The discursive production of classroom mathematics

    Science.gov (United States)

    Smith, Kim; Hodson, Elaine; Brown, Tony

    2013-09-01

    School mathematics is a function of its discursive environment where the language being used formats mathematical activity. The paper explores this theme through an extended example in which the conduct of mathematical teaching and learning is restricted by regulative educational policies. It considers how mathematics is discursively produced by student teachers within an employment-based model of teacher education in England where there is a low university input. It is argued that teacher reflections on mathematical learning and teaching within the course are patterned discursively in line with formal curriculum framings, assessment requirements and the local demands of their placement school. Both teachers and students are subject to regulative discourses that shape their actions and as a consequence this regulation influences the forms of mathematical activity that can take place. It is shown how university sessions can provide a limited critical platform from which to interrogate these restrictions and renegotiate them.

  13. The Framing Discussion: Connecting Student Experience with Mathematical Knowledge

    Science.gov (United States)

    Henning, John E.; Balong, Megan

    2011-01-01

    This article introduces the framing discussion, an informal discussion of a mathematical problem that takes place at the beginning of a lesson or unit. The purpose of the framing discussion is to assess student knowledge, motivate student interest, and to serve as a basis for guiding students to more formal mathematical knowledge. The article…

  14. Generalizing Prototype Theory: A Formal Quantum Framework

    Directory of Open Access Journals (Sweden)

    Diederik eAerts

    2016-03-01

    Full Text Available Theories of natural language and concepts have been unable to model the flexibility, creativity, context-dependence, and emergence, exhibited by words, concepts and their combinations. The mathematical formalism of quantum theory has instead been successful in capturing these phenomena such as graded membership, situational meaning, composition of categories, and also more complex decision making situations, which cannot be modeled in traditional probabilistic approaches. We show how a formal quantum approach to concepts and their combinations can provide a powerful extension of prototype theory. We explain how prototypes can interfere in conceptual combinations as a consequence of their contextual interactions, and provide an illustration of this using an intuitive wave-like diagram. This quantum-conceptual approach gives new life to original prototype theory, without however making it a privileged concept theory, as we explain at the end of our paper.

  15. Generalizing Prototype Theory: A Formal Quantum Framework

    Science.gov (United States)

    Aerts, Diederik; Broekaert, Jan; Gabora, Liane; Sozzo, Sandro

    2016-01-01

    Theories of natural language and concepts have been unable to model the flexibility, creativity, context-dependence, and emergence, exhibited by words, concepts and their combinations. The mathematical formalism of quantum theory has instead been successful in capturing these phenomena such as graded membership, situational meaning, composition of categories, and also more complex decision making situations, which cannot be modeled in traditional probabilistic approaches. We show how a formal quantum approach to concepts and their combinations can provide a powerful extension of prototype theory. We explain how prototypes can interfere in conceptual combinations as a consequence of their contextual interactions, and provide an illustration of this using an intuitive wave-like diagram. This quantum-conceptual approach gives new life to original prototype theory, without however making it a privileged concept theory, as we explain at the end of our paper. PMID:27065436

  16. Picture languages formal models for picture recognition

    CERN Document Server

    Rosenfeld, Azriel

    1979-01-01

    Computer Science and Applied Mathematics: Picture Languages: Formal Models for Picture Recognition treats pictorial pattern recognition from the formal standpoint of automata theory. This book emphasizes the capabilities and relative efficiencies of two types of automata-array automata and cellular array automata, with respect to various array recognition tasks. The array automata are simple processors that perform sequences of operations on arrays, while the cellular array automata are arrays of processors that operate on pictures in a highly parallel fashion, one processor per picture element. This compilation also reviews a collection of results on two-dimensional sequential and parallel array acceptors. Some of the analogous one-dimensional results and array grammars and their relation to acceptors are likewise covered in this text. This publication is suitable for researchers, professionals, and specialists interested in pattern recognition and automata theory.

  17. Category Theory as a Formal Mathematical Foundation for Model-Based Systems Engineering

    KAUST Repository

    Mabrok, Mohamed; Ryan, Michael J.

    2017-01-01

    In this paper, we introduce Category Theory as a formal foundation for model-based systems engineering. A generalised view of the system based on category theory is presented, where any system can be considered as a category. The objects

  18. The (Mathematical) Modeling Process in Biosciences.

    Science.gov (United States)

    Torres, Nestor V; Santos, Guido

    2015-01-01

    In this communication, we introduce a general framework and discussion on the role of models and the modeling process in the field of biosciences. The objective is to sum up the common procedures during the formalization and analysis of a biological problem from the perspective of Systems Biology, which approaches the study of biological systems as a whole. We begin by presenting the definitions of (biological) system and model. Particular attention is given to the meaning of mathematical model within the context of biology. Then, we present the process of modeling and analysis of biological systems. Three stages are described in detail: conceptualization of the biological system into a model, mathematical formalization of the previous conceptual model and optimization and system management derived from the analysis of the mathematical model. All along this work the main features and shortcomings of the process are analyzed and a set of rules that could help in the task of modeling any biological system are presented. Special regard is given to the formative requirements and the interdisciplinary nature of this approach. We conclude with some general considerations on the challenges that modeling is posing to current biology.

  19. The challenge of computer mathematics.

    Science.gov (United States)

    Barendregt, Henk; Wiedijk, Freek

    2005-10-15

    Progress in the foundations of mathematics has made it possible to formulate all thinkable mathematical concepts, algorithms and proofs in one language and in an impeccable way. This is not in spite of, but partially based on the famous results of Gödel and Turing. In this way statements are about mathematical objects and algorithms, proofs show the correctness of statements and computations, and computations are dealing with objects and proofs. Interactive computer systems for a full integration of defining, computing and proving are based on this. The human defines concepts, constructs algorithms and provides proofs, while the machine checks that the definitions are well formed and the proofs and computations are correct. Results formalized so far demonstrate the feasibility of this 'computer mathematics'. Also there are very good applications. The challenge is to make the systems more mathematician-friendly, by building libraries and tools. The eventual goal is to help humans to learn, develop, communicate, referee and apply mathematics.

  20. Measurement and the mathematical apparatus of quantum physics

    International Nuclear Information System (INIS)

    Slavnov, D.A.

    2007-01-01

    A scheme for constructing quantum mechanics in which the Hilbert space and linear operators are not primary elements on the theory is described. Some variant of the algebraic approach is instead considered. The elements of a noncommutative algebra (observables) and functionals in this algebra serve as the primary components of the theory. Such a scheme allows one to use the formalism of the classical (Kolmogorovian) theory of probability, and to reproduce the mathematical formalism of standard quantum mechanics and to specify borders of its applicability. A brief review of necessary data from the theory of algebras and probability theory is given. The manner is described in which the considered mathematical scheme agrees with the theory of quantum measurements and allows one to avoid quantum paradoxes [ru

  1. Towards a formal semantics for Ada 9X

    Science.gov (United States)

    Guaspari, David; Mchugh, John; Wolfgang, Polak; Saaltink, Mark

    1995-01-01

    The Ada 9X language precision team was formed during the revisions of Ada 83, with the goal of analyzing the proposed design, identifying problems, and suggesting improvements, through the use of mathematical models. This report defines a framework for formally describing Ada 9X, based on Kahn's 'natural semantics', and applies the framework to portions of the language. The proposals for exceptions and optimization freedoms are also analyzed, using a different technique.

  2. Freedom and enforcement in action a study in formal action theory

    CERN Document Server

    Czelakowski, Janusz

    2015-01-01

    Action theory is the object of growing attention in a variety of scientific disciplines, and this is the first volume to offer a synthetic view of the range of approaches possible in the topic. The volume focuses on the nexus of formal action theory with a startlingly diverse set of subjects, which range from logic, linguistics, artificial intelligence, and automata theory to jurisprudence, deontology, and economics. It covers semantic, mathematical and logical aspects of action, showing how the problem of action breaks the boundaries of traditional branches of logic located in syntactics and semantics and now lies on lies on the borderline between logical pragmatics and praxeology.   The chapters here focus on specialized tasks in formal action theory, beginning with a thorough description and formalization of the language of action, and moving through material on the differing models of action theory to focus on probabilistic models, the relations of formal action theory to deontic logic, and its key appl...

  3. Lakatos and Hersh on Mathematical Proof

    Directory of Open Access Journals (Sweden)

    Hossein Bayat

    2015-12-01

    Full Text Available The concept of Mathematical Proof has been controversial for the past few decades. Different philosophers have offered different theories about the nature of Mathematical Proof, among which theories presented by Lakatos and Hersh have had significant similarities and differences with each other. It seems that a comparison and critical review of these two theories will lead to a better understanding of the concept of mathematical proof and will be a big step towards solving many related problems. Lakatos and Hersh argue that, firstly, “mathematical proof” has two different meanings, formal and informal; and, secondly, informal proofs are affected by human factors, such as individual decisions and collective agreements. I call these two thesis, respectively, “proof dualism” and “humanism”. But on the other hand, their theories have significant dissimilarities and are by no means equivalent. Lakatos is committed to linear proof dualism and methodological humanism, while Hersh’s theory involves some sort of parallel proof dualism and sociological humanism. According to linear proof dualism, the two main types of proofs are provided in order to achieve a common goal: incarnation of mathematical concepts and methods and truth. However, according to the parallel proof dualism, two main types of proofs are provided in order to achieve two different types of purposes: production of a valid sequence of signs (the goal of the formal proof and persuasion of the audience (the goal of the informal proof. Hersh’s humanism is informative and indicates pluralism; whereas, Lakatos’ version of humanism is normative and monistic.

  4. Barely Started and Already Left behind: A Descriptive Analysis of the Mathematics Ability Demonstrated by Young Deaf Children

    Science.gov (United States)

    Kritzer, Karen L.

    2009-01-01

    This study examined young deaf children's early informal/formal mathematical knowledge as measured by the Test of Early Mathematics Ability (TEMA-3). Findings from this study suggest that prior to the onset of formal schooling, young deaf children might already demonstrate evidence of academic delays. Of these 28 participants (4-6 years of age),…

  5. Semantic Contamination and Mathematical Proof: Can a Non-Proof Prove?

    Science.gov (United States)

    Mejia-Ramos, Juan Pablo; Inglis, Matthew

    2011-01-01

    The way words are used in natural language can influence how the same words are understood by students in formal educational contexts. Here we argue that this so-called semantic contamination effect plays a role in determining how students engage with mathematical proof, a fundamental aspect of learning mathematics. Analyses of responses to…

  6. Informal Content and Student Note-Taking in Advanced Mathematics Classes

    Science.gov (United States)

    Fukawa-Connelly, Timothy; Weber, Keith; Mejía-Ramos, Juan Pablo

    2017-01-01

    This study investigates 3 hypotheses about proof-based mathematics instruction: (a) that lectures include informal content (ways of thinking and reasoning about advanced mathematics that are not captured by formal symbolic statements), (b) that informal content is usually presented orally but not written on the board, and (c) that students do not…

  7. Formal aspects of resilience

    Directory of Open Access Journals (Sweden)

    Diana-Maria Drigă

    2015-12-01

    Full Text Available The concept of resilience has represented during the recent years a leading concern both in Romania, within the European Union and worldwide. Specialists in economics, management, finance, legal sciences, political sciences, sociology, psychology, grant a particular interest to this concept. Multidisciplinary research of resilience has materialized throughout the time in multiple conceptualizations and theorizing, but without being a consensus between specialists in terms of content, specificity and scope. Through this paper it is intended to clarify the concept of resilience, achieving an exploration of the evolution of this concept in ecological, social and economic environment. At the same time, the paper presents aspects of feedback mechanisms and proposes a formalization of resilience using the logic and mathematical analysis.

  8. Computational experiment approach to advanced secondary mathematics curriculum

    CERN Document Server

    Abramovich, Sergei

    2014-01-01

    This book promotes the experimental mathematics approach in the context of secondary mathematics curriculum by exploring mathematical models depending on parameters that were typically considered advanced in the pre-digital education era. This approach, by drawing on the power of computers to perform numerical computations and graphical constructions, stimulates formal learning of mathematics through making sense of a computational experiment. It allows one (in the spirit of Freudenthal) to bridge serious mathematical content and contemporary teaching practice. In other words, the notion of teaching experiment can be extended to include a true mathematical experiment. When used appropriately, the approach creates conditions for collateral learning (in the spirit of Dewey) to occur including the development of skills important for engineering applications of mathematics. In the context of a mathematics teacher education program, this book addresses a call for the preparation of teachers capable of utilizing mo...

  9. The mathematics of elections and voting

    CERN Document Server

    Wallis, W D

    2014-01-01

    The Mathematics of Elections and Voting  takes an in-depth look at the mathematics in the context of voting and electoral systems, with focus on simple ballots, complex elections, fairness, approval voting, ties, fair and unfair voting, and manipulation techniques. The exposition opens with a sketch of the mathematics behind the various methods used in conducting elections. The reader is lead to a comprehensive picture of the theoretical background of mathematics and elections through an analysis of Condorcet’s Principle and Arrow’s Theorem of conditions in electoral fairness. Further detailed discussion of various related topics include: methods of manipulating the outcome of an election, amendments, and voting on small committees. In recent years, electoral theory has been introduced into lower-level mathematics courses, as a way to illustrate the role of mathematics in our everyday life.  Few books have studied voting and elections from a more formal mathematical viewpoint.  This text wi...

  10. A Formal Methods Approach to the Analysis of Mode Confusion

    Science.gov (United States)

    Butler, Ricky W.; Miller, Steven P.; Potts, James N.; Carreno, Victor A.

    2004-01-01

    The goal of the new NASA Aviation Safety Program (AvSP) is to reduce the civil aviation fatal accident rate by 80% in ten years and 90% in twenty years. This program is being driven by the accident data with a focus on the most recent history. Pilot error is the most commonly cited cause for fatal accidents (up to 70%) and obviously must be given major consideration in this program. While the greatest source of pilot error is the loss of situation awareness , mode confusion is increasingly becoming a major contributor as well. The January 30, 1995 issue of Aviation Week lists 184 incidents and accidents involving mode awareness including the Bangalore A320 crash 2/14/90, the Strasbourg A320 crash 1/20/92, the Mulhouse-Habsheim A320 crash 6/26/88, and the Toulouse A330 crash 6/30/94. These incidents and accidents reveal that pilots sometimes become confused about what the cockpit automation is doing. Consequently, human factors research is an obvious investment area. However, even a cursory look at the accident data reveals that the mode confusion problem is much deeper than just training deficiencies and a lack of human-oriented design. This is readily acknowledged by human factors experts. It seems that further progress in human factors must come through a deeper scrutiny of the internals of the automation. It is in this arena that formal methods can contribute. Formal methods refers to the use of techniques from logic and discrete mathematics in the specification, design, and verification of computer systems, both hardware and software. The fundamental goal of formal methods is to capture requirements, designs and implementations in a mathematically based model that can be analyzed in a rigorous manner. Research in formal methods is aimed at automating this analysis as much as possible. By capturing the internal behavior of a flight deck in a rigorous and detailed formal model, the dark corners of a design can be analyzed. This paper will explore how formal

  11. Formal Models of the Network Co-occurrence Underlying Mental Operations.

    Directory of Open Access Journals (Sweden)

    Danilo Bzdok

    2016-06-01

    Full Text Available Systems neuroscience has identified a set of canonical large-scale networks in humans. These have predominantly been characterized by resting-state analyses of the task-unconstrained, mind-wandering brain. Their explicit relationship to defined task performance is largely unknown and remains challenging. The present work contributes a multivariate statistical learning approach that can extract the major brain networks and quantify their configuration during various psychological tasks. The method is validated in two extensive datasets (n = 500 and n = 81 by model-based generation of synthetic activity maps from recombination of shared network topographies. To study a use case, we formally revisited the poorly understood difference between neural activity underlying idling versus goal-directed behavior. We demonstrate that task-specific neural activity patterns can be explained by plausible combinations of resting-state networks. The possibility of decomposing a mental task into the relative contributions of major brain networks, the "network co-occurrence architecture" of a given task, opens an alternative access to the neural substrates of human cognition.

  12. Crossroads in the History of Mathematics and Mathematics Education. The Montana Mathematics Enthusiast: Monograph Series in Mathematics Education

    Science.gov (United States)

    Sriraman, Bharath, Ed.

    2012-01-01

    The interaction of the history of mathematics and mathematics education has long been construed as an esoteric area of inquiry. Much of the research done in this realm has been under the auspices of the history and pedagogy of mathematics group. However there is little systematization or consolidation of the existing literature aimed at…

  13. New method of contour image processing based on the formalism of spiral light beams

    Science.gov (United States)

    Volostnikov, Vladimir G.; Kishkin, S. A.; Kotova, S. P.

    2013-07-01

    The possibility of applying the mathematical formalism of spiral light beams to the problems of contour image recognition is theoretically studied. The advantages and disadvantages of the proposed approach are evaluated; the results of numerical modelling are presented.

  14. Type classes for mathematics in type theory

    OpenAIRE

    Spitters, Bas; Van der Weegen, Eelis

    2011-01-01

    The introduction of first-class type classes in the Coq system calls for re-examination of the basic interfaces used for mathematical formalization in type theory. We present a new set of type classes for mathematics and take full advantage of their unique features to make practical a particularly flexible approach formerly thought infeasible. Thus, we address both traditional proof engineering challenges as well as new ones resulting from our ambition to build upon this development a library...

  15. From Religion to Dialectics and Mathematics

    Directory of Open Access Journals (Sweden)

    Achtner Wolfgang

    2016-03-01

    Full Text Available Hermann Grassmann is known to be the founder of modern vector and tensor calculus. Having as a theologian no formal education in mathematics at a university he got his basic ideas for this mathematical innovation at least to some extent from listening to Schleiermacher’s lectures on Dialectics and, together with his brother Robert, reading its publication in 1839. The paper shows how the idea of unity and various levels of reality first formulated in Schleiermacher’s talks about religion in 1799 were transformed by him into a philosophical system in his dialectics and then were picked up by Grassmann and operationalized in his philosophical-mathematical treatise on the extension theory (German: Ausdehnungslehre in 1844.

  16. New method of contour image processing based on the formalism of spiral light beams

    International Nuclear Information System (INIS)

    Volostnikov, Vladimir G; Kishkin, S A; Kotova, S P

    2013-01-01

    The possibility of applying the mathematical formalism of spiral light beams to the problems of contour image recognition is theoretically studied. The advantages and disadvantages of the proposed approach are evaluated; the results of numerical modelling are presented. (optical image processing)

  17. Context problems in realistic mathematics education: A calculus course as an example

    NARCIS (Netherlands)

    Gravemeijer, K.P.E.; Doorman, L.M.

    1999-01-01

    This article discusses the role of context problems, as they are used in the Dutch approach that is known as realistic mathematics education (RME). In RME, context problems are intended for supporting a reinvention process that enables students to come to grips with formal mathematics. This approach

  18. Foundation and Mathematical Uses of Higher Types

    DEFF Research Database (Denmark)

    Kohlenbach, Ulrich

    2002-01-01

    This paper addresses `1),' to which S. Feferman has contributed so profoundly. We study mathematical strong, but nevertheless PRA-reducible, systems in all finite types, emphasizing the need of third order variables already for a faithful formalization of continuous functions between Polish spaces...

  19. Essential competencies analysis of a training model development for non-formal vocational teachers under the office of the non-formal and informal education in Thailand

    Directory of Open Access Journals (Sweden)

    Chayanopparat Piyanan

    2016-01-01

    Full Text Available Non-formal vocational education provides practical experiences in a particular occupational field to non-formal semi-skilled learners. Non-formal vocational teachers are the key persons to deliver particular occupational knowledge. The essential competencies enhancement for non-sformal vocational teachers will improve teaching performance. The question of the research is what the essential competencies for the nonformal vocational teachers are. The research method was 1 to review related literature, 2 to collect a needs assessment, and 3 to analyse the essential competencies for non-formal vocational teachers. The population includes non-formal vocational teachers at the executive level and nonformal vocational teachers. The results from the essential competencies analysis found that the essential competencies for non-formal vocational teachers consist of 5 capabilities including 1 Adult learning design capability, 2 Adult learning principle application capability, 3 ICT searching capability for teaching preparation, 4 Instructional plan development capability and 5 Instructional media development capability.

  20. Curci-Ferrari-type condition in Hamiltonian formalism: A free spinning relativistic particle

    Science.gov (United States)

    Shukla, A.; Bhanja, T.; Malik, R. P.

    2013-03-01

    The Curci-Ferrari (CF)-type restriction emerges in the description of a free spinning relativistic particle within the framework of the Becchi-Rouet-Stora-Tyutin (BRST) formalism when the off-shell nilpotent and absolutely anticommuting (anti-)BRST symmetry transformations for this system are derived from the application of the horizontality condition (HC) and its supersymmetric generalization (SUSY-HC) within the framework of the superfield formalism. We show that the above CF condition, which turns out to be the secondary constraint of our present theory, remains time-evolution invariant within the framework of Hamiltonian formalism. This time-evolution invariance i) physically justifies the imposition of the (anti-)BRST invariant CF-type condition on this system, and ii) mathematically implies the linear independence of BRST and anti-BRST symmetries of our present theory.

  1. Formalizing the Process of Constructing Chains of Lexical Units

    Directory of Open Access Journals (Sweden)

    Grigorij Chetverikov

    2015-06-01

    Full Text Available Formalizing the Process of Constructing Chains of Lexical Units The paper investigates mathematical aspects of describing the construction of chains of lexical units on the basis of finite-predicate algebra. Analyzing the construction peculiarities is carried out and application of the method of finding the power of linear logical transformation for removing characteristic words of a dictionary entry is given. Analysis and perspectives of the results of the study are provided.

  2. The Impact of Hands-On-Approach on Student Academic Performance in Basic Science and Mathematics

    Science.gov (United States)

    Ekwueme, Cecilia O.; Ekon, Esther E.; Ezenwa-Nebife, Dorothy C.

    2015-01-01

    Children can learn mathematics and sciences effectively even before being exposed to formal school curriculum if basic Mathematics and Sciences concepts are communicated to them early using activity oriented (Hands-on) method of teaching. Mathematics and Science are practical and activity oriented and can best be learnt through inquiry (Okebukola…

  3. Mathematical Building-Blocks in Engineering Mechanics

    Science.gov (United States)

    Boyajian, David M.

    2007-01-01

    A gamut of mathematical subjects and concepts are taught within a handful of courses formally required of the typical engineering student who so often questions the relevancy of being bound to certain lower-division prerequisites. Basic classes at the undergraduate level, in this context, include: Integral and Differential Calculus, Differential…

  4. Dirac - Kaehler formalism and the Yang-Mills model with Supersymmetry

    International Nuclear Information System (INIS)

    Goto, M.

    1985-01-01

    It is used the differential Dirac-Kahler's formalism for transposing supersymmetric models for the lattice. Such a formalism has shown itself extremely useful for these purposes because there exists a complete mathematical duality in its versions in the continuum and in the lattice. This work treats specifically the Yang-Mills, model with extended supersymmetry N = 2 in the adjoint representation; the procedure which is adopted here consists in to rewrite the essential of the model in question in the new language, first in the continuum, getting it adequate for the lattice, because it is from the property of the supercharges Q 2 = H that the lattice supersymmetric Hamiltonian will be obtained. By the way, it was constructed a lattice gauge theory within the formalism of Dirac-Kahler, it is almost a natural consequence of the adopted definitions for the lattice gauge transformations of the fields in the adjoint representation and of the two types of covariant derivatives which are necessary in the lattice. In order to carry out some calculations, it was put emphasis on the matrix representation of the Dirac-Kahler's formalism, it was also extended to a lattice. (author) [pt

  5. Using realistic mathematics education and the DAPIC problem-solving process to enhance secondary school students' mathematical literacy

    Directory of Open Access Journals (Sweden)

    Sunisa Sumirattana

    2017-09-01

    This study was based on research and development design. The main purposes of this study were to develop an instructional process for enhancing mathematical literacy among students in secondary school and to study the effects of the developed instructional process on mathematical literacy. The instructional process was developed by analyzing and synthesizing realistic mathematics education and the DAPIC problem-solving process. The developed instructional process was verified by experts and was trialed. The designated pre-test/post-test control method was used to study the effectiveness of the developed instructional process on mathematical literacy. The sample consisted of 104 ninth grade students from a secondary school in Bangkok, Thailand. The developed instructional process consisted of five steps, namely (1 posing real life problems, (2 solving problems individually or in a group, (3 presenting and discussing, (4 developing formal mathematics, and (5 applying knowledge. The mathematical literacy of the experimental group was significantly higher after being taught through the instructional process. The same results were obtained when comparing the results of the experimental group with the control group.

  6. The role of formal specifications

    International Nuclear Information System (INIS)

    McHugh, J.

    1994-01-01

    The role of formal requirements specification is discussed under the premise that the primary purpose of such specifications is to facilitate clear and unambiguous communications among the communities of interest for a given project. An example is presented in which the failure to reach such an understanding resulted in an accident at a chemical plant. Following the example, specification languages based on logical formalisms and notations are considered. These are rejected as failing to serve the communications needs of diverse communities. The notion of a specification as a surrogate for a program is also considered and rejected. The paper ends with a discussion of the type of formal notation that will serve the communications role and several encouraging developments are noted

  7. La Meme Chose: How Mathematics Can Explain the Thinking of Children and the Thinking of Children Can Illuminate Mathematical Philosophy

    Science.gov (United States)

    Cable, John

    2014-01-01

    This article offers a new interpretation of Piaget's decanting experiments, employing the mathematical notion of equivalence instead of conservation. Some reference is made to Piaget's theories and to his educational legacy, but the focus in on certain of the experiments. The key to the new analysis is the abstraction principle, which has been formally enunciated in mathematical philosophy but has universal application. It becomes necessary to identity fluid objects (both configured and unconfigured) and configured and unconfigured sets-of-objects. Issues emerge regarding the conflict between philosophic realism and anti-realism, including constructivism. Questions are asked concerning mathematics and mathematical philosophy, particularly over the nature of sets, the wisdom of the axiomatic method and aspects of the abstraction principle itself.

  8. Students Thinking Process in Compiling Mathematical Proof with Semantics Strategy

    Directory of Open Access Journals (Sweden)

    Abdussakir Abdussakir

    2015-03-01

    Full Text Available Proses Berpikir Mahasiswa dalam Menyusun Bukti Matematis dengan Strategi Semantik   Abstract: This study is aimed to reveal the thinking process in proof construction performed by students with semantic strategy. This study use descriptive-qualitative approach. The thinking process of students will be analyzed using theoretical framework of David Tall about the three worlds of mathematical thinking. The result are three ways of thinking in semantic strategy, namely (1 started from formal world  then move into the symbolic or embodied-symbolic world with possibility of more than once and ends within or outside of the formal world, (2 started from symbolic world or embodied-symbolic world then move to the formal world with possibility of more than once and ends within or outside of the formal world, and (3 all thinking processes performed outside of formal world that does not obtain formal proof. Key Words: thinking process, mathematical proof, semantic strategy   Abstrak: Penelitian ini bertujuan untuk menjelaskan proses berpikir mahasiswa dalam menyusun bukti matematis dengan strategi semantik. Penelitian ini menggunakan pendekatan deskiptif-kualitatif. Analisis data dilakukan dengan menggunakan kerangka kerja David Tall tentang tiga dunia berpikir matematik. Hasil penelitian menunjukkan bahwa terdapat enam kemungkinan jalur dalam strategi semantik ditinjau dari teori tiga dunia berpikir matematis. Hasil penelitian menunjukkan ada tiga jalur berpikir mahasiswa dalam menyusun bukti matematis dengan strategi semantik, yaitu (1 bermula dari dunia berpikir formal berpindah ke dunia berpikir wujud-simbolik atau dunia berpikir simbolik dengan proses perpindahan dimungkinkan lebih dari satu kali dan berakhir di dalam atau di luar dunia berpikir formal, (2 bermula dari dunia berpikir wujud simbolik atau dunia berpikir simbolik (non RSP lalu pindah ke dunia berpikir formal dengan proses perpindahan dimungkinkan lebih dari satu kali dan berakhir di

  9. Elementary School Quality: The Mathematics Curriculum and the Role of Local Knowledge.

    Science.gov (United States)

    Balfanz, Robert

    This report considers how the mathematical knowledge children develop on their own outside of formal school instruction can be used to increase the distribution and level of mathematical knowledge attained by students in grades K-3. Included are preliminary results of an investigation of the counting and calculating abilities brought to…

  10. Mathematics, anxiety, and the brain.

    Science.gov (United States)

    Moustafa, Ahmed A; Tindle, Richard; Ansari, Zaheda; Doyle, Margery J; Hewedi, Doaa H; Eissa, Abeer

    2017-05-24

    Given that achievement in learning mathematics at school correlates with work and social achievements, it is important to understand the cognitive processes underlying abilities to learn mathematics efficiently as well as reasons underlying the occurrence of mathematics anxiety (i.e. feelings of tension and fear upon facing mathematical problems or numbers) among certain individuals. Over the last two decades, many studies have shown that learning mathematical and numerical concepts relies on many cognitive processes, including working memory, spatial skills, and linguistic abilities. In this review, we discuss the relationship between mathematical learning and cognitive processes as well as the neural substrates underlying successful mathematical learning and problem solving. More importantly, we also discuss the relationship between these cognitive processes, mathematics anxiety, and mathematics learning disabilities (dyscalculia). Our review shows that mathematical cognition relies on a complex brain network, and dysfunction to different segments of this network leads to varying manifestations of mathematical learning disabilities.

  11. On the Equivalence of Formal Grammars and Machines.

    Science.gov (United States)

    Lund, Bruce

    1991-01-01

    Explores concepts of formal language and automata theory underlying computational linguistics. A computational formalism is described known as a "logic grammar," with which computational systems process linguistic data, with examples in declarative and procedural semantics and definite clause grammars. (13 references) (CB)

  12. Electrohydrodynamic fibrillation governed enhanced thermal transport in dielectric colloids under a field stimulus.

    Science.gov (United States)

    Dhar, Purbarun; Maganti, Lakshmi Sirisha; Harikrishnan, A R

    2018-05-30

    Electrorheological (ER) fluids are known to exhibit enhanced viscous effects under an electric field stimulus. The present article reports the hitherto unreported phenomenon of greatly enhanced thermal conductivity in such electro-active colloidal dispersions in the presence of an externally applied electric field. Typical ER fluids are synthesized employing dielectric fluids and nanoparticles and experiments are performed employing an in-house designed setup. Greatly augmented thermal conductivity under a field's influence was observed. Enhanced thermal conduction along the fibril structures under the field effect is theorized as the crux of the mechanism. The formation of fibril structures has also been experimentally verified employing microscopy. Based on classical models for ER fluids, a mathematical formalism has been developed to predict the propensity of chain formation and statistically feasible chain dynamics at given Mason numbers. Further, a thermal resistance network model is employed to computationally predict the enhanced thermal conduction across the fibrillary colloid microstructure. Good agreement between the mathematical model and the experimental observations is achieved. The domineering role of thermal conductivity over relative permittivity has been shown by proposing a modified Hashin-Shtrikman (HS) formalism. The findings have implications towards better physical understanding and design of ER fluids from both 'smart' viscoelastic as well as thermally active materials points of view.

  13. Can mathematics explain the evolution of human language?

    Science.gov (United States)

    Witzany, Guenther

    2011-09-01

    Investigation into the sequence structure of the genetic code by means of an informatic approach is a real success story. The features of human language are also the object of investigation within the realm of formal language theories. They focus on the common rules of a universal grammar that lies behind all languages and determine generation of syntactic structures. This universal grammar is a depiction of material reality, i.e., the hidden logical order of things and its relations determined by natural laws. Therefore mathematics is viewed not only as an appropriate tool to investigate human language and genetic code structures through computer science-based formal language theory but is itself a depiction of material reality. This confusion between language as a scientific tool to describe observations/experiences within cognitive constructed models and formal language as a direct depiction of material reality occurs not only in current approaches but was the central focus of the philosophy of science debate in the twentieth century, with rather unexpected results. This article recalls these results and their implications for more recent mathematical approaches that also attempt to explain the evolution of human language.

  14. A Mathematical Model, Implementation and Study of a Swarm System

    OpenAIRE

    Varghese, Blesson; McKee, Gerard

    2013-01-01

    The work reported in this paper is motivated towards the development of a mathematical model for swarm systems based on macroscopic primitives. A pattern formation and transformation model is proposed. The pattern transformation model comprises two general methods for pattern transformation, namely a macroscopic transformation and mathematical transformation method. The problem of transformation is formally expressed and four special cases of transformation are considered. Simulations to conf...

  15. Development Mathematic Assessment to Increase Mathematical Prerequisite Ability on The Student with Learning Disabilities in Inclusive Elementary School

    Science.gov (United States)

    Robiansyah, S. T. U.; Nanang, F.; Hidayat

    2018-01-01

    The purpose of this study was to introduce about mathematic assessment is a process of obtaining data or information about the mastery of a student's mathematical skills as an ingredient in preparing a learning program. With this mathematics assessment can be known obstacles, difficulties and needs of students especially in the field of mathematic, so that the learning program will be in accordance with the potential students because it is tailored to what is required of students. This research study was conducted at elementary school of inclusive precisely at SDN Sukagalih I Bandung City based learning in setting of inclusive education. This research study is motivated by the existence of a first-grade student who has disabilities learning in mathematics, the ability of the mathematical prerequisite mastery of the classification of objects by color. The results of the research can provide a profile picture of student data information, the data obtained from the results of the development of systematic and formal mathematical assessment. After doing the development of mathematics assessment then the teacher gets important related information: 1. process the analysis of students’ learning needs, especially in the field of mathematics, 2. preparing the learning program planning according to student learning needs, 3. Designing procedural of method remedial program.

  16. Matching biomedical ontologies based on formal concept analysis.

    Science.gov (United States)

    Zhao, Mengyi; Zhang, Songmao; Li, Weizhuo; Chen, Guowei

    2018-03-19

    The goal of ontology matching is to identify correspondences between entities from different yet overlapping ontologies so as to facilitate semantic integration, reuse and interoperability. As a well developed mathematical model for analyzing individuals and structuring concepts, Formal Concept Analysis (FCA) has been applied to ontology matching (OM) tasks since the beginning of OM research, whereas ontological knowledge exploited in FCA-based methods is limited. This motivates the study in this paper, i.e., to empower FCA with as much as ontological knowledge as possible for identifying mappings across ontologies. We propose a method based on Formal Concept Analysis to identify and validate mappings across ontologies, including one-to-one mappings, complex mappings and correspondences between object properties. Our method, called FCA-Map, incrementally generates a total of five types of formal contexts and extracts mappings from the lattices derived. First, the token-based formal context describes how class names, labels and synonyms share lexical tokens, leading to lexical mappings (anchors) across ontologies. Second, the relation-based formal context describes how classes are in taxonomic, partonomic and disjoint relationships with the anchors, leading to positive and negative structural evidence for validating the lexical matching. Third, the positive relation-based context can be used to discover structural mappings. Afterwards, the property-based formal context describes how object properties are used in axioms to connect anchor classes across ontologies, leading to property mappings. Last, the restriction-based formal context describes co-occurrence of classes across ontologies in anonymous ancestors of anchors, from which extended structural mappings and complex mappings can be identified. Evaluation on the Anatomy, the Large Biomedical Ontologies, and the Disease and Phenotype track of the 2016 Ontology Alignment Evaluation Initiative campaign

  17. Formalization of the Integral Calculus in the PVS Theorem Prover

    Science.gov (United States)

    Butler, Ricky W.

    2004-01-01

    The PVS Theorem prover is a widely used formal verification tool used for the analysis of safety-critical systems. The PVS prover, though fully equipped to support deduction in a very general logic framework, namely higher-order logic, it must nevertheless, be augmented with the definitions and associated theorems for every branch of mathematics and Computer Science that is used in a verification. This is a formidable task, ultimately requiring the contributions of researchers and developers all over the world. This paper reports on the formalization of the integral calculus in the PVS theorem prover. All of the basic definitions and theorems covered in a first course on integral calculus have been completed.The theory and proofs were based on Rosenlicht's classic text on real analysis and follow the traditional epsilon-delta method. The goal of this work was to provide a practical set of PVS theories that could be used for verification of hybrid systems that arise in air traffic management systems and other aerospace applications. All of the basic linearity, integrability, boundedness, and continuity properties of the integral calculus were proved. The work culminated in the proof of the Fundamental Theorem Of Calculus. There is a brief discussion about why mechanically checked proofs are so much longer than standard mathematics textbook proofs.

  18. Formalization of Hostel Management System. | Obi | Journal of the ...

    African Journals Online (AJOL)

    HMS) can invariably contribute greatly to the success, profitability and customerbased approach of such an organization. The use of formal specification creates a formal approach for specifying the underlying functions and properties of the ...

  19. ANS acuity and mathematics ability in preschoolers from low-income homes: contributions of inhibitory control.

    Science.gov (United States)

    Fuhs, Mary Wagner; McNeil, Nicole M

    2013-01-01

    Recent findings by Libertus, Feigenson, and Halberda (2011) suggest that there is an association between the acuity of young children's approximate number system (ANS) and their mathematics ability before exposure to instruction in formal schooling. The present study examined the generalizability and validity of these findings in a sample of preschoolers from low-income homes. Children attending Head Start (N = 103) completed measures to assess ANS acuity, mathematics ability, receptive vocabulary, and inhibitory control. Results showed only a weak association between ANS acuity and mathematics ability that was reduced to non-significance when controlling for a direct measure of receptive vocabulary. Results also revealed that inhibitory control plays an important role in the relation between ANS acuity and mathematics ability. Specifically, ANS acuity accounted for significant variance in mathematics ability over and above receptive vocabulary, but only for ANS acuity trials in which surface area conflicted with numerosity. Moreover, this association became non-significant when controlling for inhibitory control. These results suggest that early mathematical experiences prior to formal schooling may influence the strength of the association between ANS acuity and mathematics ability and that inhibitory control may drive that association in young children. © 2012 Blackwell Publishing Ltd.

  20. Essential competencies analysis of a training model development for non-formal vocational teachers under the office of the non-formal and informal education in Thailand

    OpenAIRE

    Chayanopparat Piyanan; Charungkaittikul Suwithida; Ratana-Ubol Archanya

    2016-01-01

    Non-formal vocational education provides practical experiences in a particular occupational field to non-formal semi-skilled learners. Non-formal vocational teachers are the key persons to deliver particular occupational knowledge. The essential competencies enhancement for non-sformal vocational teachers will improve teaching performance. The question of the research is what the essential competencies for the nonformal vocational teachers are. The research method was 1) to review related lit...

  1. Mathematical modelling of unglazed solar collectors under extreme operating conditions

    DEFF Research Database (Denmark)

    Bunea, M.; Perers, Bengt; Eicher, S.

    2015-01-01

    average temperature levels at the evaporator. Simulation of these systems requires a collector model that can take into account operation at very low temperatures (below freezing) and under various weather conditions, particularly operation without solar irradiation.A solar collector mathematical model......Combined heat pumps and solar collectors got a renewed interest on the heating system market worldwide. Connected to the heat pump evaporator, unglazed solar collectors can considerably increase their efficiency, but they also raise the coefficient of performance of the heat pump with higher...... was found due to the condensation phenomenon and up to 40% due to frost under no solar irradiation. This work also points out the influence of the operating conditions on the collector's characteristics.Based on experiments carried out at a test facility, every heat flux on the absorber was separately...

  2. Generalized Bondi-Sachs equations for characteristic formalism of numerical relativity

    Science.gov (United States)

    Cao, Zhoujian; He, Xiaokai

    2013-11-01

    The Cauchy formalism of numerical relativity has been successfully applied to simulate various dynamical spacetimes without any symmetry assumption. But discovering how to set a mathematically consistent and physically realistic boundary condition is still an open problem for Cauchy formalism. In addition, the numerical truncation error and finite region ambiguity affect the accuracy of gravitational wave form calculation. As to the finite region ambiguity issue, the characteristic extraction method helps much. But it does not solve all of the above issues. Besides the above problems for Cauchy formalism, the computational efficiency is another problem. Although characteristic formalism of numerical relativity suffers the difficulty from caustics in the inner near zone, it has advantages in relation to all of the issues listed above. Cauchy-characteristic matching (CCM) is a possible way to take advantage of characteristic formalism regarding these issues and treat the inner caustics at the same time. CCM has difficulty treating the gauge difference between the Cauchy part and the characteristic part. We propose generalized Bondi-Sachs equations for characteristic formalism for the Cauchy-characteristic matching end. Our proposal gives out a possible same numerical evolution scheme for both the Cauchy part and the characteristic part. And our generalized Bondi-Sachs equations have one adjustable gauge freedom which can be used to relate the gauge used in the Cauchy part. Then these equations can make the Cauchy part and the characteristic part share a consistent gauge condition. So our proposal gives a possible new starting point for Cauchy-characteristic matching.

  3. A Survey of Formal Methods for Intelligent Swarms

    Science.gov (United States)

    Truszkowski, Walt; Rash, James; Hinchey, Mike; Rouff, Chrustopher A.

    2004-01-01

    cutting edge in system correctness, and requires higher levels of assurance than other (traditional) missions that use a single or small number of spacecraft that are deterministic in nature and have near continuous communication access. One of the highest possible levels of assurance comes from the application of formal methods. Formal methods are mathematics-based tools and techniques for specifying and verifying (software and hardware) systems. They are particularly useful for specifying complex parallel systems, such as exemplified by the ANTS mission, where the entire system is difficult for a single person to fully understand, a problem that is multiplied with multiple developers. Once written, a formal specification can be used to prove properties of a system (e.g., the underlying system will go from one state to another or not into a specific state) and check for particular types of errors (e.g., race or livelock conditions). A formal specification can also be used as input to a model checker for further validation. This report gives the results of a survey of formal methods techniques for verification and validation of space missions that use swarm technology. Multiple formal methods were evaluated to determine their effectiveness in modeling and assuring the behavior of swarms of spacecraft using the ANTS mission as an example system. This report is the first result of the project to determine formal approaches that are promising for formally specifying swarm-based systems. From this survey, the most promising approaches were selected and are discussed relative to their possible application to the ANTS mission. Future work will include the application of an integrated approach, based on the selected approaches identified in this report, to the formal specification of the ANTS mission.

  4. History of Mathematics

    DEFF Research Database (Denmark)

    Hansen, Vagn Lundsgaard; Gray, Jeremy

    Volume 1 in Theme on "History of Mathematics", in "Encyclopedia of Life Support Systems (EOLSS), developed under the auspices of the UNESCO.......Volume 1 in Theme on "History of Mathematics", in "Encyclopedia of Life Support Systems (EOLSS), developed under the auspices of the UNESCO....

  5. Using formal specification in the Guidance and Control Software (GCS) experiment. Formal design and verification technology for life critical systems

    Science.gov (United States)

    Weber, Doug; Jamsek, Damir

    1994-01-01

    The goal of this task was to investigate how formal methods could be incorporated into a software engineering process for flight-control systems under DO-178B and to demonstrate that process by developing a formal specification for NASA's Guidance and Controls Software (GCS) Experiment. GCS is software to control the descent of a spacecraft onto a planet's surface. The GCS example is simplified from a real example spacecraft, but exhibits the characteristics of realistic spacecraft control software. The formal specification is written in Larch.

  6. Cyto-Sim: a formal language model and stochastic simulator of membrane-enclosed biochemical processes.

    Science.gov (United States)

    Sedwards, Sean; Mazza, Tommaso

    2007-10-15

    Compartments and membranes are the basis of cell topology and more than 30% of the human genome codes for membrane proteins. While it is possible to represent compartments and membrane proteins in a nominal way with many mathematical formalisms used in systems biology, few, if any, explicitly model the topology of the membranes themselves. Discrete stochastic simulation potentially offers the most accurate representation of cell dynamics. Since the details of every molecular interaction in a pathway are often not known, the relationship between chemical species in not necessarily best described at the lowest level, i.e. by mass action. Simulation is a form of computer-aided analysis, relying on human interpretation to derive meaning. To improve efficiency and gain meaning in an automatic way, it is necessary to have a formalism based on a model which has decidable properties. We present Cyto-Sim, a stochastic simulator of membrane-enclosed hierarchies of biochemical processes, where the membranes comprise an inner, outer and integral layer. The underlying model is based on formal language theory and has been shown to have decidable properties (Cavaliere and Sedwards, 2006), allowing formal analysis in addition to simulation. The simulator provides variable levels of abstraction via arbitrary chemical kinetics which link to ordinary differential equations. In addition to its compact native syntax, Cyto-Sim currently supports models described as Petri nets, can import all versions of SBML and can export SBML and MATLAB m-files. Cyto-Sim is available free, either as an applet or a stand-alone Java program via the web page (http://www.cosbi.eu/Rpty_Soft_CytoSim.php). Other versions can be made available upon request.

  7. ABOUT THREE PROCESSES IN MATHEMATICS EDUCATION FOR SOLIDARITY ECONOMY ENTERPRISES

    Directory of Open Access Journals (Sweden)

    Renata Cristina Geromel Meneghetti

    2013-07-01

    Full Text Available This paper focuses on Mathematics Education in the context of Solidarity Economy and aims to approach our performance, aiming to answer demands of Mathematics Education of the three Solidarity Economy Enterprises (SEE: a cooperative cleaning, of a women carpenter’s group and a group manufacturing homemade soap. Based on the Ethnomathematics, a pedagogical intervention with these SEE was performed, in which we seek to work the Mathematics within the cultural context of these enterprises through problem situations related to their daily work. The research followed a qualitative research through action research. As a result we found that the approach applied has contributed to changes some attitudes, it was favorable to the learning of concepts and also the socioeconomic reintegration, in the direction of a posture more critical and emancipatory. The interventions were inserted in the Non Formal Education, and we point out that realize this type of education can indeed contribute to the ideals of Education in the Solidarity Economy as a way include those who have been socially excluded by formal education provided at school.

  8. Mathematical Formalization Of Theories Of Motivation Proposed By Abraham Maslow And Frederick Herzberg

    OpenAIRE

    Ivan Kotliarov

    2008-01-01

    the present article gives an outline of a mathematical model of theories of motivation proposed by Abraham Maslow and Frederick Herzberg. This model is built on a basis of special non-continuous functions.

  9. Reasoning and mathematical skills contribute to normatively superior decision making under risk: evidence from the game of dice task.

    Science.gov (United States)

    Pertl, Marie-Theres; Zamarian, Laura; Delazer, Margarete

    2017-08-01

    In this study, we assessed to what extent reasoning improves performance in decision making under risk in a laboratory gambling task (Game of Dice Task-Double, GDT-D). We also investigated to what degree individuals with above average mathematical competence decide better than those with average mathematical competence. Eighty-five participants performed the GDT-D and several numerical tasks. Forty-two individuals were asked to calculate the probabilities and the outcomes associated with the different options of the GDT-D before performing it. The other 43 individuals performed the GDT-D at the beginning of the test session. Both reasoning and mathematical competence had a positive effect on decision making. Different measures of mathematical competence correlated with advantageous performance in decision making. Results suggest that decision making under explicit risk conditions improves when individuals are encouraged to reflect about the contingencies of a decision situation. Interventions based on numerical reasoning may also be useful for patients with difficulties in decision making.

  10. Cognitive science in the field: A preschool intervention durably enhances intuitive but not formal mathematics.

    Science.gov (United States)

    Dillon, Moira R; Kannan, Harini; Dean, Joshua T; Spelke, Elizabeth S; Duflo, Esther

    2017-07-07

    Many poor children are underprepared for demanding primary school curricula. Research in cognitive science suggests that school achievement could be improved by preschool pedagogy in which numerate adults engage children's spontaneous, nonsymbolic mathematical concepts. To test this suggestion, we designed and evaluated a game-based preschool curriculum intended to exercise children's emerging skills in number and geometry. In a randomized field experiment with 1540 children (average age 4.9 years) in 214 Indian preschools, 4 months of math game play yielded marked and enduring improvement on the exercised intuitive abilities, relative to no-treatment and active control conditions. Math-trained children also showed immediate gains on symbolic mathematical skills but displayed no advantage in subsequent learning of the language and concepts of school mathematics. Copyright © 2017, American Association for the Advancement of Science.

  11. Mutagenesis and mathematics: The allure of numbers

    International Nuclear Information System (INIS)

    Haynes, R.H.

    1989-01-01

    This paper sets out the formal, empirical, and mechanistic equations that my colleagues and I have developed for the description and analysis of dose-response data on the lethal and genetic effects of mutagens in microorganisms. These three types of equations are interrelated inasmuch as they are all based ultimately on the use of the Poisson distribution in the formal definition of lethal and mutational hit functions. Explicit mathematical expressions for these functions can be written down in either empirical or mechanistic terms. The empirical equations are obtained simply by writing the hit functions as finite polynomials with adjustable coefficients. The mechanistic equations are based on the assumptions of the DNA damage-repair hypothesis. The mathematical formulation of this hypothesis entails an important change in the definition of the word hit from that used in the classical hit/target theory of radiation biology. The theoretical and practical applications of these various equations in mutation research are summarized briefly and their merits are assessed in light of recent advances in our understanding of the biochemical basis of mutagenesis

  12. Formalization of the Integral Calculus in the PVS Theorem Prover

    Directory of Open Access Journals (Sweden)

    Ricky Wayne Butler

    2009-04-01

    Full Text Available The PVS Theorem prover is a widely used formal verification tool used for the analysis of safetycritical systems. The PVS prover, though fully equipped to support deduction in a very general logic framework, namely higher-order logic, it must nevertheless, be augmented with the definitions and associated theorems for every branch of mathematics and Computer Science that is used in a verification. This is a formidable task, ultimately requiring the contributions of researchers and developers all over the world. This paper reports on the formalization of the integral calculus in the PVS theorem prover. All of the basic definitions and theorems covered in a first course on integral calculus have been completed.The theory and proofs were based on Rosenlicht’s classic text on real analysis and follow the traditional epsilon-delta method. The goal of this work was to provide a practical set of PVS theories that could be used for verification of hybrid systems that arise in air traffic management systems and other aerospace applications. All of the basic linearity, integrability, boundedness, and continuity properties of the integral calculus were proved. The work culminated in the proof of the Fundamental Theorem Of Calculus. There is a brief discussion about why mechanically checked proofs are so much longer than standard mathematics textbook proofs.

  13. Creativity in Unique Problem-Solving in Mathematics and Its Influence on Motivation for Learning

    Science.gov (United States)

    Bishara, Saied

    2016-01-01

    This research study investigates the ability of students to tackle the solving of unique mathematical problems in the domain of numerical series, verbal and formal, and its influence on the motivation of junior high students with learning disabilities in the Arab sector. Two instruments were used to collect the data: mathematical series were…

  14. There is More to the Teaching and Learning of Mathematics Than the Use of Local Languages: Mathematics Teacher Practices

    Directory of Open Access Journals (Sweden)

    Nancy Chitera

    2016-11-01

    Full Text Available In this article, we present a discussion about the type of mathematical discourse that is being produced in classrooms where the language of learning and teaching is local languages.  We also further explore the tensions in the mathematical discourse being produced. The study sample was 4 mathematics teachers from a semi-urban primary school in Malawi. The methods of data collection included classroom observations, pre-observation focus group discussions and reflective interviews. The results show that even though both students and teachers were able to communicate freely in local languages in the mathematics classroom, the mathematical discourse that came was distorted. This is mainly caused by lack of a well-developed mathematical discourse in local languages, which in turn takes away the confidence of mathematics teachers in the classroom. As a result, the mathematics classrooms are still being characterized by teachers not being creative, use of word by word from books, focus more on procedural than conceptual and thus teacher centered is still dominant in these classrooms. Furthermore, it is found that there are tensions between the formal and informal mathematical language in local languages. These results in turn have promoted a more in-depth understanding to the teaching and learning of mathematics when local language is the language of learning and teaching. Therefore, this article argues for a well-balanced approach when it comes to teaching and learning of mathematics rather than just focusing on the use of local languages.

  15. Financial mathematics

    CERN Document Server

    Jothi, A Lenin

    2009-01-01

    Financial services, particularly banking and insurance services is the prominent sector for the development of a nation. After the liberalisation of financial sector in India, the scope of getting career opportunities has been widened. It is heartening to note that various universities in India have introduced professional courses on banking and insurance. A new field of applied mathematics has come into prominence under the name of Financial Mathematics. Financial mathematics has attained much importance in the recent years because of the role played by mathematical concepts in decision - m

  16. Formal matrices

    CERN Document Server

    Krylov, Piotr

    2017-01-01

    This monograph is a comprehensive account of formal matrices, examining homological properties of modules over formal matrix rings and summarising the interplay between Morita contexts and K theory. While various special types of formal matrix rings have been studied for a long time from several points of view and appear in various textbooks, for instance to examine equivalences of module categories and to illustrate rings with one-sided non-symmetric properties, this particular class of rings has, so far, not been treated systematically. Exploring formal matrix rings of order 2 and introducing the notion of the determinant of a formal matrix over a commutative ring, this monograph further covers the Grothendieck and Whitehead groups of rings. Graduate students and researchers interested in ring theory, module theory and operator algebras will find this book particularly valuable. Containing numerous examples, Formal Matrices is a largely self-contained and accessible introduction to the topic, assuming a sol...

  17. Non-linear wave equations:Mathematical techniques

    International Nuclear Information System (INIS)

    1978-01-01

    An account of certain well-established mathematical methods, which prove useful to deal with non-linear partial differential equations is presented. Within the strict framework of Functional Analysis, it describes Semigroup Techniques in Banach Spaces as well as variational approaches towards critical points. Detailed proofs are given of the existence of local and global solutions of the Cauchy problem and of the stability of stationary solutions. The formal approach based upon invariance under Lie transformations deserves attention due to its wide range of applicability, even if the explicit solutions thus obtained do not allow for a deep analysis of the equations. A compre ensive introduction to the inverse scattering approach and to the solution concept for certain non-linear equations of physical interest are also presented. A detailed discussion is made about certain convergence and stability problems which arise in importance need not be emphasized. (author) [es

  18. Formal verification of reactor process control software using assertion checking environment

    International Nuclear Information System (INIS)

    Sharma, Babita; Balaji, Sowmya; John, Ajith K.; Bhattacharjee, A.K.; Dhodapkar, S.D.

    2005-01-01

    Assertion Checking Environment (ACE) was developed in-house for carrying out formal (rigorous/ mathematical) functional verification of embedded software written in MISRA C. MISRA C is an industrially sponsored safe sub-set of C programming language and is well accepted in the automotive and aerospace industries. ACE uses static assertion checking technique for verification of MISRA C programs. First the functional specifications of the program are derived from the specifications in the form of pre- and post-conditions for each C function. These pre- and post-conditions are then introduced as assertions (formal comments) in the program code. The annotated C code is then formally verified using ACE. In this paper we present our experience of using ACE for the formal verification of process control software of a nuclear reactor. The Software Requirements Document (SRD) contained textual specifications of the process control software. The SRD was used by the designers to draw logic diagrams which were given as input to a code generator. The verification of the generated C code was done at 2 levels viz. (i) verification against specifications derived from logic diagrams, and (ii) verification against specifications derived from SRD. In this work we checked approximately 600 functional specifications of the software having roughly 15000 lines of code. (author)

  19. An Investigation of the Mathematical Models of Piaget's Psychological Theory of Cognitive Learning. Final Report.

    Science.gov (United States)

    Kalechofsky, Robert

    This research paper proposes several mathematical models which help clarify Piaget's theory of cognition on the concrete and formal operational stages. Some modified lattice models were used for the concrete stage and a combined Boolean Algebra and group theory model was used for the formal stage. The researcher used experiments cited in the…

  20. The 1989 progress report: Mathematics

    International Nuclear Information System (INIS)

    Demazure, M.

    1989-01-01

    The 1989 progress report of the laboratory of Mathematics of the Polytechnic School (France) is presented. The investigations reported were performed in the following fields: analysis of nonlinear partial differential equations, quantum mechanics, scattering, fluid dynamics and homogenization, equations, varieties with negative curvature, elliptical problems on surfaces, Dirac operator, geometry of algorithms and formal calculus, singularities, Lie groups, dynamics systems. The published papers, the conferences and the Laboratory staff are listed [fr

  1. Improving of Junior High School Visual Thinking Representation Ability in Mathematical Problem Solving by CTL

    Science.gov (United States)

    Surya, Edy; Sabandar, Jozua; Kusumah, Yaya S.; Darhim

    2013-01-01

    The students' difficulty which was found is in the problem of understanding, drawing diagrams, reading the charts correctly, conceptual formal mathematical understanding, and mathematical problem solving. The appropriate problem representation is the basic way in order to understand the problem itself and make a plan to solve it. This research was…

  2. Towards unified performance measures for evaluating nuclear safeguard systems: mathematical foundations and formal comparison of existing models

    International Nuclear Information System (INIS)

    Corynen, G.C.

    1979-01-01

    An important step in the analysis of large-scale systems is the development of economical and meaningful measures of system performance. In the literature on analysis of nuclear safeguard systems, many performance measures have been advanced, but their interrelationships and their relevance to overall system objectives have not received attention commensurate with the effort spent in developing detailed safeguard models. The work reported here is an attempt to improve the development and evaluation of performance measures for nuclear safeguard systems. This work falls into three main areas. First, we develop a new framework which provides an initial basis for defining and structuring performance measures. To demonstrate that this framework allows a clear understanding of the purposes of nuclear safeguard systems, we employ it to state various safeguard questions clearly and concisely. The framework reflects the rough subsystem structure of safeguard systems - the detection and response subsystems - and formally accommodates various safeguard models. We especially emphasize two of these models which are under development at Lawrence Livermore Laboratory, the structured assessment approach (SAA) and the systems vulnerability assessment method (SVAM). Second, we examine some performance measures presently used in the nuclear safeguards area and in reliability theory in general. Some of these we accept and modify to obtain system performance measures that are an additive combination of subsystem performance measures, a very convenient form indeed. Others we reject as impractical and meaningless. Finally, we determine some common features between the SAA and SVAM models by formally comparing these models in our framework

  3. Formal Specification and Automatic Analysis of Business Processes under Authorization Constraints: An Action-Based Approach

    Science.gov (United States)

    Armando, Alessandro; Giunchiglia, Enrico; Ponta, Serena Elisa

    We present an approach to the formal specification and automatic analysis of business processes under authorization constraints based on the action language \\cal{C}. The use of \\cal{C} allows for a natural and concise modeling of the business process and the associated security policy and for the automatic analysis of the resulting specification by using the Causal Calculator (CCALC). Our approach improves upon previous work by greatly simplifying the specification step while retaining the ability to perform a fully automatic analysis. To illustrate the effectiveness of the approach we describe its application to a version of a business process taken from the banking domain and use CCALC to determine resource allocation plans complying with the security policy.

  4. Mathematical methods of many-body quantum field theory

    CERN Document Server

    Lehmann, Detlef

    2004-01-01

    Mathematical Methods of Many-Body Quantum Field Theory offers a comprehensive, mathematically rigorous treatment of many-body physics. It develops the mathematical tools for describing quantum many-body systems and applies them to the many-electron system. These tools include the formalism of second quantization, field theoretical perturbation theory, functional integral methods, bosonic and fermionic, and estimation and summation techniques for Feynman diagrams. Among the physical effects discussed in this context are BCS superconductivity, s-wave and higher l-wave, and the fractional quantum Hall effect. While the presentation is mathematically rigorous, the author does not focus solely on precise definitions and proofs, but also shows how to actually perform the computations.Presenting many recent advances and clarifying difficult concepts, this book provides the background, results, and detail needed to further explore the issue of when the standard approximation schemes in this field actually work and wh...

  5. Spinor formalism and complex-vector formalism of general relativity

    International Nuclear Information System (INIS)

    Han-ying, G.; Yong-shi, W.; Gendao, L.

    1974-01-01

    In this paper, using E. Cartan's exterior calculus, we give the spinor form of the structure equations, which leads naturally to the Newman--Penrose equations. Furthermore, starting from the spinor spaces and the el (2C) algebra, we construct the general complex-vector formalism of general relativity. We find that both the Cahen--Debever--Defrise complex-vector formalism and that of Brans are its special cases. Thus, the spinor formalism and the complex-vector formalism of general relativity are unified on the basis of the uni-modular group SL(2C) and its Lie algebra

  6. Formal Ontologies and Uncertainty. In Geographical Knowledge

    Directory of Open Access Journals (Sweden)

    Matteo Caglioni

    2014-05-01

    Full Text Available Formal ontologies have proved to be a very useful tool to manage interoperability among data, systems and knowledge. In this paper we will show how formal ontologies can evolve from a crisp, deterministic framework (ontologies of hard knowledge to new probabilistic, fuzzy or possibilistic frameworks (ontologies of soft knowledge. This can considerably enlarge the application potential of formal ontologies in geographic analysis and planning, where soft knowledge is intrinsically linked to the complexity of the phenomena under study.  The paper briefly presents these new uncertainty-based formal ontologies. It then highlights how ontologies are formal tools to define both concepts and relations among concepts. An example from the domain of urban geography finally shows how the cause-to-effect relation between household preferences and urban sprawl can be encoded within a crisp, a probabilistic and a possibilistic ontology, respectively. The ontology formalism will also determine the kind of reasoning that can be developed from available knowledge. Uncertain ontologies can be seen as the preliminary phase of more complex uncertainty-based models. The advantages of moving to uncertainty-based models is evident: whether it is in the analysis of geographic space or in decision support for planning, reasoning on geographic space is almost always reasoning with uncertain knowledge of geographic phenomena.

  7. Academic Mathematicians' Dispositions toward Software Use in Mathematics Instruction: What Are the Underlying Reasons?

    Science.gov (United States)

    Khoshaim, Heba Bakr

    2012-01-01

    Academic mathematicians' opinions are divided regarding software use in undergraduate mathematics instruction. This study explored these opinions through interviews and a subsequent survey of mathematicians at PhD-granting institutions in the United States regarding their dispositions and the underlying attitudes. Most prior related work had…

  8. Mathematics in Chemistry: Indeterminate Forms and Their Meaning

    Science.gov (United States)

    Segurado, Manuel A. P.; Silva, Margarida F. B.; Castro, Rita

    2011-01-01

    The mathematical language and its tools are complementary to the formalism in chemistry, in particular at an advanced level. It is thus crucial, for its understanding, that students acquire a solid knowledge in Calculus and that they know how to apply it. The frequent occurrence of indeterminate forms in multiple areas, particularly in Physical…

  9. SBME : Exploring boundaries between formal, non-formal, and informal learning

    OpenAIRE

    Shahoumian, Armineh; Parchoma, Gale; Saunders, Murray; Hanson, Jacky; Dickinson, Mike; Pimblett, Mark

    2013-01-01

    In medical education learning extends beyond university settings into practice. Non-formal and informal learning support learners’ efforts to meet externally set and learner-identified objectives. In SBME research, boundaries between formal, non-formal, and informal learning have not been widely explored. Whether SBME fits within or challenges these categories can make a contribution. Formal learning is described in relation to educational settings, planning, assessment, and accreditation. In...

  10. Representing the Electromagnetic Field: How Maxwell's Mathematics Empowered Faraday's Field Theory

    Science.gov (United States)

    Tweney, Ryan D.

    2011-07-01

    James Clerk Maxwell `translated' Michael Faraday's experimentally-based field theory into the mathematical representation now known as `Maxwell's Equations.' Working with a variety of mathematical representations and physical models Maxwell extended the reach of Faraday's theory and brought it into consistency with other results in the physics of electricity and magnetism. Examination of Maxwell's procedures opens many issues about the role of mathematical representation in physics and the learning background required for its success. Specifically, Maxwell's training in `Cambridge University' mathematical physics emphasized the use of analogous equations across fields of physics and the repeated solving of extremely difficult problems in physics. Such training develops an array of overlearned mathematical representations supported by highly sophisticated cognitive mechanisms for the retrieval of relevant information from long term memory. For Maxwell, mathematics constituted a new form of representation in physics, enhancing the formal derivational and calculational role of mathematics and opening a cognitive means for the conduct of `experiments in the mind' and for sophisticated representations of theory.

  11. Formal modeling of a system of chemical reactions under uncertainty.

    Science.gov (United States)

    Ghosh, Krishnendu; Schlipf, John

    2014-10-01

    We describe a novel formalism representing a system of chemical reactions, with imprecise rates of reactions and concentrations of chemicals, and describe a model reduction method, pruning, based on the chemical properties. We present two algorithms, midpoint approximation and interval approximation, for construction of efficient model abstractions with uncertainty in data. We evaluate computational feasibility by posing queries in computation tree logic (CTL) on a prototype of extracellular-signal-regulated kinase (ERK) pathway.

  12. Formal Darwinism, the individual-as-maximizing-agent analogy and bet-hedging

    Science.gov (United States)

    Grafen, A.

    1999-01-01

    The central argument of The origin of species was that mechanical processes (inheritance of features and the differential reproduction they cause) can give rise to the appearance of design. The 'mechanical processes' are now mathematically represented by the dynamic systems of population genetics, and the appearance of design by optimization and game theory in which the individual plays the part of the maximizing agent. Establishing a precise individual-as-maximizing-agent (IMA) analogy for a population-genetics system justifies optimization approaches, and so provides a modern formal representation of the core of Darwinism. It is a hitherto unnoticed implication of recent population-genetics models that, contrary to a decades-long consensus, an IMA analogy can be found in models with stochastic environments (subject to a convexity assumption), in which individuals maximize expected reproductive value. The key is that the total reproductive value of a species must be considered as constant, so therefore reproductive value should always be calculated in relative terms. This result removes a major obstacle from the theoretical challenge to find a unifying framework which establishes the IMA analogy for all of Darwinian biology, including as special cases inclusive fitness, evolutionarily stable strategies, evolutionary life-history theory, age-structured models and sex ratio theory. This would provide a formal, mathematical justification of fruitful and widespread but 'intentional' terms in evolutionary biology, such as 'selfish', 'altruism' and 'conflict'.

  13. AVIATION SECURITY AS AN OBJECT OF MATHEMATICAL MODELING

    Directory of Open Access Journals (Sweden)

    N. Elisov Lev

    2017-01-01

    Full Text Available The paper presents a mathematical formulation of the problem formalization of the subject area related to aviation security in civil aviation. The formalization task is determined by the modern issue of providing aviation security. Aviationsecurity in modern systems is based upon organizational standard of security control. This standard doesn’t require calcu- lating the security level. It allows solving the aviation security task without estimating the solution and evaluating the per- formance of security facilities. The issue of acceptable aviation security level stays unsolved, because its control lies in inspections that determine whether the object security facilities meet the requirements or not. The pending problem is also in whether the requirements are calculable and the evaluation is subjective.Lately, there has been determined quite a certain tendency to consider aviation security issues from the perspective of its level optimal control with the following identification, calculation and evaluation problems solving and decision mak- ing. The obtained results analysis in this direction shows that it’s strongly recommended to move to object formalization problem, which provides a mathematical modeling for aviation security control optimization.In this case, the authors assume to find the answer in the process of object formalization. Therefore aviation secu- rity is presented as some security environment condition, which defines the parameters associated with the object protec-tion system quality that depends on the use of protective equipment in conditions of counteraction to factors of external andinternal threats. It is shown that the proposed model belongs to a class of boundary value problems described by differential equations in partial derivatives. The classification of boundary value problems is presented.

  14. Accounting for primitive terms in mathematics

    Directory of Open Access Journals (Sweden)

    D.F.M. Strauss

    2005-07-01

    Full Text Available The philosophical problem of unity and diversity entails a challenge to the rationalist aim to define everything. Definitions of this kind surface in various academic disciplines in formulations like uniqueness, irreducibility, and what has acquired the designation “primitive terms”. Not even the most “exact” disciplines, such as mathematics, can avoid the implications entailed in giving an account of such primitive terms. A mere look at the historical development of mathematics highlights the fact that alternative perspectives prevailed – from the arithmeticism of Pythagoreanism, the eventual geometrisation of mathematics after the discovery of incommensurability up to the revival of arithmeticism in the mathematics of Cauchy, Weierstrass, Dedekind and Cantor (with the later orientation of Frege, who completed the circle by returning to the view that mathematics essentially is geometry. An assessment of logicism and axiomatic formalism is followed by looking at the primitive meaning of wholeness (and the whole-parts relation. With reference to the views of Hilbert, Weyl and Bernays the article concludes by suggesting that in opposition to arithmeticism and geometricism an alternative option ought to be pursued – one in which both the uniqueness and mutual coherence between the aspects of number and space are acknowledged.

  15. SELF-EFFICACY OF FORMALLY AND NON-FORMALLY TRAINED PUBLIC SECTOR TEACHERS

    Directory of Open Access Journals (Sweden)

    Muhammad Nadeem ANWAR

    2009-07-01

    Full Text Available The main objective of the study was to compare the formally and non-formally trained in-service public sector teachers’ Self-efficacy. Five hypotheses were developed describing no difference in the self-efficacy of formally and non-formally trained teachers to influence decision making, influence school resources, instructional self-efficacy, disciplinary self-efficacy and create positive school climate. Teacher Efficacy Instrument (TSES developed by Bandura (2001 consisting of thirty 9-point items was used in the study. 342 formally trained and 255 non-formally trained respondents’ questionnaires were received out of 1500 mailed. The analysis of data revealed that the formally trained public sector teachers are high in their self-efficacy on all the five categories: to influence decision making, to influence school resources, instructional self-efficacy, disciplinary self-efficacy and self-efficacy to create positive school climate.

  16. Higher order temporal finite element methods through mixed formalisms.

    Science.gov (United States)

    Kim, Jinkyu

    2014-01-01

    The extended framework of Hamilton's principle and the mixed convolved action principle provide new rigorous weak variational formalism for a broad range of initial boundary value problems in mathematical physics and mechanics. In this paper, their potential when adopting temporally higher order approximations is investigated. The classical single-degree-of-freedom dynamical systems are primarily considered to validate and to investigate the performance of the numerical algorithms developed from both formulations. For the undamped system, all the algorithms are symplectic and unconditionally stable with respect to the time step. For the damped system, they are shown to be accurate with good convergence characteristics.

  17. Masses of Formal Philosophy

    DEFF Research Database (Denmark)

    Masses of Formal Philosophy is an outgrowth of Formal Philosophy. That book gathered the responses of some of the most prominent formal philosophers to five relatively open and broad questions initiating a discussion of metaphilosophical themes and problems surrounding the use of formal methods i...... in philosophy. Including contributions from a wide range of philosophers, Masses of Formal Philosophy contains important new responses to the original five questions.......Masses of Formal Philosophy is an outgrowth of Formal Philosophy. That book gathered the responses of some of the most prominent formal philosophers to five relatively open and broad questions initiating a discussion of metaphilosophical themes and problems surrounding the use of formal methods...

  18. Mathematics and engineering in real life through mathematical competitions

    Science.gov (United States)

    More, M.

    2018-02-01

    We bring out an experience of organizing mathematical competitions that can be used as a medium to motivate the student and teacher minds in new directions of thinking. This can contribute to fostering research, innovation and provide a hands-on experience of mathematical concepts with the real world. Mathematical competitions can be used to build curiosity and give an understanding of mathematical applications in real life. Participation in the competition has been classified under four broad categories. Student can showcase their findings in various forms of expression like model, poster, soft presentation, animation, live performance, art and poetry. The basic focus of the competition is on using open source computation tools and modern technology, to emphasize the relationship of mathematical concepts with engineering applications in real life.

  19. Formal modeling of virtual machines

    Science.gov (United States)

    Cremers, A. B.; Hibbard, T. N.

    1978-01-01

    Systematic software design can be based on the development of a 'hierarchy of virtual machines', each representing a 'level of abstraction' of the design process. The reported investigation presents the concept of 'data space' as a formal model for virtual machines. The presented model of a data space combines the notions of data type and mathematical machine to express the close interaction between data and control structures which takes place in a virtual machine. One of the main objectives of the investigation is to show that control-independent data type implementation is only of limited usefulness as an isolated tool of program development, and that the representation of data is generally dictated by the control context of a virtual machine. As a second objective, a better understanding is to be developed of virtual machine state structures than was heretofore provided by the view of the state space as a Cartesian product.

  20. Programming-Languages as a Conceptual Framework for Teaching Mathematics

    Science.gov (United States)

    Feurzeig, Wallace; Papert, Seymour A.

    2011-01-01

    Formal mathematical methods remain, for most high school students, mysterious, artificial and not a part of their regular intuitive thinking. The authors develop some themes that could lead to a radically new approach. According to this thesis, the teaching of programming languages as a regular part of academic progress can contribute effectively…

  1. Structure and randomness pages from year one of a mathematical blog

    CERN Document Server

    Tao, Terence

    2009-01-01

    There are many bits and pieces of folklore in mathematics that are passed down from advisor to student, or from collaborator to collaborator, but which are too fuzzy and non-rigorous to be discussed in the formal literature. Traditionally, it was a matter of luck and location as to who learned such folklore mathematics. But today, such bits and pieces can be communicated effectively and efficiently via the semiformal medium of research blogging. This book grew from such a blog. In 2007, Terry Tao began a mathematical blog, as an outgrowth of his own website at UCLA. This book is based on a sel

  2. 29 CFR 1690.306 - Formal submission in absence of consultation.

    Science.gov (United States)

    2010-07-01

    ... 29 Labor 4 2010-07-01 2010-07-01 false Formal submission in absence of consultation. 1690.306... § 1690.306 Formal submission in absence of consultation. If an initiating agency has an issuance which was already under development on or before July 1, 1978, when Executive Order 12067 became effective...

  3. The Constructed Objectivity of Mathematics and the Cognitive Subject

    Science.gov (United States)

    Longo, Giuseppe

    Mathematics is engendered in conjunction with other forms of knowledge, physics in particular. It is a "genealogy of concepts" (Riemann), that stems from our active reconstruction of the world. Mathematics organizes space and time. It stabilizes notions and concepts as no other language, while isolating by them a few intelligible fragments of "reality" at the phenomenal level. Thus an epistemological analysis of mathematics is proposed, as a foundation that departs from and complements the logico-formal approaches: Mathematics is grounded in a formation of sense, of a congnitive and historical nature, which preceeds the explicit formulation of axioms and rules. The genesis of some conceptual invariants will be sketched (numbers, continua, infinity, proofs, etc.). From these, categories as structural invariants (objects) and "invariant preserving maps" (morphisms, functors) are derived, in a reflective equilibrium of theories that parallels our endeavour to gain knowledge of the physical world.

  4. The Effect of the Courses of School Experience and Teaching Practice on Primary School Mathematics Teachers

    Science.gov (United States)

    Huseyin, Aksu Hasan

    2015-01-01

    The aim of this study is to determine elementary mathematics teachers' thoughts and feelings on the courses of school-experience and teacher-practice. In this study was used the qualitative research method. Those involved in the study were 20 mathematics teachers employed in formal/government primary schools in the Province of Giresun and in the…

  5. Formalization and Transformation of Informal Analysis Models into Executive REFINE (trademark) Specifications

    Science.gov (United States)

    1992-12-01

    describing how. 5. EDDA . EDDA is an attempt to add mathematical formalism to SADT. Because it is based on SADT, it cannot easily represent any other...design methodology. EDDA has two forms: G- EDDA , the standard graphical version of SADT, and S- EDDA , a textual language that partially represents the...used. "* EDDA only supports the SADT methodology and is too limited in scope to be useful in our research. "* SAMM lacks the semantic richness of

  6. Mathematical modelling as basis for efficient enterprise management

    Directory of Open Access Journals (Sweden)

    Kalmykova Svetlana

    2017-01-01

    Full Text Available The choice of the most effective HR- management style at the enterprise is based on modeling various socio-economic situations. The article describes the formalization of the managing processes aimed at the interaction between the allocated management subsystems. The mathematical modelling tools are used to determine the time spent on recruiting personnel for key positions in the management hierarchy selection.

  7. The Integration of Formal and Non-formal Education: The Dutch “brede school”

    Directory of Open Access Journals (Sweden)

    du Bois-Reymond, Manuela

    2009-12-01

    courses and support for under-achievers who are often students with migrant background. In both sectors, primary and secondary, it is the formal school organization with its professionals which determines the character of a BS; there is no full integration of formal and non-formal education resulting in one non-disruptive learning trajectory, nor is there the intention to go in that direction. Non-formal pedagogues are partly professionals, like youth- and social workers, partly volunteers, like parents, partly non-educational partners, like school-police, psycho-medical help or commercial leisure providers. Besides that, the BS is regarded by government educational and social policy as a potential partner and anchor for community development. It is too early to make reliable statements about the effects of the BS movement in the Netherlands concerning the educational opportunities for disadvantaged children and their families, especially those with migrant background, and combat further segregation. Evaluation studies made so far are moderately positive but also point to problems of overly bureaucratized structures and layers, lack of sufficient financial resources and, again, are uncertain about long-term effects.

  8. Formalizing Informal Logic

    Directory of Open Access Journals (Sweden)

    Douglas Walton

    2015-12-01

    Full Text Available This paper presents a formalization of informal logic using the Carneades Argumentation System (CAS, a formal, computational model of argument that consists of a formal model of argument graphs and audiences. Conflicts between pro and con arguments are resolved using proof standards, such as preponderance of the evidence. CAS also formalizes argumentation schemes. Schemes can be used to check whether a given argument instantiates the types of argument deemed normatively appropriate for the type of dialogue.

  9. The formal path integral and quantum mechanics

    International Nuclear Information System (INIS)

    Johnson-Freyd, Theo

    2010-01-01

    Given an arbitrary Lagrangian function on R d and a choice of classical path, one can try to define Feynman's path integral supported near the classical path as a formal power series parameterized by 'Feynman diagrams', although these diagrams may diverge. We compute this expansion and show that it is (formally, if there are ultraviolet divergences) invariant under volume-preserving changes of coordinates. We prove that if the ultraviolet divergences cancel at each order, then our formal path integral satisfies a 'Fubini theorem' expressing the standard composition law for the time evolution operator in quantum mechanics. Moreover, we show that when the Lagrangian is inhomogeneous quadratic in velocity such that its homogeneous-quadratic part is given by a matrix with constant determinant, then the divergences cancel at each order. Thus, by 'cutting and pasting' and choosing volume-compatible local coordinates, our construction defines a Feynman-diagrammatic 'formal path integral' for the nonrelativistic quantum mechanics of a charged particle moving in a Riemannian manifold with an external electromagnetic field.

  10. Effects of Mathematics Anxiety and Mathematical Metacognition on Word Problem Solving in Children with and without Mathematical Learning Difficulties

    Science.gov (United States)

    Lai, Yinghui; Zhu, Xiaoshuang; Chen, Yinghe; Li, Yanjun

    2015-01-01

    Mathematics is one of the most objective, logical, and practical academic disciplines. Yet, in addition to cognitive skills, mathematical problem solving also involves affective factors. In the current study, we first investigated effects of mathematics anxiety (MA) and mathematical metacognition on word problem solving (WPS). We tested 224 children (116 boys, M = 10.15 years old, SD = 0.56) with the Mathematics Anxiety Scale for Children, the Chinese Revised-edition Questionnaire of Pupil’s Metacognitive Ability in Mathematics, and WPS tasks. The results indicated that mathematical metacognition mediated the effect of MA on WPS after controlling for IQ. Second, we divided the children into four mathematics achievement groups including high achieving (HA), typical achieving (TA), low achieving (LA), and mathematical learning difficulty (MLD). Because mathematical metacognition and MA predicted mathematics achievement, we compared group differences in metacognition and MA with IQ partialled out. The results showed that children with MLD scored lower in self-image and higher in learning mathematics anxiety (LMA) than the TA and HA children, but not in mathematical evaluation anxiety (MEA). MLD children’s LMA was also higher than that of their LA counterparts. These results provide insight into factors that may mediate poor WPS performance which emerges under pressure in mathematics. These results also suggest that the anxiety during learning mathematics should be taken into account in mathematical learning difficulty interventions. PMID:26090806

  11. Effects of Mathematics Anxiety and Mathematical Metacognition on Word Problem Solving in Children with and without Mathematical Learning Difficulties.

    Directory of Open Access Journals (Sweden)

    Yinghui Lai

    Full Text Available Mathematics is one of the most objective, logical, and practical academic disciplines. Yet, in addition to cognitive skills, mathematical problem solving also involves affective factors. In the current study, we first investigated effects of mathematics anxiety (MA and mathematical metacognition on word problem solving (WPS. We tested 224 children (116 boys, M = 10.15 years old, SD = 0.56 with the Mathematics Anxiety Scale for Children, the Chinese Revised-edition Questionnaire of Pupil's Metacognitive Ability in Mathematics, and WPS tasks. The results indicated that mathematical metacognition mediated the effect of MA on WPS after controlling for IQ. Second, we divided the children into four mathematics achievement groups including high achieving (HA, typical achieving (TA, low achieving (LA, and mathematical learning difficulty (MLD. Because mathematical metacognition and MA predicted mathematics achievement, we compared group differences in metacognition and MA with IQ partialled out. The results showed that children with MLD scored lower in self-image and higher in learning mathematics anxiety (LMA than the TA and HA children, but not in mathematical evaluation anxiety (MEA. MLD children's LMA was also higher than that of their LA counterparts. These results provide insight into factors that may mediate poor WPS performance which emerges under pressure in mathematics. These results also suggest that the anxiety during learning mathematics should be taken into account in mathematical learning difficulty interventions.

  12. Effects of Mathematics Anxiety and Mathematical Metacognition on Word Problem Solving in Children with and without Mathematical Learning Difficulties.

    Science.gov (United States)

    Lai, Yinghui; Zhu, Xiaoshuang; Chen, Yinghe; Li, Yanjun

    2015-01-01

    Mathematics is one of the most objective, logical, and practical academic disciplines. Yet, in addition to cognitive skills, mathematical problem solving also involves affective factors. In the current study, we first investigated effects of mathematics anxiety (MA) and mathematical metacognition on word problem solving (WPS). We tested 224 children (116 boys, M = 10.15 years old, SD = 0.56) with the Mathematics Anxiety Scale for Children, the Chinese Revised-edition Questionnaire of Pupil's Metacognitive Ability in Mathematics, and WPS tasks. The results indicated that mathematical metacognition mediated the effect of MA on WPS after controlling for IQ. Second, we divided the children into four mathematics achievement groups including high achieving (HA), typical achieving (TA), low achieving (LA), and mathematical learning difficulty (MLD). Because mathematical metacognition and MA predicted mathematics achievement, we compared group differences in metacognition and MA with IQ partialled out. The results showed that children with MLD scored lower in self-image and higher in learning mathematics anxiety (LMA) than the TA and HA children, but not in mathematical evaluation anxiety (MEA). MLD children's LMA was also higher than that of their LA counterparts. These results provide insight into factors that may mediate poor WPS performance which emerges under pressure in mathematics. These results also suggest that the anxiety during learning mathematics should be taken into account in mathematical learning difficulty interventions.

  13. An epsilon of room, II pages from year three of a mathematical blog

    CERN Document Server

    Tao, Terence

    2011-01-01

    There are many bits and pieces of folklore in mathematics that are passed down from advisor to student, or from collaborator to collaborator, but which are too fuzzy and nonrigorous to be discussed in the formal literature. Traditionally, it was a matter of luck and location as to who learned such "folklore mathematics". But today, such bits and pieces can be communicated effectively and efficiently via the semiformal medium of research blogging. This book grew from such a blog. In 2007 Terry Tao began a mathematical blog to cover a variety of topics, ranging from his own research and other re

  14. Marriages of mathematics and physics: A challenge for biology.

    Science.gov (United States)

    Islami, Arezoo; Longo, Giuseppe

    2017-12-01

    The human attempts to access, measure and organize physical phenomena have led to a manifold construction of mathematical and physical spaces. We will survey the evolution of geometries from Euclid to the Algebraic Geometry of the 20th century. The role of Persian/Arabic Algebra in this transition and its Western symbolic development is emphasized. In this relation, we will also discuss changes in the ontological attitudes toward mathematics and its applications. Historically, the encounter of geometric and algebraic perspectives enriched the mathematical practices and their foundations. Yet, the collapse of Euclidean certitudes, of over 2300 years, and the crisis in the mathematical analysis of the 19th century, led to the exclusion of "geometric judgments" from the foundations of Mathematics. After the success and the limits of the logico-formal analysis, it is necessary to broaden our foundational tools and re-examine the interactions with natural sciences. In particular, the way the geometric and algebraic approaches organize knowledge is analyzed as a cross-disciplinary and cross-cultural issue and will be examined in Mathematical Physics and Biology. We finally discuss how the current notions of mathematical (phase) "space" should be revisited for the purposes of life sciences. Copyright © 2017. Published by Elsevier Ltd.

  15. The Effects of Formalism on Teacher Trainees' Algebraic and Geometric Interpretation of the Notions of Linear Dependency/Independency

    Science.gov (United States)

    Ertekin, E.; Solak, S.; Yazici, E.

    2010-01-01

    The aim of this study is to identify the effects of formalism in teaching on primary and secondary school mathematics teacher trainees' algebraic and geometric interpretations of the notions of linear dependency/independency. Quantitative research methods are drawn in order to determine differences in success levels between algebraic and geometric…

  16. Methods of Information Subjects and Objects Interaction Rules Formalization in the Electronic Trading Platform System

    Directory of Open Access Journals (Sweden)

    Emma Emanuilova Yandybaeva

    2015-03-01

    Full Text Available The methods of information subjects and objects interaction rules formalization in the electronic trading platform system has been developed. They are based on mathematical model of mandatory role-based access control. As a result of the work we have defined set of user roles and constructed roles hierarchy. For the roles hierarchy restrictions have been imposed to ensure the safety of the information system.

  17. Focus in High School Mathematics: Reasoning and Sense Making in Geometry

    Science.gov (United States)

    National Council of Teachers of Mathematics, 2010

    2010-01-01

    Classically, geometry has been the subject in which students encounter mathematical proof based on formal deduction. Attention to proof in the geometry curriculum is strengthened by a focus on reasoning and sense making. This book examines the four key elements (conjecturing about geometric objects, construction and evaluation of geometric…

  18. Fourier Series Formalization in ACL2(r

    Directory of Open Access Journals (Sweden)

    Cuong K. Chau

    2015-09-01

    Full Text Available We formalize some basic properties of Fourier series in the logic of ACL2(r, which is a variant of ACL2 that supports reasoning about the real and complex numbers by way of non-standard analysis. More specifically, we extend a framework for formally evaluating definite integrals of real-valued, continuous functions using the Second Fundamental Theorem of Calculus. Our extended framework is also applied to functions containing free arguments. Using this framework, we are able to prove the orthogonality relationships between trigonometric functions, which are the essential properties in Fourier series analysis. The sum rule for definite integrals of indexed sums is also formalized by applying the extended framework along with the First Fundamental Theorem of Calculus and the sum rule for differentiation. The Fourier coefficient formulas of periodic functions are then formalized from the orthogonality relations and the sum rule for integration. Consequently, the uniqueness of Fourier sums is a straightforward corollary. We also present our formalization of the sum rule for definite integrals of infinite series in ACL2(r. Part of this task is to prove the Dini Uniform Convergence Theorem and the continuity of a limit function under certain conditions. A key technique in our proofs of these theorems is to apply the overspill principle from non-standard analysis.

  19. A formalized design process for bacterial consortia that perform logic computing.

    Directory of Open Access Journals (Sweden)

    Weiyue Ji

    Full Text Available The concept of microbial consortia is of great attractiveness in synthetic biology. Despite of all its benefits, however, there are still problems remaining for large-scaled multicellular gene circuits, for example, how to reliably design and distribute the circuits in microbial consortia with limited number of well-behaved genetic modules and wiring quorum-sensing molecules. To manage such problem, here we propose a formalized design process: (i determine the basic logic units (AND, OR and NOT gates based on mathematical and biological considerations; (ii establish rules to search and distribute simplest logic design; (iii assemble assigned basic logic units in each logic operating cell; and (iv fine-tune the circuiting interface between logic operators. We in silico analyzed gene circuits with inputs ranging from two to four, comparing our method with the pre-existing ones. Results showed that this formalized design process is more feasible concerning numbers of cells required. Furthermore, as a proof of principle, an Escherichia coli consortium that performs XOR function, a typical complex computing operation, was designed. The construction and characterization of logic operators is independent of "wiring" and provides predictive information for fine-tuning. This formalized design process provides guidance for the design of microbial consortia that perform distributed biological computation.

  20. Systematic perspectives on diverging mathematical orientations

    Directory of Open Access Journals (Sweden)

    D.F.M. Strauss

    2005-07-01

    Full Text Available The popular view that mathematics is “objective” and “neutral” in the sense that it does not know different standpoints is contradicted by the factual state of modern mathematics. In the light of the dominant one-sided trends in the history of mathe-matics, fluctuating between arithmeticism and a geometrisation of this discipline, this article explores some provisional starting-points for a different view. This third option is explored by investigating some features of an acknowledgement of the uniqueness of number and space without neglecting the inter-aspectual connections between these two modal functions. An argument is advanced regarding the inevitability of employing analogical (or elementary basic concepts, and this perspective is articulated in terms of the theory of modal aspects. Numerical and spatial terms are discussed and eventually focused on a deepened understanding of the meaning of infinity. In addition to a brief look at the circularity present in the arithmeticist claim that mathematics could be fully arithmetised (Grünbaum, attention is also asked for the agreement between Aristotle and Cantor regarding the nature of continuity – assessed in terms of the irreducibility of the numerical and spatial aspects of reality. Finally a characterisation is given of the ontological assumpt-ions of intuitionism and axiomatic formalism.

  1. Choking under Pressure: When an Additional Positive Stereotype Affects Performance for Domain Identified Male Mathematics Students

    Science.gov (United States)

    Rosenthal, Harriet E. S.; Crisp, Richard J.

    2007-01-01

    This research aimed to establish if the presentation of two positive stereotypes would result in choking under pressure for identified male mathematics students. Seventy-five 16 year old men, who had just commenced their AS-level study, were either made aware of their gender group membership (single positive stereotype), their school group…

  2. Logical thinking in the pyramidal schema of concepts the logical and mathematical elements

    CERN Document Server

    Geldsetzer, Lutz

    2014-01-01

    This book proposes a new way of formalizing in logic and mathematics - a "pyramidal graph system," devised by the author and based on Porphyrian trees and modern concepts of classification, in both of which pyramids act as the organizing schema.

  3. Quaternions and the heuristic role of mathematical structures in physics

    International Nuclear Information System (INIS)

    Anderson, R.S.J.; Joshi, G.C.

    1992-07-01

    One of the important ways development takes place in mathematics is via a process of generalization. On the basis of a recent characterization of the process the authors propose that generalizations of mathematical structures that are already part of successful physical theories serve as good guides for the development of new physical theories. The principle is a more formal presentation and extension of a position stated earlier this century by Dirac. Quaternions form an excellent example of such a generalization, and a number of the ways in which their use in physical theories illustrates this principle, are discussed. 114 refs

  4. How Do Higher-Education Students Use Their Initial Understanding to Deal with Contextual Logic-Based Problems in Discrete Mathematics?

    Science.gov (United States)

    Lubis, Asrin; Nasution, Andrea Arifsyah

    2017-01-01

    Mathematical reasoning in logical context has now received much attention in the mathematics curriculum documents of many countries, including Indonesia. In Indonesia, students start formally learning about logic when they pursue to senior-high school. Before, they previously have many experiences to deal with logic, but the earlier assignments do…

  5. Modularizing Remedial Mathematics

    Science.gov (United States)

    Wong, Aaron

    2013-01-01

    As remedial mathematics education has become an increasingly important topic of conversation in higher education. Mathematics departments have been put under increased pressure to change their programs to increase the student success rate. A number of models have been introduced over the last decade that represent a wide range of new ideas and…

  6. Formal Analysis of Self-Efficacy in Job Interviewee’s Mental State Model

    Science.gov (United States)

    Ajoge, N. S.; Aziz, A. A.; Yusof, S. A. Mohd

    2017-08-01

    This paper presents a formal analysis approach for self-efficacy model of interviewee’s mental state during a job interview session. Self-efficacy is a construct that has been hypothesised to combine with motivation and interviewee anxiety to define state influence of interviewees. The conceptual model was built based on psychological theories and models related to self-efficacy. A number of well-known relations between events and the course of self-efficacy are summarized from the literature and it is shown that the proposed model exhibits those patterns. In addition, this formal model has been mathematically analysed to find out which stable situations exist. Finally, it is pointed out how this model can be used in a software agent or robot-based platform. Such platform can provide an interview coaching approach where support to the user is provided based on their individual metal state during interview sessions.

  7. ABOUT THE RELEVANCE AND METHODOLOGY ASPECTS OF TEACHING THE MATHEMATICAL MODELING TO PEDAGOGICAL STUDENTS

    Directory of Open Access Journals (Sweden)

    Y. A. Perminov

    2014-01-01

    Full Text Available The paper substantiates the need for profile training in mathematical modeling for pedagogical students, caused by the total penetration of mathematics into different sciences, including the humanities; fast development of the information communications technologies; and growing importance of mathematical modeling, combining the informal scientific and formal mathematical languages with the unique opportunities of computer programming. The author singles out the reasons for mastering and using the mathematical apparatus by teaches in every discipline. Indeed, among all the modern mathematical methods and ideas, mathematical modeling retains its priority in all professional spheres. Therefore, the discipline of “Mathematical Modeling” can play an important role in integrating different components of specialists training in various profiles. By mastering the basics of mathematical modeling, students acquire skills of methodological thinking; learn the principles of analysis, synthesis, generalization of ideas and methods in different disciplines and scientific spheres; and achieve general culture competences. In conclusion, the author recommends incorporating the “Methods of Profile Training in Mathematical Modeling” into the pedagogical magistracy curricula. 

  8. Analysis of Formal Methods for Specification of E-Commerce Applications

    Directory of Open Access Journals (Sweden)

    Sadiq Ali Khan

    2016-01-01

    Full Text Available E-commerce based application characteristics portray elevated dynamics while incorporating decentralized nature. Extreme emphasis influencing structural design plus implementation, positions such applications highly appreciated. Significant research articles reveal that, applying formal methods addressing challenges incumbent with E-commerce based applications, contribute towards reliability and robustness obliging the system. Anticipating and designing sturdy e-process and concurrent implementation, allows application behavior extra strength against errors, frauds and hacking, minimizing program faults during application operations. Programmers find extreme difficulty guaranteeing correct processing under all circumstances, however, not impossible. Concealed flaws and errors, triggered only under unexpected and unanticipated scenarios, pilot subtle mistakes and appalling failures. Code authors utilize various formal methods for reducing these flaws. Mentioning prominent methods would include, ASM (Abstract State Machines, B-Method, z-Language, UML (Unified Modelling Language etc. This paper primarily focuses different formal methods applied while deliberating specification and verification techniques for cost effective.

  9. Formality in Brackets

    DEFF Research Database (Denmark)

    Garsten, Christina; Nyqvist, Anette

    Ethnographic work in formal organizations involves learning to recognize the many layers of front stage and back stage of organized life, and to bracket formality. It means to be alert to the fact that what is formal and front stage for one some actors, and in some situations, may in fact be back...... stage and informal for others. Walking the talk, donning the appropriate attire, wearing the proper suit, may be part of what is takes to figure out the code of formal organizational settings – an entrance ticket to the backstage, as it were. Oftentimes, it involves a degree of mimicry, of ‘following...... suits’ (Nyqvist 2013), and of doing ‘ethnography by failure’ (Garsten 2013). In this paper, we explore the layers of informality and formality in our fieldwork experiences among financial investors and policy experts, and discuss how to ethnographically represent embodied fieldwork practices. How do we...

  10. Poincaré's legacies, part I pages from year two of a mathematical blog

    CERN Document Server

    Tao, Terence

    2009-01-01

    There are many bits and pieces of folklore in mathematics that are passed down from advisor to student, or from collaborator to collaborator, but which are too fuzzy and non-rigorous to be discussed in the formal literature. Traditionally, it was a matter of luck and location as to who learned such folklore mathematics. But today, such bits and pieces can be communicated effectively and efficiently via the semiformal medium of research blogging. This book grew from such a blog. In 2007, Terry Tao began a mathematical blog to cover a variety of topics, ranging from his own research and other re

  11. Poincaré's legacies, part II pages from year two of a mathematical blog

    CERN Document Server

    Tao, Terence

    2009-01-01

    There are many bits and pieces of folklore in mathematics that are passed down from advisor to student, or from collaborator to collaborator, but which are too fuzzy and non-rigorous to be discussed in the formal literature. Traditionally, it was a matter of luck and location as to who learned such folklore mathematics. But today, such bits and pieces can be communicated effectively and efficiently via the semiformal medium of research blogging. This book grew from such a blog. In 2007, Terry Tao began a mathematical blog to cover a variety of topics, ranging from his own research and other re

  12. Logic as a Key to Interdisciplinary Integration for Students in the Mathematical Sciences

    Directory of Open Access Journals (Sweden)

    Thomas Marlowe

    2017-08-01

    Full Text Available We describe the creation and development of a course on mathematical logic and its extensions and limitations, in which coverage of technical material is interleaved with and related to discussion of relevant historical, linguistic, philosophical, and theological issues and of individuals of note. The new course, Logic, Limitations to Knowledge, and Christianity, presents an overview of topics in and related to logic, including development of formal logic and an axiomatic first-order logic. It explores the history of mathematics and logic in the Catholic Intellectual and wider Western Traditions, as well as the mutual interactions of mathematics, philosophy, language, and religion. It then considers extensions of first-order logic, and provable limits to knowledge: the three unsolvable problems of Euclidean geometry, and examples from Gödel, Turing, Arrow, quantum physics, and others. Epistemological issues will be emphasized throughout the course. The translation between natural language and expression in logical and reasoning formalisms is emphasized throughout. As a Core Curriculum course at Seton Hall University, fundamental questions such as "What is logic?" and "What are its limits?" will be considered within the framework of Christianity's broader view of the human person and human intelligence.

  13. Software Formal Inspections Guidebook

    Science.gov (United States)

    1993-01-01

    The Software Formal Inspections Guidebook is designed to support the inspection process of software developed by and for NASA. This document provides information on how to implement a recommended and proven method for conducting formal inspections of NASA software. This Guidebook is a companion document to NASA Standard 2202-93, Software Formal Inspections Standard, approved April 1993, which provides the rules, procedures, and specific requirements for conducting software formal inspections. Application of the Formal Inspections Standard is optional to NASA program or project management. In cases where program or project management decide to use the formal inspections method, this Guidebook provides additional information on how to establish and implement the process. The goal of the formal inspections process as documented in the above-mentioned Standard and this Guidebook is to provide a framework and model for an inspection process that will enable the detection and elimination of defects as early as possible in the software life cycle. An ancillary aspect of the formal inspection process incorporates the collection and analysis of inspection data to effect continual improvement in the inspection process and the quality of the software subjected to the process.

  14. Logic, mathematics, and computer science modern foundations with practical applications

    CERN Document Server

    Nievergelt, Yves

    2015-01-01

    This text for the first or second year undergraduate in mathematics, logic, computer science, or social sciences, introduces the reader to logic, proofs, sets, and number theory. It also serves as an excellent independent study reference and resource for instructors. Adapted from Foundations of Logic and Mathematics: Applications to Science and Cryptography © 2002 Birkhӓuser, this second edition provides a modern introduction to the foundations of logic, mathematics, and computers science, developing the theory that demonstrates construction of all mathematics and theoretical computer science from logic and set theory.  The focus is on foundations, with specific statements of all the associated axioms and rules of logic and set theory, and  provides complete details and derivations of formal proofs. Copious references to literature that document historical development is also provided. Answers are found to many questions that usually remain unanswered: Why is the truth table for logical implication so uni...

  15. Mathematical foundations of epistemology based on experiments

    Directory of Open Access Journals (Sweden)

    Sergey M. Krylov

    2015-09-01

    Full Text Available The paper deals with basic prerequisites for the development of epistemology, which uses information concerning real experiments in the real world (with real objects. Such experiments are conducted by “formal-technological” analogs of Turing Machines. These analogs are called “universal synthesizers-analyzers”. They can perform syntheses and analyses of various objects or constructions (obtained by conjunctions of finite number of smaller objects called basic elements with the help of various algorithmic systems having some restrictions. Such algorithmic systems are called Formal Technologies. They have formal structures that are very similar to the formal structure of Maltsev's algebraic systems. This formal closeness allows us, first, to set up a hypothesis concerning algorithmic basis of almost all surrounding physical processes, as understandable as well as till non-understandable ones, that partially explains the wide applicability of mathematics to the outer world; second, this closeness allows one to formulate and prove some theorems (called assertions concerning features and peculiar properties of cognitive algorithms in one-, two- or three-dimensional surroundings for various formal technological systems, including a so called “acquired knowledge effectiveness theorem”. The theorem (assertion can be applied to a very wide class of formal technologies which use an equality predicate for objects analyses. In the paper various cognitive algorithms are listed and proved. These algorithms have different sets of technological operations resembling syntheses and decompositions, as well as different sets of analytical operations including equality predicates, “random stationary mapping” operations (which use unknown algorithms to obtain stationary results, therefore these operations are very similar to oracles in Turing Machines, operations that define object shapes, and so on. The structure of automatic cognitive devices called

  16. Formal, Non-Formal and Informal Learning in the Sciences

    Science.gov (United States)

    Ainsworth, Heather L.; Eaton, Sarah Elaine

    2010-01-01

    This research report investigates the links between formal, non-formal and informal learning and the differences between them. In particular, the report aims to link these notions of learning to the field of sciences and engineering in Canada and the United States, including professional development of adults working in these fields. It offers…

  17. A stream-based mathematical model for distributed information processing systems - SysLab system model

    OpenAIRE

    Klein, Cornel; Rumpe, Bernhard; Broy, Manfred

    2014-01-01

    In the SysLab project we develop a software engineering method based on a mathematical foundation. The SysLab system model serves as an abstract mathematical model for information systems and their components. It is used to formalize the semantics of all used description techniques such as object diagrams state automata sequence charts or data-flow diagrams. Based on the requirements for such a reference model, we define the system model including its different views and their relationships.

  18. The Proof is in the Pudding The Changing Nature of Mathematical Proof

    CERN Document Server

    Krantz, Steven G

    2011-01-01

    This text explores the many transformations that the mathematical proof has undergone from its inception to its versatile, present-day use, considering the advent of high-speed computing machines. Though there are many truths to be discovered in this book, by the end it is clear that there is no formalized approach or standard method of discovery to date. Most of the proofs are discussed in detail with figures and equations accompanying them, allowing both the professional mathematician and those less familiar with mathematics to derive the same joy from reading this book.

  19. Fear of the Formal

    DEFF Research Database (Denmark)

    du Gay, Paul; Lopdrup-Hjorth, Thomas

    Over recent decades, institutions exhibiting high degrees of formality have come in for severe criticism. From the private to the public sector, and across a whole spectrum of actors spanning from practitioners to academics, formal organization is viewed with increasing doubt and skepticism....... In a “Schumpetarian world” (Teece et al., 1997: 509) of dynamic competition and incessant reform, formal organization appears as well suited to survival as a fish out of water. Indeed, formal organization, and its closely overlapping semantic twin bureaucracy, are not only represented as ill suited to the realities...... is that formal organization is an obstacle to be overcome. For that very reason, critics, intellectuals and reformers alike have urged public and private organizations to break out of the stifling straightjacket of formality, to dispense with bureaucracy, and to tear down hierarchies. This could either be done...

  20. Mathematical Modeling of Column-Base Connections under Monotonic Loading

    Directory of Open Access Journals (Sweden)

    Gholamreza Abdollahzadeh

    2014-12-01

    Full Text Available Some considerable damage to steel structures during the Hyogo-ken Nanbu Earthquake occurred. Among them, many exposed-type column bases failed in several consistent patterns, such as brittle base plate fracture, excessive bolt elongation, unexpected early bolt failure, and inferior construction work, etc. The lessons from these phenomena led to the need for improved understanding of column base behavior. Joint behavior must be modeled when analyzing semi-rigid frames, which is associated with a mathematical model of the moment–rotation curve. The most accurate model uses continuous nonlinear functions. This article presents three areas of steel joint research: (1 analysis methods of semi-rigid joints; (2 prediction methods for the mechanical behavior of joints; (3 mathematical representations of the moment–rotation curve. In the current study, a new exponential model to depict the moment–rotation relationship of column base connection is proposed. The proposed nonlinear model represents an approach to the prediction of M–θ curves, taking into account the possible failure modes and the deformation characteristics of the connection elements. The new model has three physical parameters, along with two curve-fitted factors. These physical parameters are generated from dimensional details of the connection, as well as the material properties. The M–θ curves obtained by the model are compared with published connection tests and 3D FEM research. The proposed mathematical model adequately comes close to characterizing M–θ behavior through the full range of loading/rotations. As a result, modeling of column base connections using the proposed mathematical model can give crucial beforehand information, and overcome the disadvantages of time consuming workmanship and cost of experimental studies.

  1. A Unique Mathematical Derivation of the Fundamental Laws of Nature Based on a New Algebraic-Axiomatic (Matrix Approach ‡

    Directory of Open Access Journals (Sweden)

    Ramin Zahedi

    2017-09-01

    Full Text Available In this article, as a new mathematical approach to origin of the laws of nature, using a new basic algebraic axiomatic (matrix formalism based on the ring theory and Clifford algebras (presented in Section 2, “it is shown that certain mathematical forms of fundamental laws of nature, including laws governing the fundamental forces of nature (represented by a set of two definite classes of general covariant massive field equations, with new matrix formalisms, are derived uniquely from only a very few axioms.” In agreement with the rational Lorentz group, it is also basically assumed that the components of relativistic energy-momentum can only take rational values. In essence, the main scheme of this new mathematical axiomatic approach to the fundamental laws of nature is as follows: First, based on the assumption of the rationality of D-momentum and by linearization (along with a parameterization procedure of the Lorentz invariant energy-momentum quadratic relation, a unique set of Lorentz invariant systems of homogeneous linear equations (with matrix formalisms compatible with certain Clifford and symmetric algebras is derived. Then by an initial quantization (followed by a basic procedure of minimal coupling to space-time geometry of these determined systems of linear equations, a set of two classes of general covariant massive (tensor field equations (with matrix formalisms compatible with certain Clifford, and Weyl algebras is derived uniquely as well.

  2. Necessity of Integral Formalism

    International Nuclear Information System (INIS)

    Tao Yong

    2011-01-01

    To describe the physical reality, there are two ways of constructing the dynamical equation of field, differential formalism and integral formalism. The importance of this fact is firstly emphasized by Yang in case of gauge field [Phys. Rev. Lett. 33 (1974) 445], where the fact has given rise to a deeper understanding for Aharonov-Bohm phase and magnetic monopole [Phys. Rev. D 12 (1975) 3845]. In this paper we shall point out that such a fact also holds in general wave function of matter, it may give rise to a deeper understanding for Berry phase. Most importantly, we shall prove a point that, for general wave function of matter, in the adiabatic limit, there is an intrinsic difference between its integral formalism and differential formalism. It is neglect of this difference that leads to an inconsistency of quantum adiabatic theorem pointed out by Marzlin and Sanders [Phys. Rev. Lett. 93 (2004) 160408]. It has been widely accepted that there is no physical difference of using differential operator or integral operator to construct the dynamical equation of field. Nevertheless, our study shows that the Schrödinger differential equation (i.e., differential formalism for wave function) shall lead to vanishing Berry phase and that the Schrödinger integral equation (i.e., integral formalism for wave function), in the adiabatic limit, can satisfactorily give the Berry phase. Therefore, we reach a conclusion: There are two ways of describing physical reality, differential formalism and integral formalism; but the integral formalism is a unique way of complete description. (general)

  3. δ M formalism and anisotropic chaotic inflation power spectrum

    Science.gov (United States)

    Talebian-Ashkezari, A.; Ahmadi, N.

    2018-05-01

    A new analytical approach to linear perturbations in anisotropic inflation has been introduced in [A. Talebian-Ashkezari, N. Ahmadi and A.A. Abolhasani, JCAP 03 (2018) 001] under the name of δ M formalism. In this paper we apply the mentioned approach to a model of anisotropic inflation driven by a scalar field, coupled to the kinetic term of a vector field with a U(1) symmetry. The δ M formalism provides an efficient way of computing tensor-tensor, tensor-scalar as well as scalar-scalar 2-point correlations that are needed for the analysis of the observational features of an anisotropic model on the CMB. A comparison between δ M results and the tedious calculations using in-in formalism shows the aptitude of the δ M formalism in calculating accurate two point correlation functions between physical modes of the system.

  4. An Intervention for Early Mathematical Success: Outcomes from the Hybrid Version of the Building Math Readiness Parents as Partners (MRPP) Project

    Science.gov (United States)

    Kritzer, Karen L.; Pagliaro, Claudia M.

    2013-01-01

    The Building Math Readiness in Young Deaf/Hard-of-Hearing Children: Parents as Partners (MRPP) Project works with parents to increase the understanding of foundational mathematics concepts in their preschool deaf/hard-of-hearing (d/hh) children in preparation for formal mathematics education. A multiple-case/single-unit case study incorporating…

  5. Pragmatics for formal semantics

    DEFF Research Database (Denmark)

    Danvy, Olivier

    2011-01-01

    This tech talk describes how to write and how to inter-derive formal semantics for sequential programming languages. The progress reported here is (1) concrete guidelines to write each formal semantics to alleviate their proof obligations, and (2) simple calculational tools to obtain a formal...

  6. COORDINATION IN MULTILEVEL NETWORK-CENTRIC CONTROL SYSTEMS OF REGIONAL SECURITY: APPROACH AND FORMAL MODEL

    Directory of Open Access Journals (Sweden)

    A. V. Masloboev

    2015-01-01

    Full Text Available The paper deals with development of methods and tools for mathematical and computer modeling of the multilevel network-centric control systems of regional security. This research is carried out under development strategy implementation of the Arctic zone of the Russian Federation and national safeguarding for the period before 2020 in the Murmansk region territory. Creation of unified interdepartmental multilevel computer-aided system is proposed intended for decision-making information support and socio-economic security monitoring of the Arctic regions of Russia. The distinctive features of the investigated system class are openness, self-organization, decentralization of management functions and decision-making, weak hierarchy in the decision-making circuit and goal generation capability inside itself. Research techniques include functional-target approach, mathematical apparatus of multilevel hierarchical system theory and principles of network-centric control of distributed systems with pro-active components and variable structure. The work considers network-centric management local decisions coordination problem-solving within the multilevel distributed systems intended for information support of regional security. The coordination problem-solving approach and problem formalization in the multilevel network-centric control systems of regional security have been proposed based on developed multilevel recurrent hierarchical model of regional socio-economic system complex security. The model provides coordination of regional security indexes, optimized by the different elements of multilevel control systems, subject to decentralized decision-making. The model specificity consists in application of functional-target technology and mathematical apparatus of multilevel hierarchical system theory for coordination procedures implementation of the network-centric management local decisions. The work-out and research results can find further

  7. Algorithmic Principles of Mathematical Programming

    NARCIS (Netherlands)

    Faigle, Ulrich; Kern, Walter; Still, Georg

    2002-01-01

    Algorithmic Principles of Mathematical Programming investigates the mathematical structures and principles underlying the design of efficient algorithms for optimization problems. Recent advances in algorithmic theory have shown that the traditionally separate areas of discrete optimization, linear

  8. The Role of Automata and Machine Theory in School and College Mathematics Syllabuses.

    Science.gov (United States)

    Holcombe, M.

    1981-01-01

    The introduction of certain topics in the theory of machines and languages into school and college mathematics courses in place of the more usual discussion of groups and formal logic is proposed. Examples of machines and languages and their interconnections suitable for such courses are outlined. (MP)

  9. Implementation of Bourbaki's Elements of Mathematics in Coq: Part One, Theory of Sets

    Directory of Open Access Journals (Sweden)

    José Grimm

    2010-01-01

    Full Text Available This paper presents a formalization of the first book of the series ``Elements of Mathematics'' by Nicolas Bourbaki, using the Coq proof assistant.It discusses formalization of mathematics, and explains in which sense a computer proof of a statement corresponds to a proof in the Bourbaki sense, given that the Coq quantifiers are not defined in terms of Hilbert's epsilon function. The list of axioms and axiom schemes of Bourbaki is compared to the more usual Zermelo-Fraenkel theory, and to those proposed by Carlos Simpson, which form the basis of the Gaia software. Some basic constructions (union, intersection, product, function, equivalence and order relation are described, as well as some properties; this corresponds to Sections 1 to 6 of Chapter II, and the first two sections of Chapter III. A commented proof of Zermelo's theorem is also given. The code (including almost all exercises is available on the Web, underhttp://www-sop.inria.fr/apics/gaia.

  10. Industrial use of formal methods formal verification

    CERN Document Server

    Boulanger, Jean-Louis

    2012-01-01

    At present the literature gives students and researchers of the very general books on the formal technics. The purpose of this book is to present in a single book, a return of experience on the used of the "formal technics" (such proof and model-checking) on industrial examples for the transportation domain. This book is based on the experience of people which are completely involved in the realization and the evaluation of safety critical system software based.  The implication of the industrialists allows to raise the problems of confidentiality which could appear and so allow

  11. MATHEMATICAL MODELLING OF AIRCRAFT PILOTING PROSSESS UNDER SPECIFIED FLIGHT PATH

    Directory of Open Access Journals (Sweden)

    И. Кузнецов

    2012-04-01

    Full Text Available The author suggests mathematical model of pilot’s activity as follow up system and mathematical methods of pilot’s activity description. The main idea of the model is flight path forming and aircraft stabilization on it during instrument flight. Input of given follow up system is offered to be aircraft deflection from given path observed by pilot by means of sight and output is offered to be pilot’s regulating actions for aircraft stabilization on flight path.

  12. Understanding organizational congruence: formal model and simulation framework.

    NARCIS (Netherlands)

    Dignum, M.V.; Dignum, F.P.M.

    2007-01-01

    Despite a large number of studies, the effect of organizational structure on the performance and the individual cognition of its members is still not well understood. Our research aims at developing tools and formalisms to model organizations and evaluate their performance under different

  13. Theorema 2.0: Computer-Assisted Natural-Style Mathematics

    Directory of Open Access Journals (Sweden)

    Bruno Buchberger

    2016-01-01

    Full Text Available The Theorema project aims at the development of a computer assistant for the working mathematician. Support should be given throughout all phases of mathematical activity, from introducing new mathematical concepts by definitions or axioms, through first (computational experiments, the formulation of theorems, their justification by an exact proof, the application of a theorem as an algorithm, until to the dissemination of the results in form of a mathematical publication, the build up of bigger libraries of certified mathematical content and the like. This ambitious project is exactly along the lines of the QED manifesto issued in 1994 (see e.g. http://www.cs.ru.nl/~freek/qed/qed.html and it was initiated in the mid-1990s by Bruno Buchberger. The Theorema system is a computer implementation of the ideas behind the Theorema project. One focus lies on the natural style of system input (in form of definitions, theorems, algorithms, etc., system output (mainly in form of mathematical proofs and user interaction. Another focus is theory exploration, i.e. the development of large consistent mathematical theories in a formal frame, in contrast to just proving single isolated theorems. When using the Theorema system, a user should not have to follow a certain style of mathematics enforced by the system (e.g. basing all of mathematics on set theory or certain variants of type theory, rather should the system support the user in her preferred flavour of doing math. The new implementation of the system, which we refer to as Theorema 2.0, is open-source and available through GitHub.

  14. The formalisms of quantum mechanics an introduction

    CERN Document Server

    David, Francois

    2015-01-01

    These lecture notes present a concise and introductory, yet as far as possible coherent, view of the main formalizations of quantum mechanics and of quantum field theories, their interrelations and their theoretical foundations. The “standard” formulation of quantum mechanics (involving the Hilbert space of pure states, self-adjoint operators as physical observables, and the probabilistic interpretation given by the Born rule) on one hand, and the path integral and functional integral representations of probabilities amplitudes on the other, are the standard tools used in most applications of quantum theory in physics and chemistry. Yet, other mathematical representations of quantum mechanics sometimes allow better comprehension and justification of quantum theory. This text focuses on two of such representations: the algebraic formulation of quantum mechanics and the “quantum logic” approach. Last but not least, some emphasis will also be put on understanding the relation between quantum physics and ...

  15. The Laws of Nature and the Effectiveness of Mathematics

    Science.gov (United States)

    Dorato, Mauro

    In this paper I try to evaluate what I regard as the main attempts at explaining the effectiveness of mathematics in the natural sciences, namely (1) Antinaturalism, (2) Kantism, (3) Semanticism, (4) Algorithmic Complexity Theory. The first position has been defended by Mark Steiner, who claims that the "user friendliness" of nature for the applied mathematician is the best argument against a naturalistic explanation of the origin of the universe. The second is naturalistic and mixes the Kantian tradition with evolutionary studies about our innate mathematical abilities. The third turns to the Fregean tradition and considers mathematics a particular kind of language, thus treating the effectiveness of mathematics as a particular instance of the effectiveness of natural languages. The fourth hypothesis, building on formal results by Kolmogorov, Solomonov and Chaitin, claims that mathematics is so useful in describing the natural world because it is the science of the abbreviation of sequences, and mathematically formulated laws of nature enable us to compress the information contained in the sequence of numbers in which we code our observations. In this tradition, laws are equivalent to the shortest algorithms capable of generating the lists of zeros and ones representing the empirical data. Along the way, I present and reject the "deflationary explanation", which claims that in wondering about the applicability of so many mathematical structures to nature, we tend to forget the many cases in which no application is possible.

  16. A Comparison of Participation Patterns in Selected Formal, Non-Formal, and Informal Online Learning Environments

    Science.gov (United States)

    Schwier, Richard A.; Seaton, J. X.

    2013-01-01

    Does learner participation vary depending on the learning context? Are there characteristic features of participation evident in formal, non-formal, and informal online learning environments? Six online learning environments were chosen as epitomes of formal, non-formal, and informal learning contexts and compared. Transcripts of online…

  17. Chronoprojective invariance of the five-dimensional Schroedinger formalism

    International Nuclear Information System (INIS)

    Perrin, M.; Burdet, G.; Duval, C.

    1984-10-01

    Invariance properties of the five-dimensional Schroedinger formalism describing a quantum test particle in the Newton-Cartan theory of gravitation are studied. The geometry which underlies these invariance properties is presented as a reduction of the 0(5,2) conformal geometry various applications are given

  18. Improving of Junior High School Visual Thinking Representation Ability in Mathematical Problem Solving by CTL

    Directory of Open Access Journals (Sweden)

    Edy Surya

    2013-01-01

    Full Text Available The students’  difficulty which was found is in the problem of understanding, drawing diagrams, reading the charts correctly, conceptual formal  mathematical understanding, and  mathematical problem solving. The appropriate problem representation is the basic way in order to understand the problem itself and make a plan to solve it. This research was the experimental classroom design with a pretest-posttest control in order to increase the representation of visual thinking ability on mathematical problem solving approach  with  contextual learning. The research instrument was a test, observation and interviews. Contextual approach increases of mathematical representations ability increases in students with high initial category, medium, and low compared to conventional approaches. Keywords: Visual Thinking Representation, Mathematical  Problem Solving, Contextual Teaching Learning Approach DOI: http://dx.doi.org/10.22342/jme.4.1.568.113-126

  19. Artificial grammar learning meets formal language theory: an overview

    Science.gov (United States)

    Fitch, W. Tecumseh; Friederici, Angela D.

    2012-01-01

    Formal language theory (FLT), part of the broader mathematical theory of computation, provides a systematic terminology and set of conventions for describing rules and the structures they generate, along with a rich body of discoveries and theorems concerning generative rule systems. Despite its name, FLT is not limited to human language, but is equally applicable to computer programs, music, visual patterns, animal vocalizations, RNA structure and even dance. In the last decade, this theory has been profitably used to frame hypotheses and to design brain imaging and animal-learning experiments, mostly using the ‘artificial grammar-learning’ paradigm. We offer a brief, non-technical introduction to FLT and then a more detailed analysis of empirical research based on this theory. We suggest that progress has been hampered by a pervasive conflation of distinct issues, including hierarchy, dependency, complexity and recursion. We offer clarifications of several relevant hypotheses and the experimental designs necessary to test them. We finally review the recent brain imaging literature, using formal languages, identifying areas of convergence and outstanding debates. We conclude that FLT has much to offer scientists who are interested in rigorous empirical investigations of human cognition from a neuroscientific and comparative perspective. PMID:22688631

  20. Improving Learner Outcomes in Lifelong Education: Formal Pedagogies in Non-Formal Learning Contexts?

    Science.gov (United States)

    Zepke, Nick; Leach, Linda

    2006-01-01

    This article explores how far research findings about successful pedagogies in formal post-school education might be used in non-formal learning contexts--settings where learning may not lead to formal qualifications. It does this by examining a learner outcomes model adapted from a synthesis of research into retention. The article first…

  1. Group adaptation, formal darwinism and contextual analysis.

    Science.gov (United States)

    Okasha, S; Paternotte, C

    2012-06-01

    We consider the question: under what circumstances can the concept of adaptation be applied to groups, rather than individuals? Gardner and Grafen (2009, J. Evol. Biol.22: 659-671) develop a novel approach to this question, building on Grafen's 'formal Darwinism' project, which defines adaptation in terms of links between evolutionary dynamics and optimization. They conclude that only clonal groups, and to a lesser extent groups in which reproductive competition is repressed, can be considered as adaptive units. We re-examine the conditions under which the selection-optimization links hold at the group level. We focus on an important distinction between two ways of understanding the links, which have different implications regarding group adaptationism. We show how the formal Darwinism approach can be reconciled with G.C. Williams' famous analysis of group adaptation, and we consider the relationships between group adaptation, the Price equation approach to multi-level selection, and the alternative approach based on contextual analysis. © 2012 The Authors. Journal of Evolutionary Biology © 2012 European Society For Evolutionary Biology.

  2. Propagator formalism and computer simulation of restricted diffusion behaviors of inter-molecular multiple-quantum coherences

    International Nuclear Information System (INIS)

    Cai Congbo; Chen Zhong; Cai Shuhui; Zhong Jianhui

    2005-01-01

    In this paper, behaviors of single-quantum coherences and inter-molecular multiple-quantum coherences under restricted diffusion in nuclear magnetic resonance experiments were investigated. The propagator formalism based on the loss of spin phase memory during random motion was applied to describe the diffusion-induced signal attenuation. The exact expression of the signal attenuation under the short gradient pulse approximation for restricted diffusion between two parallel plates was obtained using this propagator method. For long gradient pulses, a modified formalism was proposed. The simulated signal attenuation under the effects of gradient pulses of different width based on the Monte Carlo method agrees with the theoretical predictions. The propagator formalism and computer simulation can provide convenient, intuitive and precise methods for the study of the diffusion behaviors

  3. An experimental and mathematical analysis of lymphopoiesis dynamics under continuous irradiation

    International Nuclear Information System (INIS)

    Zukhbaya, T.M.; Smirnova, O.A.

    1991-01-01

    A mathematical model describing the dynamics of lymphopoiesis in mammals continuously exposed to ionizing radiation has been developed. It is based on the theory of chalone regulation of hematopoiesis. The model comprises a system of nine differential equations. Results from the model were compared with our experimental data for bone marrow and blood lymphocytes of rats continuously exposed to gamma radiation in a wide range of dose rates. The model reproduces the lymphopoiesis dynamics that we observed in our experiment, in particular, the radiation hormesis at low dose rates, the reduction of lymphopoiesis at intermediate dose rates, and extinction of lymphopoiesis at high dose rates of continuous radiation. The possible explanation of the hormesis is suggested by the framework of the model. The model can be used for predicting the lymphopoiesis dynamics in mammals under continuous irradiation

  4. Review of the helicity formalism

    International Nuclear Information System (INIS)

    Barreiro, F.; Cerrada, M.; Fernandez, E.

    1972-01-01

    Our purpose in these notes has been to present a brief and general review of the helicity formalism. We begin by discussing Lorentz invariance, spin and helicity ideas, in section 1 . In section 2 we deal with the construction of relativistic states and scattering amplitudes in the helicity basis and we study their transformation properties under discrete symmetries. Finally we present some more sophisticated topics like kinematical singularities of helicity amplitudes, kinematical constraints and crossing relations 3, 4, 5 respectively. (Author) 8 refs

  5. Combining Formal, Non-Formal and Informal Learning for Workforce Skill Development

    Science.gov (United States)

    Misko, Josie

    2008-01-01

    This literature review, undertaken for Australian Industry Group, shows how multiple variations and combinations of formal, informal and non-formal learning, accompanied by various government incentives and organisational initiatives (including job redesign, cross-skilling, multi-skilling, diversified career pathways, action learning projects,…

  6. The role of information technologies in organization of non-formal education

    Directory of Open Access Journals (Sweden)

    Elkina Irina

    2016-01-01

    Full Text Available The authors consider the role of information technologies in realization of non-formal education in the modern information society. Cultural and leisure institutions, libraries etc. become facilitators of non-formal education. Introduction to cultural values, to the new knowledge, obtaining positive emotions attracts the representatives of various professional and social groups to this kind of education and additionally favors their familiarization with the Humanities. A large choice of new, game forms and methods of training, learners’ active participation – all this empowers non-formal education and a skill to learn and work under the conditions of redundant information is one of the most relevant in the modern society.

  7. Where is the bigger picture in the teaching and learning of mathematics?

    Directory of Open Access Journals (Sweden)

    Satsope Maoto

    2016-11-01

    Full Text Available This article presents an interpretive analysis of three different mathematics teaching cases to establish where the bigger picture should lie in the teaching and learning of mathematics. We use pre-existing data collected through pre-observation and post-observation interviews and passive classroom observation undertaken by the third author in two different Grade 11 classes taught by two different teachers at one high school. Another set of data was collected through participant observation of the second author’s Year 2 University class. We analyse the presence or absence of the bigger picture, especially, in the teachers’ questioning strategies and their approach to content, guided by Tall’s framework of three worlds of mathematics, namely the ‘conceptual-embodied’ world, the ‘proceptual-symbolic’ world and the ‘axiomatic-formal’ world. Within this broad framework we acknowledge Pirie and Kieren’s notion of folding back towards the attainment of an axiomatic-formal world. We argue that the teaching and learning of mathematics should remain anchored in the bigger picture and, in that way, mathematics is meaningful, accessible, expandable and transferable.

  8. Understanding visualization: a formal approach using category theory and semiotics.

    Science.gov (United States)

    Vickers, Paul; Faith, Joe; Rossiter, Nick

    2013-06-01

    This paper combines the vocabulary of semiotics and category theory to provide a formal analysis of visualization. It shows how familiar processes of visualization fit the semiotic frameworks of both Saussure and Peirce, and extends these structures using the tools of category theory to provide a general framework for understanding visualization in practice, including: Relationships between systems, data collected from those systems, renderings of those data in the form of representations, the reading of those representations to create visualizations, and the use of those visualizations to create knowledge and understanding of the system under inspection. The resulting framework is validated by demonstrating how familiar information visualization concepts (such as literalness, sensitivity, redundancy, ambiguity, generalizability, and chart junk) arise naturally from it and can be defined formally and precisely. This paper generalizes previous work on the formal characterization of visualization by, inter alia, Ziemkiewicz and Kosara and allows us to formally distinguish properties of the visualization process that previous work does not.

  9. A Possible Neural Representation of Mathematical Group Structures.

    Science.gov (United States)

    Pomi, Andrés

    2016-09-01

    Every cognitive activity has a neural representation in the brain. When humans deal with abstract mathematical structures, for instance finite groups, certain patterns of activity are occurring in the brain that constitute their neural representation. A formal neurocognitive theory must account for all the activities developed by our brain and provide a possible neural representation for them. Associative memories are neural network models that have a good chance of achieving a universal representation of cognitive phenomena. In this work, we present a possible neural representation of mathematical group structures based on associative memory models that store finite groups through their Cayley graphs. A context-dependent associative memory stores the transitions between elements of the group when multiplied by each generator of a given presentation of the group. Under a convenient election of the vector basis mapping the elements of the group in the neural activity, the input of a vector corresponding to a generator of the group collapses the context-dependent rectangular matrix into a virtual square permutation matrix that is the matrix representation of the generator. This neural representation corresponds to the regular representation of the group, in which to each element is assigned a permutation matrix. This action of the generator on the memory matrix can also be seen as the dissection of the corresponding monochromatic subgraph of the Cayley graph of the group, and the adjacency matrix of this subgraph is the permutation matrix corresponding to the generator.

  10. Improvement of Statistical Decisions under Parametric Uncertainty

    Science.gov (United States)

    Nechval, Nicholas A.; Nechval, Konstantin N.; Purgailis, Maris; Berzins, Gundars; Rozevskis, Uldis

    2011-10-01

    A large number of problems in production planning and scheduling, location, transportation, finance, and engineering design require that decisions be made in the presence of uncertainty. Decision-making under uncertainty is a central problem in statistical inference, and has been formally studied in virtually all approaches to inference. The aim of the present paper is to show how the invariant embedding technique, the idea of which belongs to the authors, may be employed in the particular case of finding the improved statistical decisions under parametric uncertainty. This technique represents a simple and computationally attractive statistical method based on the constructive use of the invariance principle in mathematical statistics. Unlike the Bayesian approach, an invariant embedding technique is independent of the choice of priors. It allows one to eliminate unknown parameters from the problem and to find the best invariant decision rule, which has smaller risk than any of the well-known decision rules. To illustrate the proposed technique, application examples are given.

  11. TEACHING MATHEMATICAL DISCIPLINES AT THE MEDICAL UNIVERSITY

    Directory of Open Access Journals (Sweden)

    V. Ya. Gelman

    2018-01-01

    designing which is being complicated by existing imbalance between the amount of training material and time frame for its studying. The authors suppose that it is possible to improve the quality of education through the increase or redistribution of the number of teaching hours; stimulation students’ motivation; enhancement of content and methodical components of teaching by means of active use of electronic resources and information technologies. Teachers should aspire to avoid excessive mathematical formalism as well to form in students the skills of independent work through the use of mathematical and computer methods.Practical significance. The authors come to the conclusion that the transition from traditional teaching to the teaching through the technological application of mathematical methods in medical practice and independent conduction of medical research is required for improvement the quality of Mathematics teaching of future physicians. 

  12. Beyond formalism

    Science.gov (United States)

    Denning, Peter J.

    1991-01-01

    The ongoing debate over the role of formalism and formal specifications in software features many speakers with diverse positions. Yet, in the end, they share the conviction that the requirements of a software system can be unambiguously specified, that acceptable software is a product demonstrably meeting the specifications, and that the design process can be carried out with little interaction between designers and users once the specification has been agreed to. This conviction is part of a larger paradigm prevalent in American management thinking, which holds that organizations are systems that can be precisely specified and optimized. This paradigm, which traces historically to the works of Frederick Taylor in the early 1900s, is no longer sufficient for organizations and software systems today. In the domain of software, a new paradigm, called user-centered design, overcomes the limitations of pure formalism. Pioneered in Scandinavia, user-centered design is spreading through Europe and is beginning to make its way into the U.S.

  13. Integrated formal operations plan

    Energy Technology Data Exchange (ETDEWEB)

    Cort, G.; Dearholt, W.; Donahue, S.; Frank, J.; Perkins, B.; Tyler, R.; Wrye, J.

    1994-01-05

    The concept of formal operations (that is, a collection of business practices to assure effective, accountable operations) has vexed the Laboratory for many years. To date most attempts at developing such programs have been based upon rigid, compliance-based interpretations of a veritable mountain of Department of Energy (DOE) orders, directives, notices, and standards. These DOE dictates seldom take the broad view but focus on highly specialized programs isolated from the overall context of formal operations. The result is a confusing array of specific, and often contradictory, requirements that produce a patchwork of overlapping niche programs. This unnecessary duplication wastes precious resources, dramatically increases the complexity of our work processes, and communicates a sense of confusion to our customers and regulators. Coupled with the artificial divisions that have historically existed among the Laboratory`s formal operations organizations (quality assurance, configuration management, records management, training, etc.), this approach has produced layers of increasingly vague and complex formal operations plans, each of which interprets its parent and adds additional requirements of its own. Organizational gridlock ensues whenever an activity attempts to implement these bureaucratic monstrosities. The integrated formal operations plan presented is to establish a set of requirements that must be met by an integrated formal operations program, assign responsibilities for implementation and operation of the program, and specify criteria against which the performance of the program will be measured. The accountable line manager specifies the items, processes, and information (the controlled elements) to which the formal operations program specified applies. The formal operations program is implemented using a graded approach based on the level of importance of the various controlled elements and the scope of the activities in which they are involved.

  14. The profile of conceptual comprehension of pre-service teacher in the mathematical problem solving with low emotional intelligence

    Science.gov (United States)

    Prayitno, S. H.; Suwarsono, St.; Siswono, T. Y. E.

    2018-03-01

    Conceptual comprehension in this research is the ability to use the procedures that are owned by pre-service teachers to solve problems by finding the relation of the concept to another, or can be done by identifying the type of problem and associating it with a troubleshooting procedures, or connect the mathematical symbols with mathematical ideas and incorporate them into a series of logical reasoning, or by using prior knowledge that occurred directly, through its conceptual knowledge. The goal of this research is to describe the profile of conceptual comprehensin of pre-service teachers with low emotional intelligence in mathematical problems solving. Through observation and in-depth interview with the research subject the conclusion was that: pre-service teachers with low emotional intelligence pertained to the level of formal understanding in understanding the issues, relatively to the level of intuitive understanding in planning problem solving, to the level of relational understanding in implementing the relational problem solving plan, and pertained to the level of formal understanding in looking back to solve the problem.

  15. Mathematical Methods of System Analysis in Construction Materials

    Science.gov (United States)

    Garkina, Irina; Danilov, Alexander

    2017-10-01

    System attributes of construction materials are defined: complexity of an object, integrity of set of elements, existence of essential, stable relations between elements defining integrative properties of system, existence of structure, etc. On the basis of cognitive modelling (intensive and extensive properties; the operating parameters) materials (as difficult systems) and creation of the cognitive map the hierarchical modular structure of criteria of quality is under construction. It actually is a basis for preparation of the specification on development of material (the required organization and properties). Proceeding from a modern paradigm (model of statement of problems and their decisions) of development of materials, levels and modules are specified in structure of material. It when using the principles of the system analysis allows to considered technological process as the difficult system consisting of elements of the distinguished specification level: from atomic before separate process. Each element of system depending on an effective objective is considered as separate system with more detailed levels of decomposition. Among them, semantic and qualitative analyses of an object (are considered a research objective, decomposition levels, separate elements and communications between them come to light). Further formalization of the available knowledge in the form of mathematical models (structural identification) is carried out; communications between input and output parameters (parametrical identification) are defined. Hierarchical structures of criteria of quality are under construction for each allocated level. On her the relevant hierarchical structures of system (material) are under construction. Regularities of structurization and formation of properties, generally are considered at the levels from micro to a macrostructure. The mathematical model of material is represented as set of the models corresponding to private criteria by which separate

  16. The Beyträge at 200: Bolzano's quiet revolution in the philosophy of mathematics

    Directory of Open Access Journals (Sweden)

    Jan Sebestik

    2013-02-01

    Full Text Available This paper surveys Bolzano's Beyträge zu einer begründeteren Darstellung der Mathematik (Contributions to a better-grounded presentation of mathematics on the 200th anniversary of its publication.  The first and only published issue presents a definition of mathematics, a classification of its subdisciplines, and an essay on mathematical method, or logic.  Though underdeveloped in some areas (including,somewhat surprisingly, in logic, it is nonetheless a radically innovative work, where Bolzano presents a remarkably modern account of axiomatics and the epistemology of the formal sciences.  We also discuss the second, unfinished and unpublished issue, where Bolzano develops his views on universal mathematics. Here we find the beginnings of his theory of collections, for him the most fundamental of the mathematical disciplines.  Though not exactly the same as the later Cantorian set theory, Bolzano's theory of collections was used in very similar ways in mathematics, notably in analysis.  In retrospect, Bolzano's debut in philosophy was a remarkably successful one, though its fruits would only become generally known much later.

  17. Unlatching the Gate – Helping Adult Students Learn Mathematics by Katherine Safford-Ramus, (2008

    Directory of Open Access Journals (Sweden)

    Armin Hollenstein

    2010-08-01

    Full Text Available Katherine Safford-Ramus is an associate professor of mathematics at Saint Peter’s College, a Jesuit College in New Jersey, USA. She has been teaching introductory mathematics courses at the tertiary level for 24 years at a community college. This book is based on her doctoral thesis. In Chapter 1, Unlatching the Gate deliberates a rich specra of conditions for, and peculiarities of, mathematics learning by adults in a formal environment. Influential theories and empirical findings in the fields of educational psychology, adult education and mathematics education are surveyed with a focus on adult learners and – of course –teachers and institutions. The text does not discuss empirical research undertaken by the author; it examines her broad personal teaching experience in the light of the above-mentioned body of knowledge and proposes directions for the development of adult mathematics education. In this sense, Unlatching the Gate is a theoretical book reflecting on practical issues. The target audience would be adult educators and students of post secondary mathematics education.

  18. Multiscale mathematical modeling of the hypothalamo-pituitary-gonadal axis.

    Science.gov (United States)

    Clément, Frédérique

    2016-07-01

    Although the fields of systems and integrative biology are in full expansion, few teams are involved worldwide into the study of reproductive function from the mathematical modeling viewpoint. This may be due to the fact that the reproductive function is not compulsory for individual organism survival, even if it is for species survival. Alternatively, the complexity of reproductive physiology may be discouraging. Indeed, the hypothalamo-pituitary-gonadal (HPG) axis involves not only several organs and tissues but also intricate time (from the neuronal millisecond timescale to circannual rhythmicity) and space (from molecules to organs) scales. Yet, mathematical modeling, and especially multiscale modeling, can renew our approaches of the molecular, cellular, and physiological processes underlying the control of reproductive functions. In turn, the remarkable dynamic features exhibited by the HPG axis raise intriguing and challenging questions to modelers and applied mathematicians. In this article, we draw a panoramic review of some mathematical models designed in the framework of the female HPG, with a special focus on the gonadal and central control of follicular development. On the gonadal side, the modeling of follicular development calls to the generic formalism of structured cell populations, that allows one to make mechanistic links between the control of cell fate (proliferation, differentiation, or apoptosis) and that of the follicle fate (ovulation or degeneration) or to investigate how the functional interactions between the oocyte and its surrounding cells shape the follicle morphogenesis. On the central, mainly hypothalamic side, models based on dynamical systems with multiple timescales allow one to represent within a single framework both the pulsatile and surge patterns of the neurohormone GnRH. Beyond their interest in basic research investigations, mathematical models can also be at the source of useful tools to study the encoding and decoding of

  19. Formal education in outdoor studies: introduction

    OpenAIRE

    Prince, Heather

    2015-01-01

    Regional cultural perspectives involve outdoor studies in different ways in formal curricula. This section focuses on Western Europe, particularly the UK and Scandinavia, although also has a more international reach in Backman’s consideration of the training of teachers and in place-responsive teaching as described by Mannion and Lynch. ‘Outdoor studies’ is not seen in curricula per se but under various more specialised aspects such as outdoor play, outdoor learning, environmental education, ...

  20. Integrating semi-formal and formal requirements

    NARCIS (Netherlands)

    Wieringa, Roelf J.; Olivé, Antoni; Dubois, Eric; Pastor, Joan Antoni; Huyts, Sander

    1997-01-01

    In this paper, we report on the integration of informal, semiformal and formal requirements specification techniques. We present a framework for requirements specification called TRADE, within which several well-known semiformal specification techniques are placed. TRADE is based on an analysis of

  1. Versatile Formal Methods Applied to Quantum Information.

    Energy Technology Data Exchange (ETDEWEB)

    Witzel, Wayne [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Rudinger, Kenneth Michael [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Sarovar, Mohan [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

    2015-11-01

    Using a novel formal methods approach, we have generated computer-veri ed proofs of major theorems pertinent to the quantum phase estimation algorithm. This was accomplished using our Prove-It software package in Python. While many formal methods tools are available, their practical utility is limited. Translating a problem of interest into these systems and working through the steps of a proof is an art form that requires much expertise. One must surrender to the preferences and restrictions of the tool regarding how mathematical notions are expressed and what deductions are allowed. Automation is a major driver that forces restrictions. Our focus, on the other hand, is to produce a tool that allows users the ability to con rm proofs that are essentially known already. This goal is valuable in itself. We demonstrate the viability of our approach that allows the user great exibility in expressing state- ments and composing derivations. There were no major obstacles in following a textbook proof of the quantum phase estimation algorithm. There were tedious details of algebraic manipulations that we needed to implement (and a few that we did not have time to enter into our system) and some basic components that we needed to rethink, but there were no serious roadblocks. In the process, we made a number of convenient additions to our Prove-It package that will make certain algebraic manipulations easier to perform in the future. In fact, our intent is for our system to build upon itself in this manner.

  2. Principles of protection: a formal approach for evaluating dose distributions

    International Nuclear Information System (INIS)

    Wikman-Svahn, Per; Peterson, Martin; Hansson, Sven Ove

    2006-01-01

    One of the central issues in radiation protection consists in determining what weight should be given to individual doses in relation to collective or aggregated doses. A mathematical framework is introduced in which such assessments can be made precisely in terms of comparisons between alternative distributions of individual doses. In addition to evaluation principles that are well known from radiation protection, a series of principles that are derived from parallel discussions in moral philosophy and welfare economics is investigated. A battery of formal properties is then used to investigate the evaluative principles. The results indicate that one of the new principles, bilinear prioritarianism, may be preferable to current practices, since it satisfies efficiency-related properties better without sacrificing other desirable properties

  3. Classroom observation data and instruction in primary mathematics education: improving design and rigour

    Science.gov (United States)

    Thompson, Carla J.; Davis, Sandra B.

    2014-06-01

    The use of formal observation in primary mathematics classrooms is supported in the literature as a viable method of determining effective teaching strategies and appropriate tasks for inclusion in the early years of mathematics learning. The twofold aim of this study was to (a) investigate predictive relationships between primary mathematics classroom observational data and student achievement data, and (b) to examine the impact of providing periodic classroom observational data feedback to teachers using a Relational-Feedback-Intervention (RFI) Database Model. This observational research effort focused on an empirical examination of student engagement levels in time spent on specific learning activities observed in primary mathematics classrooms as predictors of student competency outcomes in mathematics. Data were collected from more than 2,000 primary classroom observations in 17 primary schools during 2009-2011 and from standardised end-of-year tests for mathematics achievement. Results revealed predictive relationships among several types of teaching and learning tasks with student achievement. Specifically, the use of mathematics concepts, technology and hands-on materials in primary mathematics classrooms was found to produce substantive predictors of increased student mathematics achievement. Additional findings supported the use of periodic classroom observation data reporting as a positive influence on teachers' decisions in determining instructional tasks for inclusion in primary mathematics classrooms. Study results indicate classroom observational research involving a RFI Database Model is a productive tool for improving teaching and learning in primary mathematics classrooms.

  4. Formal System Verification - Extension 2

    Science.gov (United States)

    2012-08-08

    vision of truly trustworthy systems has been to provide a formally verified microkernel basis. We have previously developed the seL4 microkernel...together with a formal proof (in the theorem prover Isabelle/HOL) of its functional correctness [6]. This means that all the behaviours of the seL4 C...source code are included in the high-level, formal specification of the kernel. This work enabled us to provide further formal guarantees about seL4 , in

  5. Essential concepts and underlying theories from physics, chemistry, and mathematics for "biochemistry and molecular biology" majors.

    Science.gov (United States)

    Wright, Ann; Provost, Joseph; Roecklein-Canfield, Jennifer A; Bell, Ellis

    2013-01-01

    Over the past two years, through an NSF RCN UBE grant, the ASBMB has held regional workshops for faculty members from around the country. The workshops have focused on developing lists of Core Principles or Foundational Concepts in Biochemistry and Molecular Biology, a list of foundational skills, and foundational concepts from Physics, Chemistry, and Mathematics that all Biochemistry or Molecular Biology majors must understand to complete their major coursework. The allied fields working group created a survey to validate foundational concepts from Physics, Chemistry, and Mathematics identified from participant feedback at various workshops. One-hundred twenty participants responded to the survey and 68% of the respondents answered yes to the question: "We have identified the following as the core concepts and underlying theories from Physics, Chemistry, and Mathematics that Biochemistry majors or Molecular Biology majors need to understand after they complete their major courses: 1) mechanical concepts from Physics, 2) energy and thermodynamic concepts from Physics, 3) critical concepts of structure from chemistry, 4) critical concepts of reactions from Chemistry, and 5) essential Mathematics. In your opinion, is the above list complete?" Respondents also delineated subcategories they felt should be included in these broad categories. From the results of the survey and this analysis the allied fields working group constructed a consensus list of allied fields concepts, which will help inform Biochemistry and Molecular Biology educators when considering the ASBMB recommended curriculum for Biochemistry or Molecular Biology majors and in the development of appropriate assessment tools to gauge student understanding of how these concepts relate to biochemistry and molecular biology. © 2013 by The International Union of Biochemistry and Molecular Biology.

  6. Intuitive Mathematical Knowledge as an Essential Aspect of Contemporary Adult Learning: A case of women street vendors in the city of Gaborone

    Directory of Open Access Journals (Sweden)

    Rebecca Nthogo Lekoko

    2006-04-01

    Full Text Available The findings of a phenomenological interview study with women street vendors showed a strong link between participants’ perceptions of everyday use of mathematical literacy and the speculations that mathematical use arose spontaneously in response to a practical need. The concept of intuitive mathematics as used indicates that mathematical thinking is an indispensable element of everyday conversation. Although the study finds that intuition and spontaneity are essential principles of lifelong learning, it concludes with recommendations for an empowerment curriculum that interweaves participants’ experiences and intuition with formal/academic mathematical literacy and psychosocial skills necessary for success in a highly competitive business world.

  7. Teachers' Understanding of the Role of Executive Functions in Mathematics Learning.

    Science.gov (United States)

    Gilmore, Camilla; Cragg, Lucy

    2014-09-01

    Cognitive psychology research has suggested an important role for executive functions, the set of skills that monitor and control thought and action, in learning mathematics. However, there is currently little evidence about whether teachers are aware of the importance of these skills and, if so, how they come by this information. We conducted an online survey of teachers' views on the importance of a range of skills for mathematics learning. Teachers rated executive function skills, and in particular inhibition and shifting, to be important for mathematics. The value placed on executive function skills increased with increasing teaching experience. Most teachers reported that they were aware of these skills, although few knew the term "executive functions." This awareness had come about through their teaching experience rather than from formal instruction. Researchers and teacher educators could do more to highlight the importance of these skills to trainee or new teachers.

  8. Topical Roots of Formal Dialectic

    NARCIS (Netherlands)

    Krabbe, Erik C. W.

    Formal dialectic has its roots in ancient dialectic. We can trace this influence in Charles Hamblin's book on fallacies, in which he introduced his first formal dialectical systems. Earlier, Paul Lorenzen proposed systems of dialogical logic, which were in fact formal dialectical systems avant la

  9. Lending Policies of Informal, Formal, and Semi-formal Lenders: Evidence from Vietnam

    NARCIS (Netherlands)

    Lensink, B.W.; Pham, T.T.T.

    2007-01-01

    This paper compares lending policies of formal, informal and semiformal lenders with respect to household lending in Vietnam. The analysis suggests that the probability of using formal or semiformal credit increases if borrowers provide collateral, a guarantor and/or borrow for business-related

  10. Concepciones acerca de la maternidad en la educación formal y no formal

    Directory of Open Access Journals (Sweden)

    Alvarado Calderón, Kathia

    2005-06-01

    Full Text Available Este artículo presenta algunos resultados de la investigación desarrollada en el Instituto de Investigación en Educación (INIE, bajo el nombre "Construcción del concepto de maternidad en la educación formal y no formal". Utilizando un enfoque cualitativo de investigación, recurrimos a las técnicas de elaboración de dibujos, entrevistas y grupo focal como recursos para la recolección de la información. De esta manera, podemos acercarnos a las concepciones de la maternidad que utilizan los participantes de las diferentes instancias educativas (formal y no formal con quienes se trabajó. This article presents some results the research developed in the Instituto de Investigación en Educación (INIE, named "Construcción del concepto de maternidad en la educación formal y no formal". It begins with a theoretical analysis about social conceptions regarding motherhood in the occidental societies. Among the techniques for gathering information were thematic drawing, interview and focus group, using a qualitative approach research method. This is followed by a brief summary of main findings. The article concludes with a proposal of future working lines for the deconstruction of the motherhood concept in formal and informal education contexts.

  11. Mathematical and numerical study of nonlinear hyperbolic equations: model coupling and nonclassical shocks

    International Nuclear Information System (INIS)

    Boutin, B.

    2009-11-01

    This thesis concerns the mathematical and numerical study of nonlinear hyperbolic partial differential equations. A first part deals with an emergent problematic: the coupling of hyperbolic equations. The pursued applications are linked with the mathematical coupling of computing platforms, dedicated to an adaptative simulation of multi-scale phenomena. We propose and analyze a new coupling formalism based on extended PDE systems avoiding the geometric treatment of the interfaces. In addition, it allows to formulate the problem in a multidimensional setting, with possible covering of the coupled models. This formalism allows in particular to equip the coupling procedure with viscous regularization mechanisms, useful in the selection of natural discontinuous solutions. We analyze existence and uniqueness in the framework of a parabolic regularization a la Dafermos. Existence of a solution holds true under very general conditions but failure of uniqueness may naturally arise as soon as resonance occurs at the interfaces. Next, we highlight that our extended PDE framework gives rise to another regularization strategy based on thick interfaces. In this setting, we prove existence and uniqueness of the solutions of the Cauchy problem for initial data in L ∞ . The main tool consists in the derivation of a flexible and robust finite volume method for general triangulation which is analyzed in the setting of entropy measure-valued solutions by DiPerna. The second part is devoted to the definition of a finite volume scheme for the computing of nonclassical solutions of a scalar conservation law based on a kinetic relation. This scheme offers the feature to be stricto sensu conservative, in opposition to a Glimm approach that is only statistically conservative. The validity of our approach is illustrated through numerical examples. (author)

  12. The Cognitive Infrastructures of Markets: Empirical Studies on the Role of Categories in Valuation and Competition, and a Formal Theory of Classification Systems Based on Lattices and Order

    OpenAIRE

    Piazzai, M.

    2018-01-01

    This dissertation addresses the question of how the information encoded by category labels is interpreted by agents in a market for the purpose of decision-making. To this end, we first examine the influence of categorization on economic and strategic outcomes with two empirical studies, and then use the insights provided by these studies to develop a formal theory of classification systems. Consistently with Formal Concept Analysis (FCA), this theory builds on the fundamental mathematical no...

  13. Tanglegrams: A Reduction Tool for Mathematical Phylogenetics.

    Science.gov (United States)

    Matsen, Frederick A; Billey, Sara C; Kas, Arnold; Konvalinka, Matjaz

    2018-01-01

    Many discrete mathematics problems in phylogenetics are defined in terms of the relative labeling of pairs of leaf-labeled trees. These relative labelings are naturally formalized as tanglegrams, which have previously been an object of study in coevolutionary analysis. Although there has been considerable work on planar drawings of tanglegrams, they have not been fully explored as combinatorial objects until recently. In this paper, we describe how many discrete mathematical questions on trees "factor" through a problem on tanglegrams, and how understanding that factoring can simplify analysis. Depending on the problem, it may be useful to consider a unordered version of tanglegrams, and/or their unrooted counterparts. For all of these definitions, we show how the isomorphism types of tanglegrams can be understood in terms of double cosets of the symmetric group, and we investigate their automorphisms. Understanding tanglegrams better will isolate the distinct problems on leaf-labeled pairs of trees and reveal natural symmetries of spaces associated with such problems.

  14. Mathematical Biology Modules Based on Modern Molecular Biology and Modern Discrete Mathematics

    Science.gov (United States)

    Davies, Robin; Hodge, Terrell; Enyedi, Alexander

    2010-01-01

    We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to introduce students to mathematical methods beyond the interface of biology with calculus. Based on ongoing research, and designed to use the project-based-learning approach, the modules highlight applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. For the majority of projects, calculus is not a required prerequisite and, due to the modest amount of mathematical background needed for some of the modules, the materials can be used for an early introduction to mathematical modeling. At the same time, most modules are connected with topics in linear and abstract algebra, algebraic geometry, and probability, and they can be used as meaningful applied introductions into the relevant advanced-level mathematics courses. Open-source software is used to facilitate the relevant computations. As a detailed example, we outline a module that focuses on Boolean models of the lac operon network. PMID:20810955

  15. Mathematical biology modules based on modern molecular biology and modern discrete mathematics.

    Science.gov (United States)

    Robeva, Raina; Davies, Robin; Hodge, Terrell; Enyedi, Alexander

    2010-01-01

    We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to introduce students to mathematical methods beyond the interface of biology with calculus. Based on ongoing research, and designed to use the project-based-learning approach, the modules highlight applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. For the majority of projects, calculus is not a required prerequisite and, due to the modest amount of mathematical background needed for some of the modules, the materials can be used for an early introduction to mathematical modeling. At the same time, most modules are connected with topics in linear and abstract algebra, algebraic geometry, and probability, and they can be used as meaningful applied introductions into the relevant advanced-level mathematics courses. Open-source software is used to facilitate the relevant computations. As a detailed example, we outline a module that focuses on Boolean models of the lac operon network.

  16. An Early Mathematical Patterning Assessment: identifying young Australian Indigenous children's patterning skills

    Science.gov (United States)

    Papic, Marina

    2015-12-01

    This paper presents an Early Mathematical Patterning Assessment (EMPA) tool that provides early childhood educators with a valuable opportunity to identify young children's mathematical thinking and patterning skills through a series of hands-on and drawing tasks. EMPA was administered through one-to-one assessment interviews to children aged 4 to 5 years in the year prior to formal school. Two hundred and seventeen assessments indicated that the young low socioeconomic and predominantly Australian Indigenous children in the study group had varied patterning and counting skills. Three percent of the study group was able to consistently copy and draw an ABABAB pattern made with coloured blocks. Fifty percent could count to six by ones and count out six items with 4 % of the total group able to identify six items presented in regular formations without counting. The integration of patterning into early mathematics learning is critical to the abstraction of mathematical ideas and relationships and to the development of mathematical reasoning in young children. By using the insights into the children's thinking that the EMPA tool provides, early childhood educators can better inform mathematics teaching and learning and so help close the persistent gap in numeracy between Indigenous and non-Indigenous children.

  17. Why formal learning theory matters for cognitive science.

    Science.gov (United States)

    Fulop, Sean; Chater, Nick

    2013-01-01

    This article reviews a number of different areas in the foundations of formal learning theory. After outlining the general framework for formal models of learning, the Bayesian approach to learning is summarized. This leads to a discussion of Solomonoff's Universal Prior Distribution for Bayesian learning. Gold's model of identification in the limit is also outlined. We next discuss a number of aspects of learning theory raised in contributed papers, related to both computational and representational complexity. The article concludes with a description of how semi-supervised learning can be applied to the study of cognitive learning models. Throughout this overview, the specific points raised by our contributing authors are connected to the models and methods under review. Copyright © 2013 Cognitive Science Society, Inc.

  18. Formalized Informal Learning

    DEFF Research Database (Denmark)

    Levinsen, Karin Tweddell; Sørensen, Birgitte Holm

    2013-01-01

    are examined and the relation between network society competences, learners’ informal learning strategies and ICT in formalized school settings over time is studied. The authors find that aspects of ICT like multimodality, intuitive interaction design and instant feedback invites an informal bricoleur approach....... When integrated into certain designs for teaching and learning, this allows for Formalized Informal Learning and support is found for network society competences building....

  19. Teaching Undergraduate Mathematics Using CAS Technology: Issues and Prospects

    Science.gov (United States)

    Tobin, Patrick C.; Weiss, Vida

    2016-01-01

    The use of handheld CAS technology in undergraduate mathematics courses in Australia is paradoxically shrinking under sustained disapproval or disdain from the professional mathematics community. Mathematics education specialists argue with their mathematics colleagues over a range of issues in course development and this use of CAS or even…

  20. Generalised BRST symmetry and gaugeon formalism for perturbative quantum gravity: Novel observation

    International Nuclear Information System (INIS)

    Upadhyay, Sudhaker

    2014-01-01

    In this paper the novel features of Yokoyama gaugeon formalism are stressed out for the theory of perturbative quantum gravity in the Einstein curved spacetime. The quantum gauge transformations for the theory of perturbative gravity are demonstrated in the framework of gaugeon formalism. These quantum gauge transformations lead to renormalised gauge parameter. Further, we analyse the BRST symmetric gaugeon formalism which embeds more acceptable Kugo–Ojima subsidiary condition. Further, the BRST symmetry is made finite and field-dependent. Remarkably, the Jacobian of path integral under finite and field-dependent BRST symmetry amounts to the exact gaugeon action in the effective theory of perturbative quantum gravity. -- Highlights: •We analyse the perturbative gravity in gaugeon formalism. •The generalisation of BRST transformation is also studied in this context. •Within the generalised BRST framework we found the exact gaugeon modes in the theory

  1. Using Mathematics, Mathematical Applications, Mathematical Modelling, and Mathematical Literacy: A Theoretical Study

    Science.gov (United States)

    Mumcu, Hayal Yavuz

    2016-01-01

    The purpose of this theoretical study is to explore the relationships between the concepts of using mathematics in the daily life, mathematical applications, mathematical modelling, and mathematical literacy. As these concepts are generally taken as independent concepts in the related literature, they are confused with each other and it becomes…

  2. Mathematical Methods and Algorithms of Mobile Parallel Computing on the Base of Multi-core Processors

    Directory of Open Access Journals (Sweden)

    Alexander B. Bakulev

    2012-11-01

    Full Text Available This article deals with mathematical models and algorithms, providing mobility of sequential programs parallel representation on the high-level language, presents formal model of operation environment processes management, based on the proposed model of programs parallel representation, presenting computation process on the base of multi-core processors.

  3. Renormalization as an extension problem on the Count our ordered formalism in FFTF

    Energy Technology Data Exchange (ETDEWEB)

    Franco, D.H.T. [Centro de Estudos de Fisica Teorica (CEFT), Belo Horizonte, MG (Brazil); Acebal, J.L. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil). Coordenacao de Teoria de Campos e Particulas; Grupo de Fisica Teorica Jose Leite Lopes (GFT-JLL), Petropolis, RJ (Brazil)

    2003-06-01

    From a distributional-theoretical framework, we make efforts in order to fill a gap in the series of studies which discuss the inheritance of the renormalization behaviour of a finite temperature field theory (FTFT) from the analogous version in quantum field theory (QFT) at T=0. Renormalization is treated as a distributional extension problem having the mathematical structure disentangled as much as possible from the physical aspects. The purely technical details essential for the discussion are briefly reviewed in a handle manner for further theoretical physics applications. The analysis elucidates some qualitative and quantitative distinctions concerning the divergences in the perturbation series when it is considered the FTFT version associated to a given QFT. Despite the differences, it turns clear the reason why the leading ultraviolet behaviour keeps unaffected when it is considered the FTFT version associated to a given QFT. The study is model independent and the approach allows one to consider the FTFT both imaginary and real time formalism at once in a unified way in the contour ordered formalism. (author)

  4. A mathematical model in cellular manufacturing system considering subcontracting approach under constraints

    Directory of Open Access Journals (Sweden)

    Kamran Forghani

    2012-10-01

    Full Text Available In this paper, a new mathematical model in cellular manufacturing systems (CMSs has been presented. In order to increase the performance of manufacturing system, the production quantity of parts has been considered as a decision variable, i.e. each part can be produced and outsourced, simultaneously. This extension would be minimized the unused capacity of machines. The exceptional elements (EEs are taken into account and would be totally outsourced to the external supplier in order to remove intercellular material handling cost. The problem has been formulated as a mixed-integer programming to minimize the sum of manufacturing variable costs under budget, machines capacity and demand constraints. Also, to evaluate advantages of the model, several illustrative numerical examples have been provided to compare the performance of the proposed model with the available classical approaches in the literature.

  5. Mathematical modeling of earth's dynamical systems a primer

    CERN Document Server

    Slingerland, Rudy

    2011-01-01

    Mathematical Modeling of Earth's Dynamical Systems gives earth scientists the essential skills for translating chemical and physical systems into mathematical and computational models that provide enhanced insight into Earth's processes. Using a step-by-step method, the book identifies the important geological variables of physical-chemical geoscience problems and describes the mechanisms that control these variables. This book is directed toward upper-level undergraduate students, graduate students, researchers, and professionals who want to learn how to abstract complex systems into sets of dynamic equations. It shows students how to recognize domains of interest and key factors, and how to explain assumptions in formal terms. The book reveals what data best tests ideas of how nature works, and cautions against inadequate transport laws, unconstrained coefficients, and unfalsifiable models. Various examples of processes and systems, and ample illustrations, are provided. Students using this text should be f...

  6. The base of the iceberg: informal learning and its impact on formal and non-formal learning

    OpenAIRE

    Rogers, Alan

    2014-01-01

    The author looks at learning (formal, non-formal and informal) and examines the hidden world of informal (unconscious, unplanned) learning. He points out the importance of informal learning for creating tacit attitudes and values, knowledge and skills which influence (conscious, planned) learning - formal and non-formal. Moreover, he explores the implications of informal learning for educational planners and teachers in the context of lifelong learning. While mainly aimed at adult educators, ...

  7. Mathematical Footprints Discovering Mathematics Everywhere

    CERN Document Server

    Pappas, Theoni

    1999-01-01

    MATHEMATICAL FOOTPRINTS takes a creative look at the role mathematics has played since prehistoric times, and will play in the future, and uncovers mathematics where you least expect to find it from its many uses in medicine, the sciences, and its appearance in art to its patterns in nature and its central role in the development of computers. Pappas presents mathematical ideas in a readable non-threatening manner. MATHEMATICAL FOOTPRINTS is another gem by the creator of THE MATHEMATICS CALENDAR and author of THE JOY OF MATHEMATICS. "Pappas's books have been gold mines of mathematical ent

  8. Bildung: A hidden reason for adult mathematics?

    DEFF Research Database (Denmark)

    Johansen, Lene Østergaard

    2005-01-01

    ). PAE will be offered to all persons over 18 who wish to improve their general skills to become better equipped for the labour market and as citizens in a democratic society. The question "Why teach numeracy to adults with lack of basic mathematical skills?" has been the core question in my research...... politicians and researchers in adult numeracy education and that formal education also is a shared argument as a way to reach this ideal, however how beautiful it seems and how much it looks like a united community of practise I will show and discuss important issues where there are crucial differences...

  9. Teachers' Understanding of the Role of Executive Functions in Mathematics Learning

    Science.gov (United States)

    Gilmore, Camilla; Cragg, Lucy

    2014-01-01

    Cognitive psychology research has suggested an important role for executive functions, the set of skills that monitor and control thought and action, in learning mathematics. However, there is currently little evidence about whether teachers are aware of the importance of these skills and, if so, how they come by this information. We conducted an online survey of teachers' views on the importance of a range of skills for mathematics learning. Teachers rated executive function skills, and in particular inhibition and shifting, to be important for mathematics. The value placed on executive function skills increased with increasing teaching experience. Most teachers reported that they were aware of these skills, although few knew the term “executive functions.” This awareness had come about through their teaching experience rather than from formal instruction. Researchers and teacher educators could do more to highlight the importance of these skills to trainee or new teachers. PMID:25674156

  10. General formalism for the stability of thin-shell wormholes in 2 + 1 dimensions

    Energy Technology Data Exchange (ETDEWEB)

    Bejarano, Cecilia [Instituto de Astronomia y Fisica del Espacio, Buenos Aires (Argentina); Eiroa, Ernesto F. [Instituto de Astronomia y Fisica del Espacio, Buenos Aires (Argentina); Universidad de Buenos Aires, Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Buenos Aires (Argentina); Simeone, Claudio [Universidad de Buenos Aires, Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Buenos Aires (Argentina); IFIBA-CONICET, Buenos Aires (Argentina)

    2014-08-15

    In this article we theoretically construct circular thin-shell wormholes in a 2 + 1-dimensional spacetime. The construction is symmetric with respect to the throat. We present a general formalism for the study of the mechanical stability under perturbations preserving the circular symmetry of the configurations, adopting a linearized equation of state for the exotic matter at the throat. We apply the formalism to several examples. (orig.)

  11. General formalism for the stability of thin-shell wormholes in 2 + 1 dimensions

    International Nuclear Information System (INIS)

    Bejarano, Cecilia; Eiroa, Ernesto F.; Simeone, Claudio

    2014-01-01

    In this article we theoretically construct circular thin-shell wormholes in a 2 + 1-dimensional spacetime. The construction is symmetric with respect to the throat. We present a general formalism for the study of the mechanical stability under perturbations preserving the circular symmetry of the configurations, adopting a linearized equation of state for the exotic matter at the throat. We apply the formalism to several examples. (orig.)

  12. Memory function formalism applied to electronic transport in disordered systems

    International Nuclear Information System (INIS)

    Cunha Lima, I.C. da

    1984-01-01

    Memory function formalism is briefly reviewed and applied to electronic transport using the projection operator technique. The resistivity of a disordered 2-D electron gas under strong magnetic field is obtained in terms of force-force correlation function. (Author) [pt

  13. Formal language of Lanna Shop House’s Façade in Lampang Old city, Thailand

    Science.gov (United States)

    Phetsuriya, Natthakit

    2017-10-01

    This article aims to presents ‘the formal architectural language of Lanna Designs” that is a linguistic paradigm for decrypt the linguistic system which is hidden in the Lanna façade style. Lanna Designs present an identity of vital ordered and crucial articulated formal language which inherently set of mathematical rules for the arrangement of ornaments. The scope of this article is attempted to the morphology of façades of the ten shop houses which located in Lampang Old city and have familiar proportion and style. In this article, the sampling of façade buildings required proportion as three-stall and two-story with familiar style. The morphology is described based on terms of a symbolic encoding system that is represented as graphically building grammar. The system helps to emphasize commonalities in façade languages and propose a prototype of identified Lanna façade design. This methodology might be the option for decrypt or study in every facades style.

  14. A mathematical model for the motion analysis of embedded straight microcantilevers under a pressure-driven flow

    International Nuclear Information System (INIS)

    Ezkerra, A; Mayora, K; Ruano-López, J M; Wilson, P A

    2008-01-01

    A mathematical model that estimates the deflection of straight microcantilevers embedded in a microchannel under a pressure-driven flow at low Reynolds numbers is presented. The model makes use of the Schwarz–Christoffel mapping in order to couple the geometry of the structure and the flow passing around it. Therefore, it allows the determination of the most influential parameters and suitable modifications in order to achieve the desired performance. The model does not require specific knowledge of the flow conditions in the vicinity of the structure, which improves its practical use during the early stages of design. Estimations have been made for two straight cantilevers under a range of pressures. The results obtained show good agreement with measurements from experiments

  15. Logicism, intuitionism, and formalism

    CERN Document Server

    Symons, John

    2008-01-01

    Aims to review the programmes in the foundations of mathematics from the classical period and to assess their possible relevance for contemporary philosophy of mathematics. This work is suitable for researchers and graduate students of philosophy, logic, mathematics and theoretical computer science.

  16. Reflective Awareness in Mathematics Teachers' Learning and Teaching

    Science.gov (United States)

    Chapman, Olive

    2015-01-01

    The nature of mathematics teachers' knowledge specific to teaching mathematics [MTK] is of ongoing concern in mathematics education research. This article contributes to our under-standing of this knowledge with particular focus on reflective awareness. It discusses MTK based on ways it has been used in research. It highlights reflective awareness…

  17. Formalized Epistemology, Logic, and Grammar

    Science.gov (United States)

    Bitbol, Michel

    The task of a formal epistemology is defined. It appears that a formal epistemology must be a generalization of "logic" in the sense of Wittgenstein's Tractatus. The generalization is required because, whereas logic presupposes a strict relation between activity and language, this relation may be broken in some domains of experimental enquiry (e.g., in microscopic physics). However, a formal epistemology should also retain a major feature of Wittgenstein's "logic": It must not be a discourse about scientific knowledge, but rather a way of making manifest the structures usually implicit in knowledge-gaining activity. This strategy is applied to the formalism of quantum mechanics.

  18. DATA ANALYSIS BY FORMAL METHODS OF ESTIMATION OF INDEXES OF RATING CRITERION IN PROCESS OF ACCUMULATION OF DATA ABOUT WORKING OF THE TEACHING STAFF

    Directory of Open Access Journals (Sweden)

    Alexey E. Fedoseev

    2014-01-01

    Full Text Available The article considers the development of formal methods of assessing the rating criterion exponents. The article deals with the mathematical model, which allows to connect together quantitative rating criterion characteristics, measured in various scales, with intuitive idea of them. The solution to the problem of rating criterion estimation is proposed.

  19. Quantum mechanics formalism for biological evolution

    International Nuclear Information System (INIS)

    Bianconi, Ginestra; Rahmede, Christoph

    2012-01-01

    Highlights: ► Biological evolution is an off-equilibrium process described by path integrals over phylogenies. ► The phylogenies are sums of linear lineages for asexual populations. ► For sexual populations, each lineage is a tree and the path integral is given by a sum over these trees. ► Quantum statistics describe the stationary state of biological populations in simple cases. - Abstract: We study the evolution of sexual and asexual populations in fitness landscapes compatible with epistatic interactions. We find intriguing relations between the mathematics of biological evolution and quantum mechanics formalism. We give the general structure of the evolution of sexual and asexual populations which is in general an off-equilibrium process that can be expressed by path integrals over phylogenies. These phylogenies are the sum of linear lineages for asexual populations. For sexual populations, instead, each lineage is a tree of branching ratio two and the path integral describing the evolving population is given by a sum over these trees. Finally we show that the Bose–Einstein and the Fermi–Dirac distributions describe the stationary state of biological populations in simple cases.

  20. The Math Gap: a description of the mathematics performance of preschool-aged deaf/hard-of-hearing children.

    Science.gov (United States)

    Pagliaro, Claudia M; Kritzer, Karen L

    2013-04-01

    Over decades and across grade levels, deaf/hard-of-hearing (d/hh) student performance in mathematics has shown a gap in achievement. It is unclear, however, exactly when this gap begins to emerge and in what areas. This study describes preschool d/hh children's knowledge of early mathematics concepts. Both standardized and nonstandardized measures were used to assess understanding in number, geometry, measurement, problem solving, and patterns, reasoning and algebra. Results present strong evidence that d/hh students' difficulty in mathematics may begin prior to the start of formal schooling. Findings also show areas of strength (geometry) and weakness (problem solving and measurement) for these children. Evidence of poor foundational performance may relate to later academic achievement.

  1. Indigenous Knowledge and Education from the Quechua Community to School: Beyond the Formal/Non-Formal Dichotomy

    Science.gov (United States)

    Sumida Huaman, Elizabeth; Valdiviezo, Laura Alicia

    2014-01-01

    In this article, we propose to approach Indigenous education beyond the formal/non-formal dichotomy. We argue that there is a critical need to conscientiously include Indigenous knowledge in education processes from the school to the community; particularly, when formal systems exclude Indigenous cultures and languages. Based on ethnographic…

  2. New procedure for departure formalities

    CERN Multimedia

    HR & GS Departments

    2011-01-01

    As part of the process of simplifying procedures and rationalising administrative processes, the HR and GS Departments have introduced new personalised departure formalities on EDH. These new formalities have applied to students leaving CERN since last year and from 17 October 2011 this procedure will be extended to the following categories of CERN personnel: Staff members, Fellows and Associates. It is planned to extend this electronic procedure to the users in due course. What purpose do departure formalities serve? The departure formalities are designed to ensure that members of the personnel contact all the relevant services in order to return any necessary items (equipment, cards, keys, dosimeter, electronic equipment, books, etc.) and are aware of all the benefits to which they are entitled on termination of their contract. The new departure formalities on EDH have the advantage of tailoring the list of services that each member of the personnel must visit to suit his individual contractual and p...

  3. Framing the Adoption of Serious Games in Formal Education

    Science.gov (United States)

    Arnab, Sylvester; Berta, Riccardo; Earp, Jeffrey; de Freitas, Sara; Popescu, Maria; Romero, Margarida; Stanescu, Ioana; Usart, Mireia

    2012-01-01

    Nowadays formal education systems are under increasing pressure to respond and adapt to rapid technological innovation and associated changes in the way we work and live. As well as accommodation of technology in its ever-diversifying forms, there is a fundamental need to enhance learning processes through evolution in pedagogical approaches, so…

  4. Methods of applied mathematics with a software overview

    CERN Document Server

    Davis, Jon H

    2016-01-01

    This textbook, now in its second edition, provides students with a firm grasp of the fundamental notions and techniques of applied mathematics as well as the software skills to implement them. The text emphasizes the computational aspects of problem solving as well as the limitations and implicit assumptions inherent in the formal methods. Readers are also given a sense of the wide variety of problems in which the presented techniques are useful. Broadly organized around the theme of applied Fourier analysis, the treatment covers classical applications in partial differential equations and boundary value problems, and a substantial number of topics associated with Laplace, Fourier, and discrete transform theories. Some advanced topics are explored in the final chapters such as short-time Fourier analysis and geometrically based transforms applicable to boundary value problems. The topics covered are useful in a variety of applied fields such as continuum mechanics, mathematical physics, control theory, and si...

  5. Recent mathematical developments in 2D correlation spectroscopy

    Science.gov (United States)

    Noda, I.

    2000-03-01

    Recent mathematical developments in the field of 2D correlation spectroscopy, especially those related to the statistical theory, are reported. The notion of correlation phase angle is introduced. The significance of correlation phase angle between dynamic fluctuations of signals measured at two different spectral variables may be linked to more commonly known statistical concepts, such as coherence and correlation coefficient. This treatment provides the direct mathematical connection between the synchronous 2D correlation spectrum with a continuous form of the variance-covariance matrix. Moreover, it gives the background for the formal definition of the disrelation spectrum, which may be used as a heuristic substitution for the asynchronous 2D spectrum. The 2D correlation intensity may be separated into two independent factors representing the normalized extent of signal fluctuation coherence (i.e., correlation coefficient) and the magnitude of spectral intensity changes (i.e., variance). Such separation offers a convenient way to artificially enhance the discriminating power of 2D correlation spectra.

  6. The enhancement of students' mathematical self-efficacy through teaching with metacognitive scaffolding approach

    Science.gov (United States)

    Prabawanto, S.

    2018-05-01

    This research aims to investigate the enhancement of students’ mathematical self- efficacy through teaching with metacognitive scaffolding approach. This research used a quasi- experimental design with pre-post respon control. The subjects were pre-service elementary school teachers in a state university in Bandung. In this study, there were two groups: experimental and control groups. The experimental group consists of 60 students who acquire teaching mathematics under metacognitive approach, while the control group consists of 58 students who acquire teaching mathematics under direct approach. Students were classified into three categories based on the mathematical prior ability, namely high, middle, and low. Data collection instruments consist of mathematical self-efficacy instruments. By using mean difference test, two conclusions of the research: (1) there is a significant difference in the enhancement of mathematical self-efficacy between the students who attended the course under metacognitive scaffolding approach and students who attended the course under direct approach, and (2) there is no significant interaction effect of teaching approaches and ability level based on the mathematical prior ability toward enhancement of students’ mathematical self-efficacy.

  7. The role of mathematical models in understanding pattern formation in developmental biology.

    Science.gov (United States)

    Umulis, David M; Othmer, Hans G

    2015-05-01

    In a Wall Street Journal article published on April 5, 2013, E. O. Wilson attempted to make the case that biologists do not really need to learn any mathematics-whenever they run into difficulty with numerical issues, they can find a technician (aka mathematician) to help them out of their difficulty. He formalizes this in Wilsons Principle No. 1: "It is far easier for scientists to acquire needed collaboration from mathematicians and statisticians than it is for mathematicians and statisticians to find scientists able to make use of their equations." This reflects a complete misunderstanding of the role of mathematics in all sciences throughout history. To Wilson, mathematics is mere number crunching, but as Galileo said long ago, "The laws of Nature are written in the language of mathematics[Formula: see text] the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word." Mathematics has moved beyond the geometry-based model of Galileo's time, and in a rebuttal to Wilson, E. Frenkel has pointed out the role of mathematics in synthesizing the general principles in science (Both point and counter-point are available in Wilson and Frenkel in Notices Am Math Soc 60(7):837-838, 2013). We will take this a step further and show how mathematics has been used to make new and experimentally verified discoveries in developmental biology and how mathematics is essential for understanding a problem that has puzzled experimentalists for decades-that of how organisms can scale in size. Mathematical analysis alone cannot "solve" these problems since the validation lies at the molecular level, but conversely, a growing number of questions in biology cannot be solved without mathematical analysis and modeling. Herein, we discuss a few examples of the productive intercourse between mathematics and biology.

  8. Critical formalism or digital biomorphology. The contemporary architecture formal dilema

    Directory of Open Access Journals (Sweden)

    Beatriz Villanueva Cajide

    2018-05-01

    Full Text Available With the dawn of digital media the architecture’s formal possibilities reached a level unknown before. The Guggenheim Museo branch in Bilbao appears in 1993 as the materialisation of the possibilities of the use of digital tools in architecture’s design, starting the development of a digital based architecture which currently has reached an exhaustion level that is evident in the repetition biomorphologic shapes emerged from the digital determinism to which some contemporary architectural practices have converged. While the digitalisation of the architectural process is irreversible and desirable, it is necessary to rethink the terms of this collaboration beyond the possibilities of the digital tools themselves. This article proposes to analyse seven texts written in the very moment when digitalisation became a real possibility, between Gehry’s conception of the Guggenheim Museum in 1992 and the Congress on Morphogenesis hold in the Architectural Association in 2004, in order to explore the possibility of reversing the process that has led to the formal exhaustion of digital architecture, from the acceptance of incorporating strategies coming from a contemporary critical formalism.

  9. Y-formalism and b ghost in the non-minimal pure spinor formalism of superstrings

    International Nuclear Information System (INIS)

    Oda, Ichiro; Tonin, Mario

    2007-01-01

    We present the Y-formalism for the non-minimal pure spinor quantization of superstrings. In the framework of this formalism we compute, at the quantum level, the explicit form of the compound operators involved in the construction of the b ghost, their normal-ordering contributions and the relevant relations among them. We use these results to construct the quantum-mechanical b ghost in the non-minimal pure spinor formalism. Moreover we show that this non-minimal b ghost is cohomologically equivalent to the non-covariant b ghost

  10. Geometry and Formal Linguistics.

    Science.gov (United States)

    Huff, George A.

    This paper presents a method of encoding geometric line-drawings in a way which allows sets of such drawings to be interpreted as formal languages. A characterization of certain geometric predicates in terms of their properties as languages is obtained, and techniques usually associated with generative grammars and formal automata are then applied…

  11. Metaphorical motion in mathematical reasoning: further evidence for pre-motor implementation of structure mapping in abstract domains.

    Science.gov (United States)

    Fields, Chris

    2013-08-01

    The theory of computation and category theory both employ arrow-based notations that suggest that the basic metaphor "state changes are like motions" plays a fundamental role in all mathematical reasoning involving formal manipulations. If this is correct, structure-mapping inferences implemented by the pre-motor action planning system can be expected to be involved in solving any mathematics problems not solvable by table lookups and number line manipulations alone. Available functional imaging studies of multi-digit arithmetic, algebra, geometry and calculus problem solving are consistent with this expectation.

  12. Avoiding reification. Heuristic effectiveness of mathematics and the prediction of the Ω- particle

    Science.gov (United States)

    Ginammi, Michele

    2016-02-01

    According to Steiner (1998), in contemporary physics new important discoveries are often obtained by means of strategies which rely on purely formal mathematical considerations. In such discoveries, mathematics seems to have a peculiar and controversial role, which apparently cannot be accounted for by means of standard methodological criteria. M. Gell-Mann and Y. Ne'eman's prediction of the Ω- particle is usually considered a typical example of application of this kind of strategy. According to Bangu (2008), this prediction is apparently based on the employment of a highly controversial principle-what he calls the "reification principle". Bangu himself takes this principle to be methodologically unjustifiable, but still indispensable to make the prediction logically sound. In the present paper I will offer a new reconstruction of the reasoning that led to this prediction. By means of this reconstruction, I will show that we do not need to postulate any "reificatory" role of mathematics in contemporary physics and I will contextually clarify the representative and heuristic role of mathematics in science.

  13. Foundations in Science and Mathematics Program for Middle School and High School Students

    Science.gov (United States)

    Desai, Karna Mahadev; Yang, Jing; Hemann, Jason

    2016-01-01

    The Foundations in Science and Mathematics (FSM) is a graduate student led summer program designed to help middle school and high school students strengthen their knowledge and skills in mathematics and science. FSM provides two-week-long courses over a broad spectrum of disciplines including astronomy, biology, chemistry, computer programming, geology, mathematics, and physics. Students can chose two types of courses: (1) courses that help students learn the fundamental concepts in basic sciences and mathematics (e.g., "Precalculus"); and (2) knowledge courses that might be excluded from formal schooling (e.g., "Introduction to Universe"). FSM has served over 500 students in the Bloomington, IN, community over six years by acquiring funding from Indiana University and the Indiana Space Grant Consortium. FSM offers graduate students the opportunity to obtain first hand experience through independent teaching and curriculum design as well as leadership experience.We present the design of the program, review the achievements, and explore the challenges we face. We are open to collaboration with similar educational outreach programs. For more information, please visit http://www.indiana.edu/~fsm/ .

  14. Formal Testing of Correspondence Carrying Software

    NARCIS (Netherlands)

    Bujorianu, M.C.; Bujorianu, L.M.; Maharaj, S.

    2008-01-01

    Nowadays formal software development is characterised by use of multitude formal specification languages. Test case generation from formal specifications depends in general on a specific language, and, moreover, there are competing methods for each language. There is a need for a generic approach to

  15. Early mathematics development and later achievement: Further evidence

    Science.gov (United States)

    Aubrey, Carol; Godfrey, Ray; Dahl, Sarah

    2006-05-01

    There is a growing international recognition of the importance of the early years of schooling as well as an interest being shown in the relationship of early education to later achievement. This article focuses on a cohort of English pupils who have been tracked through primary school during the first five years of the new National Numeracy Strategy. It reports a limited longitudinal study of young children's early mathematical development, initially within three testing cycles: at the mid-point and towards the end of their reception year (at five years-of-age) and again at the mid-point of Year 1 (at six years-ofage). These cycles were located within the broader context of progress through to the end of Key Stage 1 (at seven years) and Key Stage 2 (at eleven years) on the basis of national standardised assessment tests (SATs). Results showed that children who bring into school early mathematical knowledge do appear to be advantaged in terms of their mathematical progress through primary school. Numerical attainment increases in importance across the primary years and practical problem solving remains an important element of this. This finding is significant given the current emphasis on numerical calculation in the English curriculum. It is concluded that without active intervention, it is likely that children with little mathematical knowledge at the beginning of formal schooling will remain low achievers throughout their primary years and, probably, beyond.

  16. Formal model-based development for safety-critical embedded software

    International Nuclear Information System (INIS)

    Kim, Jin Hyun; Choi, Jin Young

    2005-01-01

    Safety-critical embedded software for nuclear I and C system is developed under the safety and reliability regulation. Programmable logic controller(PLC) is a computer system for instrumentation and control (I and C) system of nuclear power plants. PLC consists of various I and C logics in software, including real-time operating system (RTOS). Hence, errors related with RTOS should be detected and eliminated in development processes. Practically, the verification and validation for errors in RTOS is performed in test procedure, in which a lot of tasks for testing are embedded in RTOS and are running under a test environments. But the test process can not be enough to guarantee the safety and reliability of RTOS. Therefore, in this paper, we introduce to applying formal methods with the development of software for the PLC. We particularity apply formal methods to a development of RTOS for PLC, which is a safety critical level. In this development, we use the state charts of I-Logix to specify and verification and model checking to verify the specification

  17. Formal model-based development for safety-critical embedded software

    Energy Technology Data Exchange (ETDEWEB)

    Kim, Jin Hyun; Choi, Jin Young [Korea University, seoul (Korea, Republic of)

    2005-11-15

    Safety-critical embedded software for nuclear I and C system is developed under the safety and reliability regulation. Programmable logic controller(PLC) is a computer system for instrumentation and control (I and C) system of nuclear power plants. PLC consists of various I and C logics in software, including real-time operating system (RTOS). Hence, errors related with RTOS should be detected and eliminated in development processes. Practically, the verification and validation for errors in RTOS is performed in test procedure, in which a lot of tasks for testing are embedded in RTOS and are running under a test environments. But the test process can not be enough to guarantee the safety and reliability of RTOS. Therefore, in this paper, we introduce to applying formal methods with the development of software for the PLC. We particularity apply formal methods to a development of RTOS for PLC, which is a safety critical level. In this development, we use the state charts of I-Logix to specify and verification and model checking to verify the specification.

  18. Mathematical aspects of the discrete space-time hypothesis

    International Nuclear Information System (INIS)

    Sardanashvili, G.A.

    1979-01-01

    A hypothesis of a microcosm space discreteness is considered from the theoretical-mathematical point of view. The type of topological spaces, which formalizes representations on the discrete space-time, is determined. It is explained, how these spaces arise in physical models. The physical task, in which the discrete space could arise as a version of its solution, is considered. It is shown that the discrete structure of space can arise with a certain interaction type in the system, for example, with its considerable self-shielding, which can take place, in particular, in the particles or in the cosmological and astrophysical singularities

  19. Formal analysis of design process dynamics

    NARCIS (Netherlands)

    Bosse, T.; Jonker, C.M.; Treur, J.

    2010-01-01

    This paper presents a formal analysis of design process dynamics. Such a formal analysis is a prerequisite to come to a formal theory of design and for the development of automated support for the dynamics of design processes. The analysis was geared toward the identification of dynamic design

  20. Formal Analysis of Design Process Dynamics

    NARCIS (Netherlands)

    Bosse, T.; Jonker, C.M.; Treur, J.

    2010-01-01

    This paper presents a formal analysis of design process dynamics. Such a formal analysis is a prerequisite to come to a formal theory of design and for the development of automated support for the dynamics of design processes. The analysis was geared toward the identification of dynamic design

  1. Towards a Formal Semantics of Flight Plans and Trajectories

    Science.gov (United States)

    Hagen, George E.; Butler, Ricky W.

    2014-01-01

    In the National Airspace System, ight plans are often used only as a planning tool by air trac controllers and aircraft operators. These plans are implicitly translated into trajectories by the pilot or by the ight management system, and subsequently own by the aircraft. This translation process inevitably introduces di erences between the plan and the trajectory. However, given the current intended usage, exact correspondence between the plan and the trajectory is not needed. To achieve greater capacity and eciency, future air trac management concepts are being designed around the use of trajectories where predictability is extremely important. In this paper, a mathematical relationship between ight plans and trajectories is explored with the goal of making feasible, highly accurate predictions of future positions and velocities of aircraft. The goal here is to describe, in mathematically precise detail, a formal language of trajectories, whereby all receivers of the trajectory information will be able to arrive at precisely the same trajectory predication and to do this without having aircraft broadcast a large amount of data. Although even a four-dimensional ight plan is simple in structure, this paper will show that it is inherently ambiguous and will explore these issues in detail. In e ect, we propose that a rigorous semantics for ight plans can be developed and this will serve as an important stepping stone towards trajectory-based operations in the National Airspace System.

  2. Formal Analysis of Domain Models

    National Research Council Canada - National Science Library

    Bharadwaj, Ramesh

    2002-01-01

    Recently, there has been a great deal of interest in the application of formal methods, in particular, precise formal notations and automatic analysis tools for the creation and analysis of requirements specifications (i.e...

  3. The Effects of Constructivist Learning Environment on Prospective Mathematics Teachers' Opinions

    Science.gov (United States)

    Narli, Serkan; Baser, Nes'e

    2010-01-01

    To explore the effects of constructivist learning environment on prospective teachers' opinions about "mathematics, department of mathematics, discrete mathematics, countable and uncountable infinity" taught under the subject of Cantorian Set Theory in discrete mathematics class, 60 first-year students in the Division of Mathematics…

  4. Applied mathematics made simple

    CERN Document Server

    Murphy, Patrick

    1982-01-01

    Applied Mathematics: Made Simple provides an elementary study of the three main branches of classical applied mathematics: statics, hydrostatics, and dynamics. The book begins with discussion of the concepts of mechanics, parallel forces and rigid bodies, kinematics, motion with uniform acceleration in a straight line, and Newton's law of motion. Separate chapters cover vector algebra and coplanar motion, relative motion, projectiles, friction, and rigid bodies in equilibrium under the action of coplanar forces. The final chapters deal with machines and hydrostatics. The standard and conte

  5. Predicting Relationships between Mathematics Anxiety, Mathematics Teaching Anxiety, Self-efficacy Beliefs towards Mathematics and Mathematics Teaching

    OpenAIRE

    Unlu, Melihan; Ertekin, Erhan; Dilmac, Bulent

    2017-01-01

    The purpose of the research is to investigate the relationships betweenself-efficacy beliefs toward mathematics, mathematics anxiety and self-efficacybeliefs toward mathematics teaching, mathematics teaching anxiety variables andtesting the relationships between these variables with structural equationmodel. The sample of the research, which was conducted in accordance withrelational survey model, consists of 380 university students, who studied atthe department of Elementary Mathematics Educ...

  6. Dependencies among Architectural Views Got from Software Requirements Based on a Formal Model

    Directory of Open Access Journals (Sweden)

    Osis Janis

    2014-12-01

    Full Text Available A system architect has software requirements and some unspecified knowledge about a problem domain (e.g., an enterprise as source information for assessment and evaluation of possible solutions and getting the target point, a preliminary software design. The solving factor is architect’s experience and expertise in the problem domain (“AS-IS”. A proposed approach is dedicated to assist a system architect in making an appropriate decision on the solution (“TO-BE”. It is based on a formal mathematical model, Topological Functioning Model (TFM. Compliant TFMs can be transformed into software architectural views. The paper demonstrates and discusses tracing dependency links from the requirements to and between the architectural views.

  7. Target-space duality between simple compact Lie groups and Lie algebras under the Hamiltonian formalism. Pt. 1. Remnants of duality at the classic level

    International Nuclear Information System (INIS)

    Alvarez, O.; Liu Chienhao

    1996-01-01

    It has been suggested that a possible classical remnant of the phenomenon of target-space duality (T-duality) would be the equivalence of the classical string Hamiltonian systems. Given a simple compact Lie group G with a bi-invariant metric and a generating function Γ suggested in the physics literature, we follow the above line of thought and work out the canonical transformation Φ generated by Γ together with an Ad-invariant metric and a B-field on the associated Lie algebra g of G so that G and g form a string target-space dual pair at the classical level under the Hamiltonian formalism. In this article, some general features of this Hamiltonian setting are discussed. We study properties of the canonical transformation Φ including a careful analysis of its domain and image. The geometry of the T-dual structure on g is lightly touched. We leave the task of tracing back the Hamiltonian formalism at the quantum level to the sequel of this paper. (orig.). With 4 figs

  8. Scalable Techniques for Formal Verification

    CERN Document Server

    Ray, Sandip

    2010-01-01

    This book presents state-of-the-art approaches to formal verification techniques to seamlessly integrate different formal verification methods within a single logical foundation. It should benefit researchers and practitioners looking to get a broad overview of the spectrum of formal verification techniques, as well as approaches to combining such techniques within a single framework. Coverage includes a range of case studies showing how such combination is fruitful in developing a scalable verification methodology for industrial designs. This book outlines both theoretical and practical issue

  9. Violent extremist group ecologies under stress.

    Science.gov (United States)

    Cebrian, Manuel; Torres, Manuel R; Huerta, Ramon; Fowler, James H

    2013-01-01

    Violent extremist groups are currently making intensive use of Internet fora for recruitment to terrorism. These fora are under constant scrutiny by security agencies, private vigilante groups, and hackers, who sometimes shut them down with cybernetic attacks. However, there is a lack of experimental and formal understanding of the recruitment dynamics of online extremist fora and the effect of strategies to control them. Here, we utilize data on ten extremist fora that we collected for four years to develop a data-driven mathematical model that is the first attempt to measure whether (and how) these external attacks induce extremist fora to self-regulate. The results suggest that an increase in the number of groups targeted for attack causes an exponential increase in the cost of enforcement and an exponential decrease in its effectiveness. Thus, a policy to occasionally attack large groups can be very efficient for limiting violent output from these fora.

  10. A Survey of Formal Methods in Software Development

    DEFF Research Database (Denmark)

    Bjørner, Dines

    2012-01-01

    The use of formal methods and formal techniques in industry is steadily growing. In this survey we shall characterise what we mean by software development and by a formal method; briefly overview a history of formal specification languages - some of which are: VDM (Vienna Development Method, 1974...... need for multi-language formalisation (Petri Nets, MSC, StateChart, Temporal Logics); the sociology of university and industry acceptance of formal methods; the inevitability of the use of formal software development methods; while referring to seminal monographs and textbooks on formal methods....

  11. Exhibition - Mathematics, A Beautiful Elsewhere

    CERN Multimedia

    2011-01-01

    From 21 October 2011 to 18 March 2012, the Fondation Cartier pour l’art contemporain will present the exhibition Mathematics: A Beautiful Elsewhere, an exhibition developed in association with the Institut des Hautes Études Scientifiques (IHÉS) and under the patronage of UNESCO. For this unprecedented event, the foundation invited mathematicians to work with artists with whom it has previously worked to create an exhibition that allows visitors to see, hear, do, interpret and think about mathematics. By bringing mathematics into its premises, the Fondation Cartier is itself undergoing the “sudden change of scenery” described by mathematician Alexandre Grothendieck. More information is available here. Fondation Cartier pour l’art contemporain 261, boulevard Raspail 75014 Paris http://fondation.cartier.com Private Visit For professors, researchers and all the staff of Mathematics departments...

  12. Towards a formal taxonomy of hybrid uncertainty representations

    Energy Technology Data Exchange (ETDEWEB)

    Joslyn, C.; Rocha, L.

    1997-02-01

    Recent years have seen a proliferation of methods in addition to probability theory to represent information and uncertainty, including fuzzy sets and systems, fuzzy measures, rough sets, random sets, possibility distributions, imprecise probabilities, etc. We can identify these fields collectively as General Information Theory. The components of GIT represent information according to different axiomatic bases, and are thus capable of capturing different semantic aspects of uncertainty. Traditionally, these semantic criteria include such categories as fuzziness, vagueness, nonspecificity, conflict, and randomness. So it is clear that there is a pressing need for the GIT community to synthesize these methods, searching out larger formal frameworks within which to place these various components with respect to each other. Ideally, syntactic (mathematical) generalization can both aid and be aided by the semantic analysis available in terms of the conceptual categories outlined above. In this paper we present some preliminary ideas about how to formally relate various uncertainty representations together in a taxonomic lattice, capturing both syntactic and semantic generalization. Some partial and provisional results are shown. Assume a simple finite universe of discourse {Omega} = (a, b, c). We want to describe a situation in which we ask a question of the sort {open_quotes}what is the value of a variable x which takes values in {Omega}?{close_quotes}. When there is no uncertainty, we have a single alternative, say x = a. In logical terms, we would say that the proposition p: {open_quotes}the value of x is a{close_quotes} is TRUE. Our approach begins with two primitive concepts which can change our knowledge of x, each of which represents a different form of uncertainty, nonspecificity and fuxxiness.

  13. Gender Differences in Solving Mathematics Problems among Two-Year College Students in a Developmental Algebra Class and Related Factors.

    Science.gov (United States)

    Schonberger, Ann K.

    A study was conducted at the University of Maine at Orono (UMO) to examine gender differences with respect to mathematical problem-solving ability, visual spatial ability, abstract reasoning ability, field independence/dependence, independent learning style, and developmental problem-solving ability (i.e., formal reasoning ability). Subjects…

  14. Integrated Design Validation: Combining Simulation and Formal Verification for Digital Integrated Circuits

    Directory of Open Access Journals (Sweden)

    Lun Li

    2006-04-01

    Full Text Available The correct design of complex hardware continues to challenge engineers. Bugs in a design that are not uncovered in early design stages can be extremely expensive. Simulation is a predominantly used tool to validate a design in industry. Formal verification overcomes the weakness of exhaustive simulation by applying mathematical methodologies to validate a design. The work described here focuses upon a technique that integrates the best characteristics of both simulation and formal verification methods to provide an effective design validation tool, referred as Integrated Design Validation (IDV. The novelty in this approach consists of three components, circuit complexity analysis, partitioning based on design hierarchy, and coverage analysis. The circuit complexity analyzer and partitioning decompose a large design into sub-components and feed sub-components to different verification and/or simulation tools based upon known existing strengths of modern verification and simulation tools. The coverage analysis unit computes the coverage of design validation and improves the coverage by further partitioning. Various simulation and verification tools comprising IDV are evaluated and an example is used to illustrate the overall validation process. The overall process successfully validates the example to a high coverage rate within a short time. The experimental result shows that our approach is a very promising design validation method.

  15. Insights into teaching mathematics

    CERN Document Server

    Orton, Anthony

    2004-01-01

    Providing essential guidance and background information about teaching mathematics, this book is intended particularly for teachers who do not regard themselves as specialists in mathematics. It deals with issues of learning and teaching, including the delivery of content and the place of problems and investigations. Difficulties which pupils encounter in connection with language and symbols form important sections of the overall discussion of how to enhance learning. The curriculum is considered in brief under the headings of number, algebra, shape and space, and data handling, and special at

  16. Concepts of modern mathematics

    CERN Document Server

    Stewart, Ian

    1995-01-01

    Some years ago, ""new math"" took the country's classrooms by storm. Based on the abstract, general style of mathematical exposition favored by research mathematicians, its goal was to teach students not just to manipulate numbers and formulas, but to grasp the underlying mathematical concepts. The result, at least at first, was a great deal of confusion among teachers, students, and parents. Since then, the negative aspects of ""new math"" have been eliminated and its positive elements assimilated into classroom instruction.In this charming volume, a noted English mathematician uses humor an

  17. Towards a Formal Model of Privacy-Sensitive Dynamic Coalitions

    Directory of Open Access Journals (Sweden)

    Sebastian Bab

    2012-04-01

    Full Text Available The concept of dynamic coalitions (also virtual organizations describes the temporary interconnection of autonomous agents, who share information or resources in order to achieve a common goal. Through modern technologies these coalitions may form across company, organization and system borders. Therefor questions of access control and security are of vital significance for the architectures supporting these coalitions. In this paper, we present our first steps to reach a formal framework for modeling and verifying the design of privacy-sensitive dynamic coalition infrastructures and their processes. In order to do so we extend existing dynamic coalition modeling approaches with an access-control-concept, which manages access to information through policies. Furthermore we regard the processes underlying these coalitions and present first works in formalizing these processes. As a result of the present paper we illustrate the usefulness of the Abstract State Machine (ASM method for this task. We demonstrate a formal treatment of privacy-sensitive dynamic coalitions by two example ASMs which model certain access control situations. A logical consideration of these ASMs can lead to a better understanding and a verification of the ASMs according to the aspired specification.

  18. An effective technique for the software requirements analysis of NPP safety-critical systems, based on software inspection, requirements traceability, and formal specification

    International Nuclear Information System (INIS)

    Koo, Seo Ryong; Seong, Poong Hyun; Yoo, Junbeom; Cha, Sung Deok; Yoo, Yeong Jae

    2005-01-01

    A thorough requirements analysis is indispensable for developing and implementing safety-critical software systems such as nuclear power plant (NPP) software systems because a single error in the requirements can generate serious software faults. However, it is very difficult to completely analyze system requirements. In this paper, an effective technique for the software requirements analysis is suggested. For requirements verification and validation (V and V) tasks, our technique uses software inspection, requirement traceability, and formal specification with structural decomposition. Software inspection and requirements traceability analysis are widely considered the most effective software V and V methods. Although formal methods are also considered an effective V and V activity, they are difficult to use properly in the nuclear fields as well as in other fields because of their mathematical nature. In this work, we propose an integrated environment (IE) approach for requirements, which is an integrated approach that enables easy inspection by combining requirement traceability and effective use of a formal method. The paper also introduces computer-aided tools for supporting IE approach for requirements. Called the nuclear software inspection support and requirements traceability (NuSISRT), the tool incorporates software inspection, requirement traceability, and formal specification capabilities. We designed the NuSISRT to partially automate software inspection and analysis of requirement traceability. In addition, for the formal specification and analysis, we used the formal requirements specification and analysis tool for nuclear engineering (NuSRS)

  19. Science teachers and docents as mentors to science and mathematics undergraduates in formal and information settings. Final report

    Energy Technology Data Exchange (ETDEWEB)

    Koran, J.J. Jr. [Florida Museum of Natural History, Gainesville, FL (United States)

    1993-10-15

    Twenty-four undergraduate science and mathematics majors who were juniors and seniors in the colleges of Liberal Arts and Sciences and Engineering were recruited, and paid, to participate in an orientation seminar and act as teacher aides in regional schools and the Florida Museum of Natural History. Aides worked with teachers in the schools one semester and as docents in the natural history museum a second semester. Mentoring took place by the principal investigator and participating teachers and docents throughout the program. Success of the program was measured by a specially prepared attitude instrument which was administered to participants before the mentoring started and when it ended each semester. Written logs (field notes) were also prepared and submitted by participants at the end of each semester. Further, a tally was kept of the number of participants who decided to go into science or mathematics teaching as a result of the experience.

  20. Predicting Relationships between Mathematics Anxiety, Mathematics Teaching Anxiety, Self-Efficacy Beliefs towards Mathematics and Mathematics Teaching

    Science.gov (United States)

    Unlu, Melihan; Ertekin, Erhan; Dilmac, Bulent

    2017-01-01

    The purpose of the research is to investigate the relationships between self-efficacy beliefs toward mathematics, mathematics anxiety and self-efficacy beliefs toward mathematics teaching, mathematics teaching anxiety variables and testing the relationships between these variables with structural equation model. The sample of the research, which…

  1. Bohmian mechanics. The physics and mathematics of quantum theory

    International Nuclear Information System (INIS)

    Duerr, Detlef; Teufel, Stefan

    2009-01-01

    Bohmian Mechanics was formulated in 1952 by David Bohm as a complete theory of quantum phenomena based on a particle picture. It was promoted some decades later by John S. Bell, who, intrigued by the manifestly nonlocal structure of the theory, was led to his famous Bell's inequalities. Experimental tests of the inequalities verified that nature is indeed nonlocal. Bohmian mechanics has since then prospered as the straightforward completion of quantum mechanics. This book provides a systematic introduction to Bohmian mechanics and to the mathematical abstractions of quantum mechanics, which range from the self-adjointness of the Schroedinger operator to scattering theory. It explains how the quantum formalism emerges when Boltzmann's ideas about statistical mechanics are applied to Bohmian mechanics. The book is self-contained, mathematically rigorous and an ideal starting point for a fundamental approach to quantum mechanics. It will appeal to students and newcomers to the field, as well as to established scientists seeking a clear exposition of the theory. (orig.)

  2. Bohmian mechanics. The physics and mathematics of quantum theory

    Energy Technology Data Exchange (ETDEWEB)

    Duerr, Detlef [Muenchen Univ. (Germany). Fakultaet Mathematik; Teufel, Stefan [Tuebingen Univ. (Germany). Mathematisches Inst.

    2009-07-01

    Bohmian Mechanics was formulated in 1952 by David Bohm as a complete theory of quantum phenomena based on a particle picture. It was promoted some decades later by John S. Bell, who, intrigued by the manifestly nonlocal structure of the theory, was led to his famous Bell's inequalities. Experimental tests of the inequalities verified that nature is indeed nonlocal. Bohmian mechanics has since then prospered as the straightforward completion of quantum mechanics. This book provides a systematic introduction to Bohmian mechanics and to the mathematical abstractions of quantum mechanics, which range from the self-adjointness of the Schroedinger operator to scattering theory. It explains how the quantum formalism emerges when Boltzmann's ideas about statistical mechanics are applied to Bohmian mechanics. The book is self-contained, mathematically rigorous and an ideal starting point for a fundamental approach to quantum mechanics. It will appeal to students and newcomers to the field, as well as to established scientists seeking a clear exposition of the theory. (orig.)

  3. A Formal Verification Method of Function Block Diagram

    International Nuclear Information System (INIS)

    Koh, Kwang Yong; Seong, Poong Hyun; Jee, Eun Kyoung; Jeon, Seung Jae; Park, Gee Yong; Kwon, Kee Choon

    2007-01-01

    Programmable Logic Controller (PLC), an industrial computer specialized for real-time applications, is widely used in diverse control systems in chemical processing plants, nuclear power plants or traffic control systems. As a PLC is often used to implement safety, critical embedded software, rigorous safety demonstration of PLC code is necessary. Function block diagram (FBD) is a standard application programming language for the PLC and currently being used in the development of a fully-digitalized reactor protection system (RPS), which is called the IDiPS, under the KNICS project. Therefore, verification issue of FBD programs is a pressing problem, and hence is of great importance. In this paper, we propose a formal verification method of FBD programs; we defined FBD programs formally in compliance with IEC 61131-3, and then translate the programs into Verilog model, and finally the model is verified using a model checker SMV. To demonstrate the feasibility and effective of this approach, we applied it to IDiPS which currently being developed under KNICS project. The remainder of this paper is organized as follows. Section 2 briefly describes Verilog and Cadence SMV. In Section 3, we introduce FBD2V which is a tool implemented to support the proposed FBD verification framework. A summary and conclusion are provided in Section 4

  4. Augmenting Reality and Formality of Informal and Non-Formal Settings to Enhance Blended Learning

    Science.gov (United States)

    Pérez-Sanagustin, Mar; Hernández-Leo, Davinia; Santos, Patricia; Kloos, Carlos Delgado; Blat, Josep

    2014-01-01

    Visits to museums and city tours have been part of higher and secondary education curriculum activities for many years. However these activities are typically considered "less formal" when compared to those carried out in the classroom, mainly because they take place in informal or non-formal settings. Augmented Reality (AR) technologies…

  5. Superfield formalism

    Indian Academy of Sciences (India)

    dimensional superfields, is a clear signature of the presence of the (anti-)BRST invariance in the original. 4D theory. Keywords. Non-Abelian 1-form gauge theory; Dirac fields; (anti-)Becchi–Roucet–Stora–. Tyutin invariance; superfield formalism; ...

  6. USE DIFFERENT LANGUAGES OF KNOWLEDGE REPRESENTATION AS A FACTOR OF MATHEMATICS EDUCATION HUMANIZATION

    Directory of Open Access Journals (Sweden)

    E. Sagan

    2014-04-01

    Full Text Available A lot of educational projects get no further development primarily due to the lack of competent academic staff. It is not only the professional knowledge, abilities and skills, but also the ability to perceive educational innovations and ability to implement them. With regard to the mathematics education the most urgent is the problem of humanization, which appears in the ratio of scientific knowledge, national and cultural revival, issues of values and new type of education content. The problem of humanizing of mathematical education isexamined in the article, in particular in the field of training ofpedagogical personnels. As for the serve of mathematicalmaterial the language of formal logic, that is regulated by thesecond alarm system, is used, it results in the deficit ofinformation of the first alarm system, that is responsible forperception, imagination, supervision, experience. Logical isthe use of such methods serves of information, thatmaximally use both сигнальних systems of man. It issuggested one of directions of upgrading of educating tomathematics of future teachers except the traditionallanguage of formal logic to use the alternative languages ofserve of material : language of semantic networks, languageof the system of frames, language of productional.

  7. Dist-Orc: A Rewriting-based Distributed Implementation of Orc with Formal Analysis

    Directory of Open Access Journals (Sweden)

    José Meseguer

    2010-09-01

    Full Text Available Orc is a theory of orchestration of services that allows structured programming of distributed and timed computations. Several formal semantics have been proposed for Orc, including a rewriting logic semantics developed by the authors. Orc also has a fully fledged implementation in Java with functional programming features. However, as with descriptions of most distributed languages, there exists a fairly substantial gap between Orc's formal semantics and its implementation, in that: (i programs in Orc are not easily deployable in a distributed implementation just by using Orc's formal semantics, and (ii they are not readily formally analyzable at the level of a distributed Orc implementation. In this work, we overcome problems (i and (ii for Orc. Specifically, we describe an implementation technique based on rewriting logic and Maude that narrows this gap considerably. The enabling feature of this technique is Maude's support for external objects through TCP sockets. We describe how sockets are used to implement Orc site calls and returns, and to provide real-time timing information to Orc expressions and sites. We then show how Orc programs in the resulting distributed implementation can be formally analyzed at a reasonable level of abstraction by defining an abstract model of time and the socket communication infrastructure, and discuss the assumptions under which the analysis can be deemed correct. Finally, the distributed implementation and the formal analysis methodology are illustrated with a case study.

  8. SOME REMARKS ON THE RELATION OF FORMAL AND INFORMAL IN SOLVING OPTIMIZATION PROBLEMS IN THE FIELD OF AVIATION SECURITY

    Directory of Open Access Journals (Sweden)

    L. N. Elisov

    2015-01-01

    Full Text Available The paper presents the authors view and some remarks on the problem of solving optimization problems in the field of aviation security related to insurmountable difficulties of formalization and mathematical interpretation of the domain formulation of such problems. It is shown that the vast majority of these problems is related to the solution of conflicts. The theory of conflicts gives analytical solution only in the simplest cases. For the rest the use of a heuristic approach is suggested.

  9. Students’ Algebraic Reasonsing In Solving Mathematical Problems With Adversity Quotient

    Science.gov (United States)

    Aryani, F.; Amin, S. M.; Sulaiman, R.

    2018-01-01

    Algebraic reasoning is a process in which students generalize mathematical ideas from a set of particular instances and express them in increasingly formal and age-appropriate ways. Using problem solving approach to develop algebraic reasoning of mathematics may enhace the long-term learning trajectory of the majority students. The purpose of this research was to describe the algebraic reasoning of quitter, camper, and climber junior high school students in solving mathematical problems. This research used qualitative descriptive method. Subjects were determined by purposive sampling. The technique of collecting data was done by task-based interviews.The results showed that the algebraic reasoning of three students in the process of pattern seeking by identifying the things that are known and asked in a similar way. But three students found the elements of pattern recognition in different ways or method. So, they are generalize the problem of pattern formation with different ways. The study of algebraic reasoning and problem solving can be a learning paradigm in the improve students’ knowledge and skills in algebra work. The goal is to help students’ improve academic competence, develop algebraic reasoning in problem solving.

  10. MOOC & B-Learning: Students' Barriers and Satisfaction in Formal and Non-Formal Learning Environments

    Science.gov (United States)

    Gutiérrez-Santiuste, Elba; Gámiz-Sánchez, Vanesa-M.; Gutiérrez-Pérez, Jose

    2015-01-01

    The study presents a comparative analysis of two virtual learning formats: one non-formal through a Massive Open Online Course (MOOC) and the other formal through b-learning. We compare the communication barriers and the satisfaction perceived by the students (N = 249) by developing a qualitative analysis using semi-structured questionnaires and…

  11. Formality of the Chinese collective leadership.

    Science.gov (United States)

    Li, Haiying; Graesser, Arthur C

    2016-09-01

    We investigated the linguistic patterns in the discourse of four generations of the collective leadership of the Communist Party of China (CPC) from 1921 to 2012. The texts of Mao Zedong, Deng Xiaoping, Jiang Zemin, and Hu Jintao were analyzed using computational linguistic techniques (a Chinese formality score) to explore the persuasive linguistic features of the leaders in the contexts of power phase, the nation's education level, power duration, and age. The study was guided by the elaboration likelihood model of persuasion, which includes a central route (represented by formal discourse) versus a peripheral route (represented by informal discourse) to persuasion. The results revealed that these leaders adopted the formal, central route more when they were in power than before they came into power. The nation's education level was a significant factor in the leaders' adoption of the persuasion strategy. The leaders' formality also decreased with their increasing age and in-power times. However, the predictability of these factors for formality had subtle differences among the different types of leaders. These results enhance our understanding of the Chinese collective leadership and the role of formality in politically persuasive messages.

  12. Proceedings – Mathematical Sciences | Indian Academy of Sciences

    Indian Academy of Sciences (India)

    Home; Journals; Proceedings – Mathematical Sciences. Shobha Madan. Articles written in Proceedings – Mathematical Sciences. Volume 113 Issue 2 May 2003 pp 171-178. Wavelet Subspaces Invariant Under Groups of Translation Operators · Biswaranjan Behera Shobha Madan · More Details Abstract Fulltext PDF.

  13. Cognitive mechanisms underlying third graders' arithmetic skills: Expanding the pathways to mathematics model.

    Science.gov (United States)

    Träff, Ulf; Olsson, Linda; Skagerlund, Kenny; Östergren, Rickard

    2018-03-01

    A modified pathways to mathematics model was used to examine the cognitive mechanisms underlying arithmetic skills in third graders. A total of 269 children were assessed on tasks tapping the four pathways and arithmetic skills. A path analysis showed that symbolic number processing was directly supported by the linguistic and approximate quantitative pathways. The direct contribution from the four pathways to arithmetic proficiency varied; the linguistic pathway supported single-digit arithmetic and word problem solving, whereas the approximate quantitative pathway supported only multi-digit calculation. The spatial processing and verbal working memory pathways supported only arithmetic word problem solving. The notion of hierarchical levels of arithmetic was supported by the results, and the different levels were supported by different constellations of pathways. However, the strongest support to the hierarchical levels of arithmetic were provided by the proximal arithmetic skills. Copyright © 2017 Elsevier Inc. All rights reserved.

  14. 40 years of formal methods

    DEFF Research Database (Denmark)

    Bjørner, Dines; Havelund, Klaus

    2014-01-01

    In this "40 years of formal methods" essay we shall first delineate, Sect. 1, what we mean by method, formal method, computer science, computing science, software engineering, and model-oriented and algebraic methods. Based on this, we shall characterize a spectrum from specification-oriented met...

  15. The Eleventh Quadrennial Review of Military Compensation. Supporting Research Papers

    Science.gov (United States)

    2012-06-01

    factors in both the FICA tax that is avoided and the value of future Social Security benefits that are foregone. Using actuarial estimates of 1.9 to 2.5...savings to more gross pay. 23. The mathematical presentation of this formal model is in Appendix C. The Eleventh Quadrennial Review of Military...the mathematical equations underlying the model developed in the section called “Exploring other factors of compensation: A formal model of military

  16. Mathematics related anxiety: Mathematics bogeyman or not?

    Directory of Open Access Journals (Sweden)

    Videnović Marina

    2011-01-01

    Full Text Available Data of the PISA 2003 survey indicate high levels of mathematics anxiety of students in Serbia. More than half of our students worry whether they will have difficulties in mathematics class or whether they will earn poor marks. Aims of this study therefore are: examining relationship between math anxiety and achievement at mathematics literacy scale; establishing possible predictors of math anxiety and identification of students' groups in relations to their relationship towards mathematics as a subject. Mathematics anxiety is statistically negatively correlated with school achievement and achievement at mathematics literacy scale. Socio-demographic factors, motivational and cognitive aspects related to learning mathematics, perception of school and classroom climate explain 40% variance of mathematics anxiety. Based on students' relationship towards mathematics they cam be divided into three groups; while dimensions that apart them are uninterested-interested in mathematics and presence-absence of anxiety. The group displaying anxiety scores lowest among the three. Applying qualitative analysis students' and teachers' attitudes on specific issues related to teaching and learning mathematics was examined.

  17. A Formalization of Linkage Analysis

    DEFF Research Database (Denmark)

    Ingolfsdottir, Anna; Christensen, A.I.; Hansen, Jens A.

    In this report a formalization of genetic linkage analysis is introduced. Linkage analysis is a computationally hard biomathematical method, which purpose is to locate genes on the human genome. It is rooted in the new area of bioinformatics and no formalization of the method has previously been ...

  18. Utility of Interactional Strategies in the Study of Formal Operations Reasoning.

    Science.gov (United States)

    Siegler, Robert S.

    This paper argues in favor of using interactional strategies in the study of formal operations reasoning. Interactional designs allow a convergent approach to specifying processes underlying the interaction of variables. In contrast, current methodologies contain two inherent disadvantages: they have limited utility in specifying the processes…

  19. Teachers' Mathematics as Mathematics-at-Work

    Science.gov (United States)

    Bednarz, Nadine; Proulx, Jérôme

    2017-01-01

    Through recognising mathematics teachers as professionals who use mathematics in their workplace, this article traces a parallel between the mathematics enacted by teachers in their practice and the mathematics used in workplaces found in studies of professionals (e.g. nurses, engineers, bankers). This parallel is developed through the five…

  20. Fundamentals of the Pure Spinor Formalism

    CERN Document Server

    Hoogeveen, Joost

    2010-01-01

    This thesis presents recent developments within the pure spinor formalism, which has simplified amplitude computations in perturbative string theory, especially when spacetime fermions are involved. Firstly the worldsheet action of both the minimal and the non-minimal pure spinor formalism is derived from first principles, i.e. from an action with two dimensional diffeomorphism and Weyl invariance. Secondly the decoupling of unphysical states in the minimal pure spinor formalism is proved

  1. EMBO Course “Formal Analysis of Genetic Regulation”

    CERN Document Server

    1979-01-01

    The E M B 0 course on "Formal Analysis of Genetic Regulation" A course entitled "Formal analysis of Genetic Regulation" was held at the University of Brussels from 6 to 16 September 1977 under the auspices of EMBO (European Molecular Biology Organization). As indicated by the title of the book (but not explicitly enough by the title of the course), the main emphasis was put on a dynamic analysis of systems using logical methods, that is, methods in which functions and variables take only a limited number of values - typically two. In this respect, this course was complementary to an EMBO course using continuous methods which was held some months later in Israel by Prof. Segel. People from four very different laboratories took an active part in teaching our course in Brussels : Drs Anne LEUSSLER and Philippe VAN HAM, from the Laboratory of Prof. Jean FLORINE (Laboratoire des Systemes logiques et numeriques, Faculte des Sciences appliquees, Universite Libre de Bruxelles). Dr Stuart KAUFFMAN (Dept. of Biochemist...

  2. Mathematical modeling of climate change and malaria transmission dynamics: a historical review.

    Science.gov (United States)

    Eikenberry, Steffen E; Gumel, Abba B

    2018-04-24

    Malaria, one of the greatest historical killers of mankind, continues to claim around half a million lives annually, with almost all deaths occurring in children under the age of five living in tropical Africa. The range of this disease is limited by climate to the warmer regions of the globe, and so anthropogenic global warming (and climate change more broadly) now threatens to alter the geographic area for potential malaria transmission, as both the Plasmodium malaria parasite and Anopheles mosquito vector have highly temperature-dependent lifecycles, while the aquatic immature Anopheles habitats are also strongly dependent upon rainfall and local hydrodynamics. A wide variety of process-based (or mechanistic) mathematical models have thus been proposed for the complex, highly nonlinear weather-driven Anopheles lifecycle and malaria transmission dynamics, but have reached somewhat disparate conclusions as to optimum temperatures for transmission, and the possible effect of increasing temperatures upon (potential) malaria distribution, with some projecting a large increase in the area at risk for malaria, but others predicting primarily a shift in the disease's geographic range. More generally, both global and local environmental changes drove the initial emergence of P. falciparum as a major human pathogen in tropical Africa some 10,000 years ago, and the disease has a long and deep history through the present. It is the goal of this paper to review major aspects of malaria biology, methods for formalizing these into mathematical forms, uncertainties and controversies in proper modeling methodology, and to provide a timeline of some major modeling efforts from the classical works of Sir Ronald Ross and George Macdonald through recent climate-focused modeling studies. Finally, we attempt to place such mathematical work within a broader historical context for the "million-murdering Death" of malaria.

  3. On the mathematics of fuzziness

    International Nuclear Information System (INIS)

    Kerre, E.

    1994-01-01

    During the past twenty-five years, the scientific community has been working very extensively on the development of reliable models for the representation and manipulation of impreciseness and uncertainty that pervade the real world. Fuzzy set theory is one of the most popular theories able to treat incomplete information. In this paper, the basic mathematical principles underlying fuzzy set theory are outlined. Special attention is paid to the way that set theory has influenced the development of mathematics in a positive way

  4. On the mathematics of fuzziness

    Energy Technology Data Exchange (ETDEWEB)

    Kerre, E. [Ghent Univ. (Belgium)

    1994-12-31

    During the past twenty-five years, the scientific community has been working very extensively on the development of reliable models for the representation and manipulation of impreciseness and uncertainty that pervade the real world. Fuzzy set theory is one of the most popular theories able to treat incomplete information. In this paper, the basic mathematical principles underlying fuzzy set theory are outlined. Special attention is paid to the way that set theory has influenced the development of mathematics in a positive way.

  5. Leibniz' First Formalization of Syllogistics

    DEFF Research Database (Denmark)

    Robering, Klaus

    2014-01-01

    of letters just those which belong to the useful, i.e., valid, modes. The set of codes of valid modes turns out to be a so-called "regular" language (in the sense of formal-language-theory). Leibniz' formalization of syllogistics in his Dissertatio thus contains an estimation of the computational complexity...

  6. Formalizing the concept phase of product development

    NARCIS (Netherlands)

    Schuts, M.; Hooman, J.

    2015-01-01

    We discuss the use of formal techniques to improve the concept phase of product realisation. As an industrial application, a new concept of interventional X-ray systems has been formalized, using model checking techniques and the simulation of formal models. cop. Springer International Publishing

  7. A survey of formal languages for contracts

    DEFF Research Database (Denmark)

    Hvitved, Tom

    2010-01-01

    In this short paper we present the current status on formal languages and models for contracts. By a formal model is meant an unambiguous and rigorous representation of contracts, in order to enable their automatic validation, execution, and analysis — activates that are collectively referred...... to as contract lifecycle management (CLM). We present a set of formalism requirements, which represent features that any ideal contract model should support, based on which we present a comparative survey of existing contract formalisms....

  8. Teaching Mathematical Modeling in Mathematics Education

    Science.gov (United States)

    Saxena, Ritu; Shrivastava, Keerty; Bhardwaj, Ramakant

    2016-01-01

    Mathematics is not only a subject but it is also a language consisting of many different symbols and relations. Taught as a compulsory subject up the 10th class, students are then able to choose whether or not to study mathematics as a main subject. The present paper discusses mathematical modeling in mathematics education. The article provides…

  9. The mathematics of soap films

    CERN Document Server

    Oprea, John

    2000-01-01

    Nature tries to minimize the surface area of a soap film through the action of surface tension. The process can be understood mathematically by using differential geometry, complex analysis, and the calculus of variations. This book employs ingredients from each of these subjects to tell the mathematical story of soap films. The text is fully self-contained, bringing together a mixture of types of mathematics along with a bit of the physics that underlies the subject. The development is primarily from first principles, requiring no advanced background material from either mathematics or physics. Through the Maple® applications, the reader is given tools for creating the shapes that are being studied. Thus, you can "see" a fluid rising up an inclined plane, create minimal surfaces from complex variables data, and investigate the "true" shape of a balloon. Oprea also includes descriptions of experiments and photographs that let you see real soap films on wire frames. The theory of minimal surfaces is a beautif...

  10. How does non-formal marine education affect student attitude and knowledge? A case study using SCDNR's Discovery program

    Science.gov (United States)

    McGovern, Mary Francis

    Non-formal environmental education provides students the opportunity to learn in ways that would not be possible in a traditional classroom setting. Outdoor learning allows students to make connections to their environment and helps to foster an appreciation for nature. This type of education can be interdisciplinary---students not only develop skills in science, but also in mathematics, social studies, technology, and critical thinking. This case study focuses on a non-formal marine education program, the South Carolina Department of Natural Resources' (SCDNR) Discovery vessel based program. The Discovery curriculum was evaluated to determine impact on student knowledge about and attitude toward the estuary. Students from two South Carolina coastal counties who attended the boat program during fall 2014 were asked to complete a brief survey before, immediately after, and two weeks following the program. The results of this study indicate that both student knowledge about and attitude significantly improved after completion of the Discovery vessel based program. Knowledge and attitude scores demonstrated a positive correlation.

  11. Mathematical Modeling and Pure Mathematics

    Science.gov (United States)

    Usiskin, Zalman

    2015-01-01

    Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…

  12. 20 CFR 702.336 - Formal hearings; new issues.

    Science.gov (United States)

    2010-04-01

    ... 20 Employees' Benefits 3 2010-04-01 2010-04-01 false Formal hearings; new issues. 702.336 Section... Procedures Formal Hearings § 702.336 Formal hearings; new issues. (a) If, during the course of the formal hearing, the evidence presented warrants consideration of an issue or issues not previously considered...

  13. The Interrelatedness of Formal, Non-Formal and Informal Learning: Evidence from Labour Market Program Participants

    Science.gov (United States)

    Cameron, Roslyn; Harrison, Jennifer L.

    2012-01-01

    Definitions, differences and relationships between formal, non-formal and informal learning have long been contentious. There has been a significant change in language and reference from adult education to what amounts to forms of learning categorised by their modes of facilitation. Nonetheless, there is currently a renewed interest in the…

  14. NON-FORMAL EDUCATION, OVEREDUCATION AND WAGES

    OpenAIRE

    SANDRA NIETO; RAÚL RAMOS

    2013-01-01

    Why do overeducated workers participate in non-formal education activities? Do not they suffer from an excess of education? Using microdata from the Spanish sample of the 2007 Adult Education Survey, we have found that overeducated workers participate more than the rest in non-formal education and that they earn higher wages than overeducated workers who did not participate. This result can be interpreted as evidence that non-formal education allows overeducated workers to acquire new abiliti...

  15. Mathematical modelling for trajectories of magnetic nanoparticles in a blood vessel under magnetic field

    International Nuclear Information System (INIS)

    Sharma, Shashi; Katiyar, V.K.; Singh, Uaday

    2015-01-01

    A mathematical model is developed to describe the trajectories of a cluster of magnetic nanoparticles in a blood vessel for the application of magnetic drug targeting (MDT). The magnetic nanoparticles are injected into a blood vessel upstream from a malignant tissue and are captured at the tumour site with help of an applied magnetic field. The applied field is produced by a rare earth cylindrical magnet positioned outside the body. All forces expected to significantly affect the transport of nanoparticles were incorporated, including magnetization force, drag force and buoyancy force. The results show that particles are slow down and captured under the influence of magnetic force, which is responsible to attract the magnetic particles towards the magnet. It is optimized that all particles are captured either before or at the centre of the magnet (z≤0) when blood vessel is very close proximity to the magnet (d=2.5 cm). However, as the distance between blood vessel and magnet (d) increases (above 4.5 cm), the magnetic nanoparticles particles become free and they flow away down the blood vessel. Further, the present model results are validated by the simulations performed using the finite element based COMSOL software. - Highlights: • A mathematical model is developed to describe the trajectories of magnetic nanoparticles. • The dominant magnetic, drag and buoyancy forces are considered. • All particles are captured when distance between blood vessel and magnet (d) is up to 4.5 cm. • Further increase in d value (above 4.5 cm) results the free movement of magnetic particles

  16. Linking Preservice Teachers' Mathematics Self-Efficacy and Mathematics Teaching Efficacy to Their Mathematical Performance

    Science.gov (United States)

    Bates, Alan B.; Latham, Nancy; Kim, Jin-ah

    2011-01-01

    This study examined preservice teachers' mathematics self-efficacy and mathematics teaching efficacy and compared them to their mathematical performance. Participants included 89 early childhood preservice teachers at a Midwestern university. Instruments included the Mathematics Self-Efficacy Scale (MSES), Mathematics Teaching Efficacy Beliefs…

  17. 40 CFR 35.938-4 - Formal advertising.

    Science.gov (United States)

    2010-07-01

    ... 40 Protection of Environment 1 2010-07-01 2010-07-01 false Formal advertising. 35.938-4 Section 35... advertising. Each contract shall be awarded after formal advertising, unless negotiation is permitted in accordance with § 35.936-18. Formal advertising shall be in accordance with the following: (a) Adequate...

  18. Seniority in projection operator formalism

    International Nuclear Information System (INIS)

    Ullah, N.

    1976-01-01

    It is shown that the concept of seniority can be introduced in projection operator formalism through the use of the operator Q, which has been defined by de-Shalit and Talmi. The usefulness of seniority concept in projection operator formalism is discussed. An example of four nucleons in j=3/2 configuration is given for illustrative purposes

  19. What Determines Firms’ Decisions to Formalize?

    OpenAIRE

    Neil McCulloch; Günther G. Schulze; Janina Voss

    2010-01-01

    In this paper we analyze the decision of small and micro firms to formalize, i.e. to obtain business and other licenses in rural Indonesia. We use the rural investment climate survey (RICS) that consists of non-farm rural enterprises, most of them microenterprises, and analyze the effect of formalization on tax payments, corruption, access to credit and revenue, taking into account the endogeneity of the formalization decision to such benefits and costs. We show, contrary to most of the liter...

  20. A new treatment planning formalism for catheter-based beta sources used in intravascular brachytherapy.

    Science.gov (United States)

    Patel, N S; Chiu-Tsao, S T; Tsao, H S; Harrison, L B

    2001-01-01

    TG-60 formalism, respectively. The reference dose rate is identical to that recommended by TG-60. The distribution factor is intended to resemble the dose profile due to the spatial distribution of activity in the elongated beta source, and it is a modified Fermi-Dirac function in mathematical form. The utility of this formalism also includes the slow-varying nature of the modulation function, allowing for more accurate treatment planning calculations based on interpolation. The transverse dose function describes the exponential fall-off of the dose in the radial direction, and an exponential or a polynomial can fit it. Simultaneously, the decoupling nature of these dose-related quantities facilitates image-based 3D treatment planning calculations for long beta sources used in IVBT. The new formalism also supports the dosimetry involving multiple dwell positions required for lesions longer than the source length. An example of the utilization of this formalism is illustrated for a 90Y coil source in a carbon dioxide-filled balloon. The pertinent dosimetric parameters were generated and tabulated for future use.

  1. Contrasts in Mathematical Challenges in A-Level Mathematics and Further Mathematics, and Undergraduate Mathematics Examinations

    Science.gov (United States)

    Darlington, Ellie

    2014-01-01

    This article describes part of a study which investigated the role of questions in students' approaches to learning mathematics at the secondary-tertiary interface, focussing on the enculturation of students at the University of Oxford. Use of the Mathematical Assessment Task Hierarchy taxonomy revealed A-level Mathematics and Further Mathematics…

  2. Discrete Wigner formalism for qubits and noncontextuality of Clifford gates on qubit stabilizer states

    Science.gov (United States)

    Kocia, Lucas; Love, Peter

    2017-12-01

    We show that qubit stabilizer states can be represented by non-negative quasiprobability distributions associated with a Wigner-Weyl-Moyal formalism where Clifford gates are positive state-independent maps. This is accomplished by generalizing the Wigner-Weyl-Moyal formalism to three generators instead of two—producing an exterior, or Grassmann, algebra—which results in Clifford group gates for qubits that act as a permutation on the finite Weyl phase space points naturally associated with stabilizer states. As a result, a non-negative probability distribution can be associated with each stabilizer state's three-generator Wigner function, and these distributions evolve deterministically to one another under Clifford gates. This corresponds to a hidden variable theory that is noncontextual and local for qubit Clifford gates while Clifford (Pauli) measurements have a context-dependent representation. Equivalently, we show that qubit Clifford gates can be expressed as propagators within the three-generator Wigner-Weyl-Moyal formalism whose semiclassical expansion is truncated at order ℏ0 with a finite number of terms. The T gate, which extends the Clifford gate set to one capable of universal quantum computation, requires a semiclassical expansion of the propagator to order ℏ1. We compare this approach to previous quasiprobability descriptions of qubits that relied on the two-generator Wigner-Weyl-Moyal formalism and find that the two-generator Weyl symbols of stabilizer states result in a description of evolution under Clifford gates that is state-dependent, in contrast to the three-generator formalism. We have thus extended Wigner non-negative quasiprobability distributions from the odd d -dimensional case to d =2 qubits, which describe the noncontextuality of Clifford gates and contextuality of Pauli measurements on qubit stabilizer states.

  3. Factors predicting recall of mathematics terms by deaf students: implications for teaching.

    Science.gov (United States)

    Lang, Harry; Pagliaro, Claudia

    2007-01-01

    In this study of deaf high school students, imagery and familiarity were found to be the best predictors of geometry word recall, whereas neither concreteness nor signability of the terms was a significant predictor variable. Recall of high imagery terms was significantly better than for low imagery terms, and the same result was found for high- over low-familiarity and signability. Concrete terms were recalled significantly better than abstract terms. Geometry terms that could be represented with single signs were recalled significantly better than those that are usually fingerspelled or those represented by compound signs. Teachers with degrees and/or certification in mathematics had significantly higher self-ratings for the strongest predictor variables, imagery (visualization), and familiarity, as compared with those without such formal training. Based on these findings, implications for mathematics instruction, teacher education, and research are provided.

  4. Lifelong Learning to Empowerment: Beyond Formal Education

    Science.gov (United States)

    Carr, Alexis; Balasubramanian, K.; Atieno, Rosemary; Onyango, James

    2018-01-01

    This paper discusses the relevance of lifelong learning vis-à-vis the Sustainable Development Goals (SDGs) and stresses the need for an approach blending formal education, non-formal and informal learning. The role of Open and Distance Learning (ODL) in moving beyond formal education and the importance of integrating pedagogy, andragogy and…

  5. Fraction magnitude understanding and its unique role in predicting general mathematics achievement at two early stages of fraction instruction.

    Science.gov (United States)

    Liu, Yingyi

    2017-09-08

    Prior studies on fraction magnitude understanding focused mainly on students with relatively sufficient formal instruction on fractions whose fraction magnitude understanding is relatively mature. This study fills a research gap by investigating fraction magnitude understanding in the early stages of fraction instruction. It extends previous findings to children with limited and primary formal fraction instruction. Thirty-five fourth graders with limited fraction instruction and forty fourth graders with primary fraction instruction were recruited from a Chinese primary school. Children's fraction magnitude understanding was assessed with a fraction number line estimation task. Approximate number system (ANS) acuity was assessed with a dot discrimination task. Whole number knowledge was assessed with a whole number line estimation task. General reading and mathematics achievements were collected concurrently and 1 year later. In children with limited fraction instruction, fraction representation was linear and fraction magnitude understanding was concurrently related to both ANS and whole number knowledge. In children with primary fraction instruction, fraction magnitude understanding appeared to (marginally) significantly predict general mathematics achievement 1 year later. Fraction magnitude understanding emerged early during formal instruction of fractions. ANS and whole number knowledge were related to fraction magnitude understanding when children first began to learn about fractions in school. The predictive value of fraction magnitude understanding is likely constrained by its sophistication level. © 2017 The British Psychological Society.

  6. The Higgs mechanism in a covariant-gauge formalism

    International Nuclear Information System (INIS)

    Yokoyama, Kan-ichi; Kubo, Reijiro.

    1975-02-01

    In a covariant-gauge formalism for gauge fields the Higgs mechanism is investigated under a spontaneous breakdown of gauge invariance. It is shown that the Goldstone bosons are in general described by a dipole-ghost field and can be consistently eliminated from the physical state-vector space by supplementary conditions. By an asymptotic condition for the relevant fields, field equations and commutators of asymptotic fields are determined. A renormalization problem and an aspect concerning gauge transformations are also discussed. (auth.)

  7. Formal Model-Driven Engineering: Generating Data and Behavioural Components

    Directory of Open Access Journals (Sweden)

    Chen-Wei Wang

    2012-12-01

    Full Text Available Model-driven engineering is the automatic production of software artefacts from abstract models of structure and functionality. By targeting a specific class of system, it is possible to automate aspects of the development process, using model transformations and code generators that encode domain knowledge and implementation strategies. Using this approach, questions of correctness for a complex, software system may be answered through analysis of abstract models of lower complexity, under the assumption that the transformations and generators employed are themselves correct. This paper shows how formal techniques can be used to establish the correctness of model transformations used in the generation of software components from precise object models. The source language is based upon existing, formal techniques; the target language is the widely-used SQL notation for database programming. Correctness is established by giving comparable, relational semantics to both languages, and checking that the transformations are semantics-preserving.

  8. Formal Symplectic Groupoid of a Deformation Quantization

    Science.gov (United States)

    Karabegov, Alexander V.

    2005-08-01

    We give a self-contained algebraic description of a formal symplectic groupoid over a Poisson manifold M. To each natural star product on M we then associate a canonical formal symplectic groupoid over M. Finally, we construct a unique formal symplectic groupoid ‘with separation of variables’ over an arbitrary Kähler-Poisson manifold.

  9. Mathematical literacy of school leaving pupils in South Africa

    NARCIS (Netherlands)

    Howie, S.; Plomp, T.

    2002-01-01

    This paper discusses some results of South African (SA) grade 12 pupils on an international test of mathematical literacy, administered in the framework of the Third International Mathematics and Science Study (TIMSS) under the auspices of the International Association for the Evaluation of

  10. multiPDEVS: A Parallel Multicomponent System Specification Formalism

    Directory of Open Access Journals (Sweden)

    Damien Foures

    2018-01-01

    Full Text Available Based on multiDEVS formalism, we introduce multiPDEVS, a parallel and nonmodular formalism for discrete event system specification. This formalism provides combined advantages of PDEVS and multiDEVS approaches, such as excellent simulation capabilities for simultaneously scheduled events and components able to influence each other using exclusively their state transitions. We next show the soundness of the formalism by giving a construction showing that any multiPDEVS model is equivalent to a PDEVS atomic model. We then present the simulation procedure associated, usually called abstract simulator. As a well-adapted formalism to express cellular automata, we finally propose to compare an implementation of multiPDEVS formalism with a more classical Cell-DEVS implementation through a fire spread application.

  11. Using Mathematics Literature with Prospective Secondary Mathematics Teachers

    Science.gov (United States)

    Jett, Christopher C.

    2014-01-01

    Literature in mathematics has been found to foster positive improvements in mathematics learning. This manuscript reports on a mathematics teacher educator's use of literature via literature circles with 11 prospective secondary mathematics teachers in a mathematics content course. Using survey and reflection data, the author found that…

  12. Mathematical Biology Modules Based on Modern Molecular Biology and Modern Discrete Mathematics

    Science.gov (United States)

    Robeva, Raina; Davies, Robin; Hodge, Terrell; Enyedi, Alexander

    2010-01-01

    We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to…

  13. Practical Formal Verification of MPI and Thread Programs

    Science.gov (United States)

    Gopalakrishnan, Ganesh; Kirby, Robert M.

    Large-scale simulation codes in science and engineering are written using the Message Passing Interface (MPI). Shared memory threads are widely used directly, or to implement higher level programming abstractions. Traditional debugging methods for MPI or thread programs are incapable of providing useful formal guarantees about coverage. They get bogged down in the sheer number of interleavings (schedules), often missing shallow bugs. In this tutorial we will introduce two practical formal verification tools: ISP (for MPI C programs) and Inspect (for Pthread C programs). Unlike other formal verification tools, ISP and Inspect run directly on user source codes (much like a debugger). They pursue only the relevant set of process interleavings, using our own customized Dynamic Partial Order Reduction algorithms. For a given test harness, DPOR allows these tools to guarantee the absence of deadlocks, instrumented MPI object leaks and communication races (using ISP), and shared memory races (using Inspect). ISP and Inspect have been used to verify large pieces of code: in excess of 10,000 lines of MPI/C for ISP in under 5 seconds, and about 5,000 lines of Pthread/C code in a few hours (and much faster with the use of a cluster or by exploiting special cases such as symmetry) for Inspect. We will also demonstrate the Microsoft Visual Studio and Eclipse Parallel Tools Platform integrations of ISP (these will be available on the LiveCD).

  14. On the growth and dissemination laws in a mathematical model of metastatic growth

    Directory of Open Access Journals (Sweden)

    Benzekry Sébastien

    2015-01-01

    Full Text Available Metastasis represents one of the main clinical challenge in cancer treatment since it is associated with the majority of deaths. Recent technological advances allow quantification of the dynamics of the process by means of noninvasive techniques such as longitudinal tracking of bioluminescent cells. The metastatic process was simplified here into two essential components – dissemination and colonization – which were mathematically formalized in terms of simple quantitative laws. The resulting mathematical model was confronted to in vivo experimental data of spontaneous metastasis after primary tumor resection. We discuss how much information can be inferred from confrontation of theories to the data with emphasis on identifiability issues. It is shown that two mutually exclusive assumptions for the secondary growth law (namely same or different from the primary tumor growth law could fit equally well the data. Similarly, the fractal dimension coeffcient in the dissemination law could not be uniquely determined from data on total metastatic burden only. Together, these results delimitate the range of information that can be recovered from fitting data of metastatic growth to already simplified mathematical models.

  15. Decision making under uncertainty: An investigation into the application of formal decision-making methods to safety issue decisions

    International Nuclear Information System (INIS)

    Bohn, M.P.

    1992-12-01

    As part of the NRC-sponsored program to study the implications of Generic Issue 57, ''Effects of Fire Protection System Actuation on Safety-Related Equipment,'' a subtask was performed to evaluate the applicability of formal decision analysis methods to generic issues cost/benefit-type decisions and to apply these methods to the GI-57 results. In this report, the numerical results obtained from the analysis of three plants (two PWRs and one BWR) as developed in the technical resolution program for GI-57 were studied. For each plant, these results included a calculation of the person-REM averted due to various accident scenarios and various proposed modifications to mitigate the accident scenarios identified. These results were recomputed to break out the benefit in terms of contributions due to random event scenarios, fire event scenarios, and seismic event scenarios. Furthermore, the benefits associated with risk (in terms of person-REM) averted from earthquakes at three different seismic ground motion levels were separately considered. Given this data, formal decision methodologies involving decision trees, value functions, and utility functions were applied to this basic data. It is shown that the formal decision methodology can be applied at several different levels. Examples are given in which the decision between several retrofits is changed from that resulting from a simple cost/benefit-ratio criterion by virtue of the decision-makinger's expressed (and assumed) preferences

  16. Bridging In-school and Out-of-school Learning: Formal, Non-Formal, and Informal Education

    Science.gov (United States)

    Eshach, Haim

    2007-04-01

    The present paper thoroughly examines how one can effectively bridge in-school and out-of-school learning. The first part discusses the difficulty in defining out-of-school learning. It proposes to distinguish three types of learning: formal, informal, and non-formal. The second part raises the question of whether out-of-school learning should be dealt with in the in-school system, in view of the fact that we experience informal learning anyway as well as considering the disadvantages and difficulties teachers are confronted with when planning and carrying out scientific fieldtrips. The voices of the teachers, the students, and the non-formal institution staff are heard to provide insights into the problem. The third part discusses the cognitive and affective aspects of non-formal learning. The fourth part presents some models explaining scientific fieldtrip learning and based on those models, suggests a novel explanation. The fifth part offers some recommendations of how to bridge in and out-of-school learning. The paper closes with some practical ideas as to how one can bring the theory described in the paper into practice. It is hoped that this paper will provide educators with an insight so that they will be able to fully exploit the great potential that scientific field trips may offer.

  17. Toward a formal ontology for narrative

    Directory of Open Access Journals (Sweden)

    Ciotti, Fabio

    2016-03-01

    Full Text Available In this paper the rationale and the first draft of a formal ontology for modeling narrative texts are presented. Building on the semiotic and structuralist narratology, and on the work carried out in the late 1980s by Giuseppe Gigliozzi in Italy, the focus of my research are the concepts of character and of narrative world/space. This formal model is expressed in the OWL 2 ontology language. The main reason to adopt a formal modeling approach is that I consider the purely probabilistic-quantitative methods (now widespread in digital literary studies inadequate. An ontology, on one hand provides a tool for the analysis of strictly literary texts. On the other hand (though beyond the scope of the present work, its formalization can also represent a significant contribution towards grounding the application of storytelling methods outside of scholarly contexts.

  18. Industrial Practice in Formal Methods : A Review

    DEFF Research Database (Denmark)

    Bicarregui, Juan C.; Fitzgerald, John; Larsen, Peter Gorm

    2009-01-01

    We examine the the industrial application of formal methods using data gathered in a review of 62 projects taking place over the last 25 years. The review suggests that formal methods are being applied in a wide range of application domains, with increasingly strong tool support. Significant chal...... challenges remain in providing usable tools that can be integrated into established development processes; in education and training; in taking formal methods from first use to second use, and in gathering and evidence to support informed selection of methods and tools.......We examine the the industrial application of formal methods using data gathered in a review of 62 projects taking place over the last 25 years. The review suggests that formal methods are being applied in a wide range of application domains, with increasingly strong tool support. Significant...

  19. Socio-functional dynamics of the mathematical contents

    Directory of Open Access Journals (Sweden)

    Isabel Alonso-Berenguer

    2018-01-01

    Full Text Available The article presents a model of the socio-functional dynamics of the mathematical contents that offers a novel theoretical-methodological basement for the development of the process of teaching-learning of the mathematical one. The investigation, of theoretical character, used the methods of analysis-synthesis, inductive-deductive and historical-logical to elaborate the one mentioned model that leaves of considering that the future professors have appropriated previously of the mathematical contents, foreseen in the curriculum, and they are, therefore, under conditions of understanding the potentialities of the same ones to facilitate the formation of socio-functional values.   

  20. Doing Mathematics with Purpose: Mathematical Text Types

    Science.gov (United States)

    Dostal, Hannah M.; Robinson, Richard

    2018-01-01

    Mathematical literacy includes learning to read and write different types of mathematical texts as part of purposeful mathematical meaning making. Thus in this article, we describe how learning to read and write mathematical texts (proof text, algorithmic text, algebraic/symbolic text, and visual text) supports the development of students'…

  1. Annual Perspectives in Mathematics Education 2016: Mathematical Modeling and Modeling Mathematics

    Science.gov (United States)

    Hirsch, Christian R., Ed.; McDuffie, Amy Roth, Ed.

    2016-01-01

    Mathematical modeling plays an increasingly important role both in real-life applications--in engineering, business, the social sciences, climate study, advanced design, and more--and within mathematics education itself. This 2016 volume of "Annual Perspectives in Mathematics Education" ("APME") focuses on this key topic from a…

  2. Universal uncertainty principle in the measurement operator formalism

    International Nuclear Information System (INIS)

    Ozawa, Masanao

    2005-01-01

    Heisenberg's uncertainty principle has been understood to set a limitation on measurements; however, the long-standing mathematical formulation established by Heisenberg, Kennard, and Robertson does not allow such an interpretation. Recently, a new relation was found to give a universally valid relation between noise and disturbance in general quantum measurements, and it has become clear that the new relation plays a role of the first principle to derive various quantum limits on measurement and information processing in a unified treatment. This paper examines the above development on the noise-disturbance uncertainty principle in the model-independent approach based on the measurement operator formalism, which is widely accepted to describe a class of generalized measurements in the field of quantum information. We obtain explicit formulae for the noise and disturbance of measurements given by measurement operators, and show that projective measurements do not satisfy the Heisenberg-type noise-disturbance relation that is typical in the gamma-ray microscope thought experiments. We also show that the disturbance on a Pauli operator of a projective measurement of another Pauli operator constantly equals √2, and examine how this measurement violates the Heisenberg-type relation but satisfies the new noise-disturbance relation

  3. Principles of mathematical modeling

    CERN Document Server

    Dym, Clive

    2004-01-01

    Science and engineering students depend heavily on concepts of mathematical modeling. In an age where almost everything is done on a computer, author Clive Dym believes that students need to understand and "own" the underlying mathematics that computers are doing on their behalf. His goal for Principles of Mathematical Modeling, Second Edition, is to engage the student reader in developing a foundational understanding of the subject that will serve them well into their careers. The first half of the book begins with a clearly defined set of modeling principles, and then introduces a set of foundational tools including dimensional analysis, scaling techniques, and approximation and validation techniques. The second half demonstrates the latest applications for these tools to a broad variety of subjects, including exponential growth and decay in fields ranging from biology to economics, traffic flow, free and forced vibration of mechanical and other systems, and optimization problems in biology, structures, an...

  4. Formalization of the Resolution Calculus for First-Order Logic

    DEFF Research Database (Denmark)

    Schlichtkrull, Anders

    2016-01-01

    A formalization in Isabelle/HOL of the resolution calculus for first-order logic is presented. Its soundness and completeness are formally proven using the substitution lemma, semantic trees, Herbrand’s theorem, and the lifting lemma. In contrast to previous formalizations of resolution, it consi......A formalization in Isabelle/HOL of the resolution calculus for first-order logic is presented. Its soundness and completeness are formally proven using the substitution lemma, semantic trees, Herbrand’s theorem, and the lifting lemma. In contrast to previous formalizations of resolution...

  5. Mathematical modelling of the destruction degree of cancer under the influence of a RF hyperthermia

    Science.gov (United States)

    Paruch, Marek; Turchan, Łukasz

    2018-01-01

    The article presents the mathematical modeling of the phenomenon of artificial hyperthermia which is caused by the interaction of an electric field. The electric field is induced by the applicator positioned within the biological tissue with cancer. In addition, in order to estimate the degree of tumor destruction under the influence of high temperature an Arrhenius integral has been used. The distribution of electric potential in the domain considered is described by the Laplace system of equations, while the temperature field is described by the Pennes system of equations. These problems are coupled by source function being the additional component in the Pennes equation and resulting from the electric field action. The boundary element method is applied to solve the coupled problem connected with the heating of biological tissues.

  6. First formal ITER negotiations make excellent progress

    International Nuclear Information System (INIS)

    Barnard, P.

    2001-01-01

    November 8 and 9 2001 marked the historic beginning of formal negotiations meetings on the ITER project. Delegations from Canada, the European Union, Japan and the Russian Federation met in Toronto, Canada, for the first in a series of Negotiations that is expected to lead, by the end of 2002, to an agreement on the joint implementation of ITER. This agreement will govern, under international law, the construction, operation and decommissioning of ITER. The Negotiations concluded by issuing a joint news release, reflecting a commitment to share the progress reports on the efforts to implement ITER

  7. A Formal Calculus for Categories

    DEFF Research Database (Denmark)

    Cáccamo, Mario José

    This dissertation studies the logic underlying category theory. In particular we present a formal calculus for reasoning about universal properties. The aim is to systematise judgements about functoriality and naturality central to categorical reasoning. The calculus is based on a language which...... extends the typed lambda calculus with new binders to represent universal constructions. The types of the languages are interpreted as locally small categories and the expressions represent functors. The logic supports a syntactic treatment of universality and duality. Contravariance requires a definition...... of universality generous enough to deal with functors of mixed variance. Ends generalise limits to cover these kinds of functors and moreover provide the basis for a very convenient algebraic manipulation of expressions. The equational theory of the lambda calculus is extended with new rules for the definitions...

  8. A multi-region multi-energy formalism for the Feynman-alpha formulas

    International Nuclear Information System (INIS)

    Malinovitch, T.; Dubi, C.

    2015-01-01

    Highlights: • A formalism of N regions and M groups for the Feynman-α method is introduced. • Using a space-energy cell notation the expressions are simplified significantly. • A simple way to incorporate the detectors in the system is used. • The results have been verified by a Monte Carlo simulation in a two-region case. - Abstract: The stochastic transport equation, describing the dynamics in time of the neutron population in a nuclear system, is used to gain expressions for the higher moments of the neutron population in a sub-critical system. Such expressions are the bone structure of the so called Feynman-α method to analyze noise experiments, aimed to determine the reactivity of sub-critical systems. In the present study, a general formalism for the stochastic transport equation in an N regions system, under the M energy groups approximation will be introduced. In particular, expressions for the Feynman variance to mean (or the Feynman-Y function) under the above mentioned restriction will be sought by using the steady state mode of the solution

  9. Math Anxiety in Second and Third Graders and Its Relation to Mathematics Achievement

    OpenAIRE

    Wu, Sarah S.; Barth, Maria; Amin, Hitha; Malcarne, Vanessa; Menon, Vinod

    2012-01-01

    Although the detrimental effects of math anxiety in adults are well understood, few studies have examined how it affects younger children who are beginning to learn math in a formal academic setting. Here, we examine the relationship between math anxiety and math achievement in second and third graders. In response to the need for a grade-appropriate measure of assessing math anxiety in this group we first describe the development of Scale for Early Mathematics Anxiety (SEMA), a new measure f...

  10. Formalizing Evaluation in Music Information Retrieval

    DEFF Research Database (Denmark)

    Sturm, Bob L.

    2013-01-01

    We develop a formalism to disambiguate the evaluation of music information retrieval systems. We define a ``system,'' what it means to ``analyze'' one, and make clear the aims, parts, design, execution, interpretation, and assumptions of its ``evaluation.'' We apply this formalism to discuss...

  11. A computational formalization for partial evaluation

    DEFF Research Database (Denmark)

    Hatcliff, John; Danvy, Olivier

    1997-01-01

    We formalize a partial evaluator for Eugenio Moggi's computational metalanguage. This formalization gives an evaluation-order independent view of binding-time analysis and program specialization, including a proper treatment of call unfolding. It also enables us to express the essence of `control...

  12. Informal work and formal plans

    DEFF Research Database (Denmark)

    Dalsted, Rikke Juul; Hølge-Hazelton, Bibi; Kousgaard, Marius Brostrøm

    2012-01-01

    INTRODUCTION: Formal pathways models outline that patients should receive information in order to experience a coherent journey but do not describe an active role for patients or their relatives. The aim of this is paper is to articulate and discuss the active role of patients during their cancer...... trajectories. METHODS AND THEORY: An in-depth case study of patient trajectories at a Danish hospital and surrounding municipality using individual interviews with patients. Theory about trajectory and work by Strauss was included. RESULTS: Patients continuously took initiatives to organize their treatment....... The patients' requests were not sufficiently supported in the professional organisation of work or formal planning. Patients' insertion and use of information in their trajectories challenged professional views and working processes. And the design of the formal pathway models limits the patients' active...

  13. Formalisms for reuse and systems integration

    CERN Document Server

    Rubin, Stuart

    2015-01-01

    Reuse and integration are defined as synergistic concepts, where reuse addresses how to minimize redundancy in the creation of components; while, integration focuses on component composition. Integration supports reuse and vice versa. These related concepts support the design of software and systems for maximizing performance while minimizing cost. Knowledge, like data, is subject to reuse; and, each can be interpreted as the other. This means that inherent complexity, a measure of the potential utility of a system, is directly proportional to the extent to which it maximizes reuse and integration. Formal methods can provide an appropriate context for the rigorous handling of these synergistic concepts. Furthermore, formal languages allow for non ambiguous model specification; and, formal verification techniques provide support for insuring the validity of reuse and integration mechanisms.   This edited book includes 12 high quality research papers written by experts in formal aspects of reuse and integratio...

  14. Math anxiety in second and third graders and its relation to mathematics achievement.

    Science.gov (United States)

    Wu, Sarah S; Barth, Maria; Amin, Hitha; Malcarne, Vanessa; Menon, Vinod

    2012-01-01

    Although the detrimental effects of math anxiety in adults are well understood, few studies have examined how it affects younger children who are beginning to learn math in a formal academic setting. Here, we examine the relationship between math anxiety and math achievement in second and third graders. In response to the need for a grade-appropriate measure of assessing math anxiety in this group we first describe the development of Scale for Early Mathematics Anxiety (SEMA), a new measure for assessing math anxiety in second and third graders that is based on the Math Anxiety Rating Scale. We demonstrate the construct validity and reliability of the SEMA and use it to characterize the effect of math anxiety on standardized measures of math abilities, as assessed using the Mathematical Reasoning and Numerical Operations subtests of the Wechsler Individual Achievement Test (WIAT-II). Math achievement, as measured by the WIAT-II Math Composite score, was significantly and negatively correlated with SEMA but not with trait anxiety scores. Additional analyses showed that SEMA scores were strongly correlated with Mathematical Reasoning scores, which involves more complex verbal problem solving. SEMA scores were weakly correlated with Numerical Operations which assesses basic computation skills, suggesting that math anxiety has a pronounced effect on more demanding calculations. We also found that math anxiety has an equally detrimental impact on math achievement regardless of whether children have an anxiety related to numbers or to the situational and social experience of doing math. Critically, these effects were unrelated to trait anxiety, providing the first evidence that the specific effects of math anxiety can be detected in the earliest stages of formal math learning in school. Our findings provide new insights into the developmental origins of math anxiety, and further underscore the need to remediate math anxiety and its deleterious effects on math achievement

  15. Formal Methods in Air Traffic Management: The Case of Unmanned Aircraft Systems

    Science.gov (United States)

    Munoz, Cesar A.

    2015-01-01

    As the technological and operational capabilities of unmanned aircraft systems (UAS) continue to grow, so too does the need to introduce these systems into civil airspace. Unmanned Aircraft Systems Integration in the National Airspace System is a NASA research project that addresses the integration of civil UAS into non-segregated airspace operations. One of the major challenges of this integration is the lack of an onboard pilot to comply with the legal requirement that pilots see and avoid other aircraft. The need to provide an equivalent to this requirement for UAS has motivated the development of a detect and avoid (DAA) capability to provide the appropriate situational awareness and maneuver guidance in avoiding and remaining well clear of traffic aircraft. Formal methods has played a fundamental role in the development of this capability. This talk reports on the formal methods work conducted under NASA's Safe Autonomous System Operations project in support of the development of DAA for UAS. This work includes specification of low-level and high-level functional requirements, formal verification of algorithms, and rigorous validation of software implementations. The talk also discusses technical challenges in formal methods research in the context of the development and safety analysis of advanced air traffic management concepts.

  16. Model-Based Design and Formal Verification Processes for Automated Waterway System Operations

    Directory of Open Access Journals (Sweden)

    Leonard Petnga

    2016-06-01

    Full Text Available Waterway and canal systems are particularly cost effective in the transport of bulk and containerized goods to support global trade. Yet, despite these benefits, they are among the most under-appreciated forms of transportation engineering systems. Looking ahead, the long-term view is not rosy. Failures, delays, incidents and accidents in aging waterway systems are doing little to attract the technical and economic assistance required for modernization and sustainability. In a step toward overcoming these challenges, this paper argues that programs for waterway and canal modernization and sustainability can benefit significantly from system thinking, supported by systems engineering techniques. We propose a multi-level multi-stage methodology for the model-based design, simulation and formal verification of automated waterway system operations. At the front-end of development, semi-formal modeling techniques are employed for the representation of project goals and scenarios, requirements and high-level models of behavior and structure. To assure the accuracy of engineering predictions and the correctness of operations, formal modeling techniques are used for the performance assessment and the formal verification of the correctness of functionality. The essential features of this methodology are highlighted in a case study examination of ship and lock-system behaviors in a two-stage lock system.

  17. A mathematical medley fifty easy pieces on mathematics

    CERN Document Server

    Szpiro, George G

    2010-01-01

    Szpiro's book provides a delightful, well-written, eclectic selection of mathematical tidbits that makes excellent airplane reading for anyone with an interest in mathematics, regardless of their mathematical background. Excellent gift material. -Keith Devlin, Stanford University, author of The Unfinished Game and The Language of Mathematics It is great to have collected in one volume the many varied, insightful and often surprising mathematical stories that George Szpiro has written in his mathematical columns for the newspapers through the years. -Marcus du Sautoy, Oxford University, author

  18. Formal Engineering Hybrid Systems: Semantic Underpinnings

    NARCIS (Netherlands)

    Bujorianu, M.C.; Bujorianu, L.M.

    2008-01-01

    In this work we investigate some issues in applying formal methods to hybrid system development and develop a categorical framework. We study the themes of stochastic reasoning, heterogeneous formal specification and retrenchment. Hybrid systems raise a rich pallets of aspects that need to be

  19. History of mathematics and history of science reunited?

    Science.gov (United States)

    Gray, Jeremy

    2011-09-01

    For some years now, the history of modern mathematics and the history of modern science have developed independently. A step toward a reunification that would benefit both disciplines could come about through a revived appreciation of mathematical practice. Detailed studies of what mathematicians actually do, whether local or broadly based, have often led in recent work to examinations of the social, cultural, and national contexts, and more can be done. Another recent approach toward a historical understanding of the abstractness of modern mathematics has been to see it as a species of modernism, and this thesis will be tested by the raft of works on the history of modern applied mathematics currently under way.

  20. Formal Analysis Of Use Case Diagrams

    Directory of Open Access Journals (Sweden)

    Radosław Klimek

    2010-01-01

    Full Text Available Use case diagrams play an important role in modeling with UML. Careful modeling is crucialin obtaining a correct and efficient system architecture. The paper refers to the formalanalysis of the use case diagrams. A formal model of use cases is proposed and its constructionfor typical relationships between use cases is described. Two methods of formal analysis andverification are presented. The first one based on a states’ exploration represents a modelchecking approach. The second one refers to the symbolic reasoning using formal methodsof temporal logic. Simple but representative example of the use case scenario verification isdiscussed.

  1. The Relationship among Elementary Teachers’ Mathematics Anxiety, Mathematics Instructional Practices, and Student Mathematics Achievement

    OpenAIRE

    Hadley, Kristin M.; Dorward, Jim

    2011-01-01

    Many elementary teachers have been found to have high levels of mathematics anxiety but the impact on student achievement was unknown. Elementary teachers (N = 692) completed the modified Mathematics Anxiety Rating Scale-Revised (Hopko, 2003) along with a questionnaire probing anxiety about teaching mathematics and current mathematics instructional practices. Student mathematics achievement data were collected for the classrooms taught by the teachers. A positive relationship was found betwee...

  2. Learning Mathematics with Creative Drama

    Directory of Open Access Journals (Sweden)

    Baki Şahin

    2018-04-01

    Full Text Available In this study, a mathematics activity that used creative drama method to teach the fifth grade standard “Expresses a position with respect to another point using direction and unit” under geometry and measurement was implemented. Twenty students attending the fifth grade of a public school participated in the study. The lesson plan involved four activities in warm-up, role-play, and evaluation stages. Activities include processes that will ensure active participation of students. The activity lasted two lesson hours. Two prospective mathematics teachers and a mathematics teacher were available in the class during the activity to observe student participation and reactions. Additionally, 10 students were interviewed to learn their views about the lesson. Comments of the observers and the responses of the students to the interview questions indicate that the lesson was successful.

  3. Competence with fractions predicts gains in mathematics achievement.

    Science.gov (United States)

    Bailey, Drew H; Hoard, Mary K; Nugent, Lara; Geary, David C

    2012-11-01

    Competence with fractions predicts later mathematics achievement, but the codevelopmental pattern between fractions knowledge and mathematics achievement is not well understood. We assessed this codevelopment through examination of the cross-lagged relation between a measure of conceptual knowledge of fractions and mathematics achievement in sixth and seventh grades (N=212). The cross-lagged effects indicated that performance on the sixth grade fractions concepts measure predicted 1-year gains in mathematics achievement (ß=.14, pmathematics achievement did not predict gains on the fractions concepts measure (ß=.03, p>.50). In a follow-up assessment, we demonstrated that measures of fluency with computational fractions significantly predicted seventh grade mathematics achievement above and beyond the influence of fluency in computational whole number arithmetic, performance on number fluency and number line tasks, central executive span, and intelligence. Results provide empirical support for the hypothesis that competence with fractions underlies, in part, subsequent gains in mathematics achievement. Copyright © 2012 Elsevier Inc. All rights reserved.

  4. Hybrid modelling framework by using mathematics-based and information-based methods

    International Nuclear Information System (INIS)

    Ghaboussi, J; Kim, J; Elnashai, A

    2010-01-01

    Mathematics-based computational mechanics involves idealization in going from the observed behaviour of a system into mathematical equations representing the underlying mechanics of that behaviour. Idealization may lead mathematical models that exclude certain aspects of the complex behaviour that may be significant. An alternative approach is data-centric modelling that constitutes a fundamental shift from mathematical equations to data that contain the required information about the underlying mechanics. However, purely data-centric methods often fail for infrequent events and large state changes. In this article, a new hybrid modelling framework is proposed to improve accuracy in simulation of real-world systems. In the hybrid framework, a mathematical model is complemented by information-based components. The role of informational components is to model aspects which the mathematical model leaves out. The missing aspects are extracted and identified through Autoprogressive Algorithms. The proposed hybrid modelling framework has a wide range of potential applications for natural and engineered systems. The potential of the hybrid methodology is illustrated through modelling highly pinched hysteretic behaviour of beam-to-column connections in steel frames.

  5. Computer programming in the UK undergraduate mathematics curriculum

    Science.gov (United States)

    Sangwin, Christopher J.; O'Toole, Claire

    2017-11-01

    This paper reports a study which investigated the extent to which undergraduate mathematics students in the United Kingdom are currently taught to programme a computer as a core part of their mathematics degree programme. We undertook an online survey, with significant follow-up correspondence, to gather data on current curricula and received replies from 46 (63%) of the departments who teach a BSc mathematics degree. We found that 78% of BSc degree courses in mathematics included computer programming in a compulsory module but 11% of mathematics degree programmes do not teach programming to all their undergraduate mathematics students. In 2016, programming is most commonly taught to undergraduate mathematics students through imperative languages, notably MATLAB, using numerical analysis as the underlying (or parallel) mathematical subject matter. Statistics is a very popular choice in optional courses, using the package R. Computer algebra systems appear to be significantly less popular for compulsory first-year courses than a decade ago, and there was no mention of logic programming, functional programming or automatic theorem proving software. The modal form of assessment of computing modules is entirely by coursework (i.e. no examination).

  6. The language of mathematics telling mathematical tales

    CERN Document Server

    Barton, Bill

    2008-01-01

    Everyday mathematical ideas are expressed differently in different languages. This book probes those differences and explores their implications for mathematics education, arguing for alternatives to how we teach and learn mathematics.

  7. Formal balancing of chemical reaction networks

    NARCIS (Netherlands)

    van der Schaft, Abraham; Rao, S.; Jayawardhana, B.

    2016-01-01

    In this paper we recall and extend the main results of Van der Schaft, Rao, Jayawardhana (2015) concerning the use of Kirchhoff’s Matrix Tree theorem in the explicit characterization of complex-balanced reaction networks and the notion of formal balancing. The notion of formal balancing corresponds

  8. Statistical Survey of Non-Formal Education

    Directory of Open Access Journals (Sweden)

    Ondřej Nývlt

    2012-12-01

    Full Text Available focused on a programme within a regular education system. Labour market flexibility and new requirements on employees create a new domain of education called non-formal education. Is there a reliable statistical source with a good methodological definition for the Czech Republic? Labour Force Survey (LFS has been the basic statistical source for time comparison of non-formal education for the last ten years. Furthermore, a special Adult Education Survey (AES in 2011 was focused on individual components of non-formal education in a detailed way. In general, the goal of the EU is to use data from both internationally comparable surveys for analyses of the particular fields of lifelong learning in the way, that annual LFS data could be enlarged by detailed information from AES in five years periods. This article describes reliability of statistical data aboutnon-formal education. This analysis is usually connected with sampling and non-sampling errors.

  9. On Mathematical Anti-Evolutionism

    Science.gov (United States)

    Rosenhouse, Jason

    2016-03-01

    The teaching of evolution in American high schools has long been a source of controversy. The past decade has seen an important shift in the rhetoric of anti-evolutionists, toward arguments of a strongly mathematical character. These mathematical arguments, while different in their specifics, follow the same general program and rely on the same underlying model of evolution. We shall discuss the nature and history of this program and model and describe general reasons for skepticism with regard to any anti-evolutionary arguments based upon them. We shall then survey the major arguments used by anti-evolutionists, to show how our general considerations make it possible to quickly identify their weakest points.

  10. Mathematical Modelling Approach in Mathematics Education

    Science.gov (United States)

    Arseven, Ayla

    2015-01-01

    The topic of models and modeling has come to be important for science and mathematics education in recent years. The topic of "Modeling" topic is especially important for examinations such as PISA which is conducted at an international level and measures a student's success in mathematics. Mathematical modeling can be defined as using…

  11. Mathematics Underground

    Science.gov (United States)

    Luther, Kenneth H.

    2012-01-01

    Mathematical modeling of groundwater flow is a topic at the intersection of mathematics and geohydrology and is rarely encountered in undergraduate mathematics. However, this subject is full of interesting and meaningful examples of truly "applied" mathematics accessible to undergraduates, from the pre-calculus to advanced mathematics levels. This…

  12. Three essays in mathematical finance

    Science.gov (United States)

    Wang, Ruming

    This dissertation uses mathematical techniques to solve three problems in mathematical finance. The first two problems are on model-independent pricing and hedging of financial derivatives. We use asymptotic expansions to express derivative prices and implied volatilities. Then just by using the first few terms in the expansions, we get simple and accurate formulas, which can also help us find connections between different products. The last problem is on optimal trading strategies in a limit order book. Under a very general setup, we solve explicitly for a dynamic decision problem involving choosing between limit order and market order.

  13. Mathematical Rigor in Introductory Physics

    Science.gov (United States)

    Vandyke, Michael; Bassichis, William

    2011-10-01

    Calculus-based introductory physics courses intended for future engineers and physicists are often designed and taught in the same fashion as those intended for students of other disciplines. A more mathematically rigorous curriculum should be more appropriate and, ultimately, more beneficial for the student in his or her future coursework. This work investigates the effects of mathematical rigor on student understanding of introductory mechanics. Using a series of diagnostic tools in conjunction with individual student course performance, a statistical analysis will be performed to examine student learning of introductory mechanics and its relation to student understanding of the underlying calculus.

  14. The Effect of Teacher Beliefs on Student Competence in Mathematical Modeling--An Intervention Study

    Science.gov (United States)

    Mischo, Christoph; Maaß, Katja

    2013-01-01

    This paper presents an intervention study whose aim was to promote teacher beliefs about mathematics and learning mathematics and student competences in mathematical modeling. In the intervention, teachers received written curriculum materials about mathematical modeling. The concept underlying the materials was based on constructivist ideas and…

  15. Mathematical bridges

    CERN Document Server

    Andreescu, Titu; Tetiva, Marian

    2017-01-01

    Building bridges between classical results and contemporary nonstandard problems, Mathematical Bridges embraces important topics in analysis and algebra from a problem-solving perspective. Blending old and new techniques, tactics and strategies used in solving challenging mathematical problems, readers will discover numerous genuine mathematical gems throughout that will heighten their appreciation of the inherent beauty of mathematics. Most of the problems are original to the authors and are intertwined in a well-motivated exposition driven by representative examples. The book is structured to assist the reader in formulating and proving conjectures, as well as devising solutions to important mathematical problems by making connections between various concepts and ideas from different areas of mathematics. Instructors and educators teaching problem-solving courses or organizing mathematics clubs, as well as motivated mathematics students from high school juniors to college seniors, will find Mathematical Bri...

  16. Exploring mathematics anxiety and attitude: Mathematics students' experiences

    Science.gov (United States)

    Sahri, Nurul Ashikin; Kamaruzaman, Wan Nur Farahdalila Wan; Jamil, Jastini Mohd.; Shaharanee, Izwan Nizal Mohd.

    2017-11-01

    A quantitative and correlational, survey methods were used to investigate the relationships among mathematical anxiety and attitude toward student's mathematics performance. Participants were 100 students volunteer to enroll in undergraduate Industrial Statistics, Decision Sciences and Business Mathematics at one of northern university in Malaysia. Survey data consisted of demographic items and Likert scale items. The collected data was analyzed by using the idea of correlation and regression analysis. The results indicated that there was a significant positive relationship between students' attitude and mathematics anxiety. Results also indicated that a substantial positive effect of students' attitude and mathematics anxiety in students' achievement. Further study can be conducted on how mathematical anxiety and attitude toward mathematics affects can be used to predict the students' performance in the class.

  17. Formalization of Many-Valued Logics

    DEFF Research Database (Denmark)

    Villadsen, Jørgen; Schlichtkrull, Anders

    2017-01-01

    Partiality is a key challenge for computational approaches to artificial intelligence in general and natural language in particular. Various extensions of classical two-valued logic to many-valued logics have been investigated in order to meet this challenge. We use the proof assistant Isabelle...... to formalize the syntax and semantics of many-valued logics with determinate as well as indeterminate truth values. The formalization allows for a concise presentation and makes automated verification possible....

  18. Helicity formalism and spin effects

    International Nuclear Information System (INIS)

    Anselmino, M.; Caruso, F.; Piovano, U.

    1990-01-01

    The helicity formalism and the technique to compute amplitudes for interaction processes involving leptons, quarks, photons and gluons are reviewed. Explicit calculations and examples of exploitation of symmetry properties are shown. The formalism is then applied to the discussion of several hadronic processes and spin effects: the experimental data, when related to the properties of the elementary constituent interactions, show many not understood features. Also the nucleon spin problem is briefly reviewed. (author)

  19. Student’s scheme in solving mathematics problems

    Science.gov (United States)

    Setyaningsih, Nining; Juniati, Dwi; Suwarsono

    2018-03-01

    The purpose of this study was to investigate students’ scheme in solving mathematics problems. Scheme are data structures for representing the concepts stored in memory. In this study, we used it in solving mathematics problems, especially ratio and proportion topics. Scheme is related to problem solving that assumes that a system is developed in the human mind by acquiring a structure in which problem solving procedures are integrated with some concepts. The data were collected by interview and students’ written works. The results of this study revealed are students’ scheme in solving the problem of ratio and proportion as follows: (1) the content scheme, where students can describe the selected components of the problem according to their prior knowledge, (2) the formal scheme, where students can explain in construct a mental model based on components that have been selected from the problem and can use existing schemes to build planning steps, create something that will be used to solve problems and (3) the language scheme, where students can identify terms, or symbols of the components of the problem.Therefore, by using the different strategies to solve the problems, the students’ scheme in solving the ratio and proportion problems will also differ.

  20. A Capstone Mathematics Course for Prospective Secondary Mathematics Teachers

    Science.gov (United States)

    Artzt, Alice F.; Sultan, Alan; Curcio, Frances R.; Gurl, Theresa

    2012-01-01

    This article describes an innovative capstone mathematics course that links college mathematics with school mathematics and pedagogy. It describes how college juniors in a secondary mathematics teacher preparation program engage in leadership experiences that enable them to learn mathematics for teaching while developing student-centered…