Mathematical foundations of computed tomography

International Nuclear Information System (INIS)

Smith, K.T.; Keinert, F.

1985-01-01

Along with a review of some of the mathematical foundations of computed tomography, the article contains new results on derivation of reconstruction formulas in a general setting encompassing all standard formulas; discussion and examples of the role of the point spread function with recipes for producing suitable ones; formulas for, and examples of, the reconstruction of certain functions of the attenuation coefficient, e.g., sharpened versions of it, some of them with the property that reconstruction at a point requires only the attenuation along rays meeting a small neighborhood of the point

The mathematical model accuracy estimation of the oil storage tank foundation soil moistening

Science.gov (United States)

Gildebrandt, M. I.; Ivanov, R. N.; Gruzin, AV; Antropova, L. B.; Kononov, S. A.

2018-04-01

The oil storage tanks foundations preparation technologies improvement is the relevant objective which achievement will make possible to reduce the material costs and spent time for the foundation preparing while providing the required operational reliability. The laboratory research revealed the nature of sandy soil layer watering with a given amount of water. The obtained data made possible developing the sandy soil layer moistening mathematical model. The performed estimation of the oil storage tank foundation soil moistening mathematical model accuracy showed the experimental and theoretical results acceptable convergence.

Mathematical foundations of the projection-operator method

International Nuclear Information System (INIS)

Moore, S.M.

1979-01-01

Mathematical foundations are determined for the projection-operator method developed by Zwanzig and Mori and used in the study of cooperative phenomena in non-equilibrium processes. It is shown that the Hilbert space of operators can be taken as the Hilbert-Schmidt class. Comments are made on the possibility of a complete formulation of quantum mechanics in terms of this Hilbert space. (author)

Mathematical foundation of geodesy selected papers of Torben Krarup

CERN Document Server

Borre, K

2006-01-01

This volume contains selected papers by Torben Krarup, one of the most important geodesists of the 20th century. The collection includes the famous booklet "A Contribution to the Mathematical Foundation of Physical Geodesy" from 1969, the unpublished "Molodenskij letters" from 1973, the final version of "Integrated Geodesy" from 1978, "Foundation of a Theory of Elasticity for Geodetic Networks" from 1974, as well as trend-setting papers on the theory of adjustment.

Mathematical foundation of the optimization-based fluid animation method

DEFF Research Database (Denmark)

Erleben, Kenny; Misztal, Marek Krzysztof; Bærentzen, Jakob Andreas

2011-01-01

We present the mathematical foundation of a fluid animation method for unstructured meshes. Key contributions not previously treated are the extension to include diffusion forces and higher order terms of non-linear force approximations. In our discretization we apply a fractional step method to ...

Quantitative graph theory mathematical foundations and applications

CERN Document Server

Dehmer, Matthias

2014-01-01

The first book devoted exclusively to quantitative graph theory, Quantitative Graph Theory: Mathematical Foundations and Applications presents and demonstrates existing and novel methods for analyzing graphs quantitatively. Incorporating interdisciplinary knowledge from graph theory, information theory, measurement theory, and statistical techniques, this book covers a wide range of quantitative-graph theoretical concepts and methods, including those pertaining to real and random graphs such as:Comparative approaches (graph similarity or distance)Graph measures to characterize graphs quantitat

Second order logic, set theory and foundations of mathematics

NARCIS (Netherlands)

Väänänen, J.A.; Dybjer, P; Lindström, S; Palmgren, E; Sundholm, G

2012-01-01

The question, whether second order logic is a better foundation for mathematics than set theory, is addressed. The main difference between second order logic and set theory is that set theory builds up a transfinite cumulative hierarchy while second order logic stays within one application of the

An Evaluation of the Mathematics Foundation Course in Sultan Qaboos University: Does High School Performance Matter?

Directory of Open Access Journals (Sweden)

Mohammad Mazharul Islam

2018-01-01

Full Text Available Although the mathematics foundation program was introduced in Sultan Qaboos University (SQU half a decade ago, there has been no evaluation or assessment of the program. The aim of this study was to evaluate the students’ performance in the Mathematics foundation course in SQU and to examine the predictive value of  a student’s high school performance for success in the math foundation course. The study considered a sample of 551 students who took the math course (MATH2107 during 2014 Spring semester. More than 95% of the students were admitted to SQU with a high school score of 80 and above.  The analysis revealed that, in general, female students were admitted to SQU with a significantly higher average high school score than the male students. The findings indicate a very unsatisfactory performance of the students in the mathematics foundation course as the mean GPA was 1.66 and more than half (59% of the students obtained a GPA less than 2 (i.e. below grade C, of which 14% failed and 35% obtained grade D. Female students outperformed male students in the mathematics course. High school mathematics performance, gender and cohort of students were identified as significant predictors of success in the mathematics foundation course.  To increase the success rate of the mathematics course, the high school curriculum needs to be aligned with the University standards and the admission authority should continue to give more attention to high school mathematics scores along with overall high school performance while making admission decisions for the College of Science in SQU.

Mathematical and numerical foundations of turbulence models and applications

CERN Document Server

Chacón Rebollo, Tomás

2014-01-01

With applications to climate, technology, and industry, the modeling and numerical simulation of turbulent flows are rich with history and modern relevance. The complexity of the problems that arise in the study of turbulence requires tools from various scientific disciplines, including mathematics, physics, engineering, and computer science. Authored by two experts in the area with a long history of collaboration, this monograph provides a current, detailed look at several turbulence models from both the theoretical and numerical perspectives. The k-epsilon, large-eddy simulation, and other models are rigorously derived and their performance is analyzed using benchmark simulations for real-world turbulent flows. Mathematical and Numerical Foundations of Turbulence Models and Applications is an ideal reference for students in applied mathematics and engineering, as well as researchers in mathematical and numerical fluid dynamics. It is also a valuable resource for advanced graduate students in fluid dynamics,...

International Comparisons of Foundation Phase Number Domain Mathematics Knowledge and Practice Standards

Science.gov (United States)

Human, Anja; van der Walt, Marthie; Posthuma, Barbara

2015-01-01

Poor mathematics performance in schools is both a national and an international concern. Teachers ought to be equipped with relevant subject matter knowledge and pedagogical content knowledge as one way to address this problem. However, no mathematics knowledge and practice standards have as yet been defined for the preparation of Foundation Phase…

Service user governors in mental health foundation trusts: accountability or business as usual?

Science.gov (United States)

MacDonald, Dee; Barnes, Marian; Crawford, Mike; Omeni, Edward; Wilson, Aaron; Rose, Diana

2015-12-01

National Health Foundation Trusts present opportunities for individual mental health service users to be active in the governance of trusts. This is one of a range of mechanisms for patient and public involvement and one which promotes an individual rather than collective approach to involvement. Within the context of a broader study of the impact of service user involvement in mental health services, the objective of this article was to explore the experience of service user governors in foundation trusts and their capacity to hold boards to account. The Council of Governors in three foundation trusts were observed for a year. Focus groups with service user governors were undertaken in each trust. Service users had different expectations and understandings of the role and approached it in different ways. Key themes that emerged concerned: the role of a governor, conduct and content of meetings, agenda setting, relationships and representation. The experiences of mental health service user governors need to be understood within the complex environment of patient and public involvement in general and of mental health service user involvement in particular. The dislocation of the service user governor role from other forms of service user activity and involvement result in confusion about how notions of holding a trust to account and representation of other service users can be addressed within a boundaried institutional environment. © 2014 John Wiley & Sons Ltd.

Mathematical and conceptual foundations of 20th-century physics

International Nuclear Information System (INIS)

Emch, G.G.

1984-01-01

This volume presents a unified mathematical account of the conceptual foundations of 20th-century Physics. Part 1 provides a survey of classical physics divided in separate chapters on mechanics, thermodynamics and statistical mechanics, and electromagnetism. This study provides opportunities to place in perspective the successive advents of calculus, of probability and statistics, of differential and sympletic geometry, and of classical functional analysis. Relativity is presented in part 2 of this book and quantum theory in part 3. The motivation provided by physical problems in the development of mathematical disciplines such as, for instance, pseudo-Riemannian geometries, Hilbert spaces and operator algebras, are emphasized. (H.W.). refs.; figs.; schemes

Mathematical foundation of quantum mechanics

CERN Document Server

Parthasarathy, K R

2005-01-01

This is a brief introduction to the mathematical foundations of quantum mechanics based on lectures given by the author to Ph.D.students at the Delhi Centre of the Indian Statistical Institute in order to initiate active research in the emerging field of quantum probability. The material in the first chapter is included in the author's book "An Introduction to Quantum Stochastic Calculus" published by Birkhauser Verlag in 1992 and the permission of the publishers to reprint it here is acknowledged. Apart from quantum probability, an understanding of the role of group representations in the development of quantum mechanics is always a fascinating theme for mathematicians. The first chapter deals with the definitions of states, observables and automorphisms of a quantum system through Gleason's theorem, Hahn-Hellinger theorem and Wigner's theorem. Mackey's imprimitivity theorem and the theorem of inducing representations of groups in stages are proved directly for projective unitary antiunitary representations ...

A mathematical foundation for controlling radiation health risks

International Nuclear Information System (INIS)

Kumazawa, S.

2000-01-01

Radiation protection is to attain an adequate control of radiation health risk compared with other risks. Our society in the 21 st century is predicted by some experts to seek the high priority of safety for expanding activity of human beings. The law of controlling risks will be a key subject to serve the safety of human beings and their environment. The main principles of the ICRP system of radiological system are strongly relating to the general law of various risk controls. The individual-based protection concept clearly gives us a mathematical model of controlling risks in general. This paper discusses the simplest formulation of controlling risks in the ICRP system, including other relating systems. First, the basic characteristics of occupational exposure as a risk control is presented by analyzing the data compiled over half a century. It shows the relation ship between dose control levels and individually controlled doses. The individual-based control also exerts some influence on the resultant collective dose. The study of occupational exposure concludes the simple mathematical expression of controlling doses under the ICRP system as shown by Kumazawa and Numakunai. Second, the typical characteristics of biological effects with repair or recovery of bio-systems are given by analyzing the data published. Those show the relationship between dose and biologically controlled or regulated response. The bio-system is undoubtedly relating to cybernetics that contains many functions of controlling risks. Consequently radiation effects might somewhat express the feature of biological risk controls. The shouldered survival of irradiated cells shows cybernetic characteristics that are assumed to be the mathematical foundation of controlling risks. The dose-response relationship shows another type of cybernetic characteristics, which could be reduced to the same basic form of controlling risks. The limited study of radiation effects definitely confirms the two

Teacher Professionalism--An Innovative Programme for Teaching Mathematics to Foundation Level Learners with Limited Language Proficiency.

Science.gov (United States)

Naude, H.; Pretorius, E.; Vandeyar, S.

2003-01-01

Details a study of the ways that limited language proficiency affected learners' readiness for mathematics instruction among disadvantaged preschoolers within a Griqua community in South Africa. Notes a link between limited language proficiency and nonreadiness for foundation level mathematics due to limited thinking skills, which constitute…

Attitude toward Mathematics among the Students at Nazarbayev University Foundation Year Programme

Science.gov (United States)

Karjanto, N.

2017-01-01

This article investigates the attitude toward mathematics among the students enrolled in the Foundation Year Programme at Nazarbayev University. The study is conducted quantitatively and an inventory developed by Tapia and Marsh II is adopted in this research. The inventory consists of 40 statements on the five-point Likert scale. Gender,…

Mathematical foundation of quantum annealing

International Nuclear Information System (INIS)

Morita, Satoshi; Nishimori, Hidetoshi

2008-01-01

Quantum annealing is a generic name of quantum algorithms that use quantum-mechanical fluctuations to search for the solution of an optimization problem. It shares the basic idea with quantum adiabatic evolution studied actively in quantum computation. The present paper reviews the mathematical and theoretical foundations of quantum annealing. In particular, theorems are presented for convergence conditions of quantum annealing to the target optimal state after an infinite-time evolution following the Schroedinger or stochastic (Monte Carlo) dynamics. It is proved that the same asymptotic behavior of the control parameter guarantees convergence for both the Schroedinger dynamics and the stochastic dynamics in spite of the essential difference of these two types of dynamics. Also described are the prescriptions to reduce errors in the final approximate solution obtained after a long but finite dynamical evolution of quantum annealing. It is shown there that we can reduce errors significantly by an ingenious choice of annealing schedule (time dependence of the control parameter) without compromising computational complexity qualitatively. A review is given on the derivation of the convergence condition for classical simulated annealing from the view point of quantum adiabaticity using a classical-quantum mapping

Attitude toward mathematics among the students at Nazarbayev University Foundation Year Programme

Science.gov (United States)

Karjanto, N.

2017-08-01

This article investigates the attitude toward mathematics among the students enrolled in the Foundation Year Programme at Nazarbayev University. The study is conducted quantitatively and an inventory developed by Tapia and Marsh II is adopted in this research. The inventory consists of 40 statements on the five-point Likert scale. Gender, specialization and final high school score in mathematics are collected. The number of valid returned questionnaires is 108. There are 55 males, 53 females, 73 Mathematical-Physics (MP), 22 Biology-Chemistry (BC) and 13 International Relations-Economics (IRE) students. Generally, they have a positive attitude toward mathematics, with the score mean and standard deviation are 3.999 and 0.531 out of five, respectively. We confirm a hypothesis on a positive correlation between previous high achievement in mathematics and favorable attitude toward it. The correlation value is r = 0.300, its effect size is medium and it is extremely significant (p-value = 0.0008 0.05). There is a very significant difference between students who specialize in IRE and MP in terms of their attitude toward mathematics (F(2, 105) = 5.6848, p-value = 0.0045 < 0.01).

Foundations of mathematics and literacy: The role of executive functioning components.

Science.gov (United States)

Purpura, David J; Schmitt, Sara A; Ganley, Colleen M

2017-01-01

The current study investigated the relations between the three cognitive processes that comprise executive functioning (EF)-response inhibition, working memory, and cognitive flexibility-and individual components of mathematics and literacy skills in preschool children. Participants were 125 preschool children ranging in age from 3.12 to 5.26years (M=4.17years, SD=0.58). Approximately 53.2% were female, and the sample was predominantly Caucasian (69.8%). Results suggest that the components of EF may be differentially related to the specific components of early mathematics and literacy. For mathematics, response inhibition was broadly related to most components. Working memory was related to more advanced mathematics skills that involve comparison or combination of numbers and quantities. Cognitive flexibility was related to more conceptual or abstract mathematics skills. For early literacy, response inhibition and cognitive flexibility were related to print knowledge, and working memory was related only to phonological awareness. None of the EF components was related to vocabulary. These findings provide initial evidence for better understanding the ways in which EF components and academic skills are related and measured. Furthermore, the findings provide a foundation for further study of the components of each domain using a broader and more diverse array of measures. Copyright © 2016 Elsevier Inc. All rights reserved.

Leśniewski's systems of logic and foundations of mathematics

CERN Document Server

Urbaniak, Rafal

2014-01-01

This meticulous critical assessment of the ground-breaking work of philosopher Stanislaw  Leśniewski focuses exclusively on primary texts and explores the full range of output by one of the master logicians of the Lvov-Warsaw school. The author’s nuanced survey eschews secondary commentary, analyzing Leśniewski's core philosophical views and evaluating the formulations that were to have such a profound influence on the evolution of mathematical logic.   One of the undisputed leaders of the cohort of brilliant logicians that congregated in Poland in the early twentieth century, Leśniewski was a guide and mentor to a generation of celebrated analytical philosophers (Alfred Tarski was his PhD student). His primary achievement was a system of foundational mathematical logic intended as an alternative to the Principia Mathematica of Alfred North Whitehead and Bertrand Russell. Its three strands—‘protothetic’, ‘ontology’, and ‘mereology’, are detailed in discrete sections of this volume, alongs...

Pre-Service Elementary Mathematics Teachers' Metaphors on Scientific Research and Foundations of Their Perceptions

Science.gov (United States)

Bas, Fatih

2016-01-01

In this study, it is aimed to investigate pre-service elementary mathematics teachers' perceptions about scientific research with metaphor analysis and determine the foundations of these perceptions. This phenomenological study was conducted with 182 participants. The data were collected with two open-ended survey forms formed for investigating…

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/ .

The Preparation of Students from National Science Foundation-Funded and Commercially Developed High School Mathematics Curricula for their First University Mathematics Course

Science.gov (United States)

Harwell, Michael; Post, Thomas R.; Cutler, Arnie; Maeda, Yukiko; Anderson, Edwin; Norman, Ke Wu; Medhanie, Amanuel

2009-01-01

The selection of K-12 mathematics curricula has become a polarizing issue for schools, teachers, parents, and other educators and has raised important questions about the long-term influence of these curricula. This study examined the impact of participation in either a National Science Foundation-funded or commercially developed mathematics…

The mathematical foundations of gauge theories

International Nuclear Information System (INIS)

Marathe, K.B.; Martucci, G.

1992-01-01

Theoretical physicists tend to discuss their theories in the language of mathematics. However, the adequate mathematical formulation may not yet be available when the physical law is first discovered. Mathematical physicists trying to develop the relevant mathematics for these theories, may obtain new insights into old mathematical structures. Gauge Theory is such a gift from physics to mathematics. This book presents a self-contained development of a differential geometric formulation of gauge theories, in particular, the theory of Yang-Mills fields. (author). refs.; figs.; tabs

Foundational aspects of non standard mathematics

CERN Document Server

Ballard, David

1994-01-01

This work proposes a major new extension of "non"standard mathematics. Addressed to a general mathematical audience, the book is intended to be philosophically provocative. The model theory on which "non"standard mathematics has been based is first reformulated within point set topology, which facilitates proofs and adds perspective. These topological techniques are then used to give new, uniform conservativity proofs for the various versions of "non"standard mathematics proposed by Nelson, Hrbáček, and Kawai. The proofs allow for sharp comparison. Addressing broader issues, Ballard then argues that what is novel in these forms of "non"standard mathematics is the introduction, however tentative, of relativity in one's mathematical environment. This hints at the possibility of a mathematical environment which is radically relativistic. The work's major and final feature is to present and prove conservative a version of "non"standard mathematics which, for the first time, illustrates this full radical relativ...

Gender Differences in Online Participation: Examining a History and a Mathematics Open Foundation Online Course

Science.gov (United States)

Morante, Annette; Djenidi, Valerie; Clark, Helene; West, Susan

2017-01-01

With enrolment and completion rates in the University of Newcastle's online Open Foundation enabling program being considerably higher for women than for men, this case study investigates the engagement of male and female students in two different subject areas. History and Mathematics students' online behaviour is examined to identify whether…

Mathematical Modeling of Hydroelastic Oscillations of the Stamp and the Plate, Resting on Pasternak Foundation

Science.gov (United States)

Mogilevich, L. I.; Popov, V. S.; Popova, A. A.; Christoforova, A. V.

2018-01-01

The forced oscillations of the elastic fixed stamp and the plate, resting on Pasternak foundation are studied. The oscillations are caused by pressure pulsation in liquid layer between the stamp and the plate. Pasternak model is chosen as an elastic foundation. The laws of the stamp movement, the plate deflection and pressure in the liquid are discovered on the basis of hydroelasticity problem analytical solution. The functions of amplitude deflection distribution and liquid pressure along the plate are constructed, as well as the stamp amplitude-frequency characteristic. The obtained mathematical model allows to investigate the dynamics of hydroelastic interaction of the stamp with the plate, resting on elastic foundation, to define resonance frequencies of the plate and the stamp and corresponding deflections amplitudes, as well as liquid presser amplitudes.

Mathematical foundation of computer science

CERN Document Server

Singh, YN

2005-01-01

The interesting feature of this book is its organization and structure. That consists of systematizing of the definitions, methods, and results that something resembling a theory. Simplicity, clarity, and precision of mathematical language makes theoretical topics more appealing to the readers who are of mathematical or non-mathematical background. For quick references and immediate attentions¾concepts and definitions, methods and theorems, and key notes are presented through highlighted points from beginning to end. Whenever, necessary and probable a visual approach of presentation is used. The amalgamation of text and figures make mathematical rigors easier to understand. Each chapter begins with the detailed contents, which are discussed inside the chapter and conclude with a summary of the material covered in the chapter. Summary provides a brief overview of all the topics covered in the chapter. To demonstrate the principles better, the applicability of the concepts discussed in each topic are illustrat...

Commonly Shared Foundation of Mathematics, Information Science, Natural Science, Social Science, and Theology

OpenAIRE

Wayne, James J.

2014-01-01

Through a simple thought experiment, this paper shows that there must be a shared foundation of mathematics, information science, natural science, social science, and theology. The thought experiment is to ask a volunteer to write down an arbitrary real number between 0 and 1 with many digits. For example, 0.19823765010367129462…. would be one of such numbers. Then we analyze this experiment result by asking five simple questions: Is the real number a random real? Can the observed real numbe...

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.

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.

Mathematical foundations of image processing and analysis

CERN Document Server

Pinoli, Jean-Charles

2014-01-01

Mathematical Imaging is currently a rapidly growing field in applied mathematics, with an increasing need for theoretical mathematics. This book, the second of two volumes, emphasizes the role of mathematics as a rigorous basis for imaging sciences. It provides a comprehensive and convenient overview of the key mathematical concepts, notions, tools and frameworks involved in the various fields of gray-tone and binary image processing and analysis, by proposing a large, but coherent, set of symbols and notations, a complete list of subjects and a detailed bibliography. It establishes a bridg

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

THE MATHEMATICAL BASIS FOR THE THEORY OF JOINT WORK OF THE FOUNDATION AND THE FOUNDATION WITH THE „ARCH” EFFECT

Directory of Open Access Journals (Sweden)

TIMCHENKO R. A.

2016-01-01

Full Text Available Statement of the problem. The review of the technical solutions of the foundation of buildings and structures revealed a number of significant shortcomings associated with the complexity of structures and a low probability of normal functioning in difficult engineering-geological conditions. When designing the building use and design measures that reduce either the amount of strain-tive effects from the base, or their impact on the structure. Experience in construction has shown that it is not always possible to completely prevent the adverse effects on structures from the base. Therefore, their effect on the structure still considered at the design stage. Purpose. On the basis of experimental and theoretical studies to justify the proposed theory of joint work the plate foundation-selfregulators (PFS with the base, including the theory of plasticity (maximum stress state and soil pressure on roofs with. Conclusion. Of all the discussed features of the joint work the PFS with the base surface is more important "arch" effect, since it is the resultant and explains the stress-strain state (SSS for PFS. Increased design resistance at 15-22% is due to the design of the PFS and the special nature of the formation of the overall limit of the SSS of the base with an increase in load to the limit values. For the construction of the PFS by more uniform distribution of the contact stresses in the ground under the foundation, regardless of the power or influence of the deformation, and large outside the proportional relationship between stress and strain. Establish the boundaries of self-regulation can be obtained by carrying out mathematical modeling of changing the compensatory possibilities of the foundation.

On the dialectical foundations of mathematics

NARCIS (Netherlands)

Damsma, D.

2008-01-01

This paper tracks the systematic dialectical determination of mathematical concepts in Hegel's Encyclopädie der philosophischen Wissenschaften (1830, 1817) and investigates the insights that can be gained from such a perspective on the mathematical. To begin with, the determination of Numbers and

On the dialectical foundations of mathematics

NARCIS (Netherlands)

Damsma, D.

2011-01-01

This paper tracks the systematic dialectical determination of mathematical concepts in Hegel’s Encyclopädie der philosophischen Wissenschaften (1830,1817) and investigates the insights that can be gained from such a perspective on the mathematical. To begin with, the determination of Numbers and

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…

An introduction to single-user information theory

CERN Document Server

Alajaji, Fady

2018-01-01

This book presents a succinct and mathematically rigorous treatment of the main pillars of Shannon’s information theory, discussing the fundamental concepts and indispensable results of Shannon’s mathematical theory of communications. It includes five meticulously written core chapters (with accompanying problems), emphasizing the key topics of information measures; lossless and lossy data compression; channel coding; and joint source-channel coding for single-user (point-to-point) communications systems. It also features two appendices covering necessary background material in real analysis and in probability theory and stochastic processes. The book is ideal for a one-semester foundational course on information theory for senior undergraduate and entry-level graduate students in mathematics, statistics, engineering, and computing and information sciences. A comprehensive instructor’s solutions manual is available.

The Impact of the GE Foundation "Developing Futures"™ in Education Program on Mathematics Performance Trends in Four Districts. Research Report # RR-74

Science.gov (United States)

Sirinides, Philip; Supovitz, Jonathan; Tognatta, Namrata; May, Henry

2013-01-01

Beginning in 2005, the GE Foundation initiated a commitment of expertise and financial resources to a set of urban school districts to improve public education and enhance student achievement in mathematics and science. This report analyzes the impacts of the GE Foundation commitment to the partner districts by examining trends in student…

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.

Wittgenstein, finitism, and the foundations of mathematics

CERN Document Server

Marion, Mathieu

2008-01-01

Mathieu Marion traces the development of Wittgenstein''s thinking from the 1920s through to the 1950s, in the context of the mathematical and philosophical work of the time, making sense of ideas that have often been misunderstood. He shows that study of Wittgenstein''s writings on mathematics is essential to a proper understanding of his philosophy. - ;Mathieu Marion offers a careful, historically informed study of Wittgenstein''s philosophy of mathematics. This area of his work has frequently been undervalued by Wittgenstein specialists and by philosophers of mathematics alike; but the surprising fact that he wrote more on this subject than on any other indicates its centrality in his thought. Marion traces the development of Wittgenstein''s thinking in the context of the mathematical and philosophical work of the times, to make. coherent sense of ideas that have too often been misunderstood because they have been presented in a disjointed and incomplete way. In particular, he illuminates the work of the ne...

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

PREDICTING ATTENUATION OF VIRUSES DURING PERCOLATION IN SOILS: 2. USER'S GUIDE TO THE VIRULO 1.0 COMPUTER MODEL

Science.gov (United States)

In the EPA document Predicting Attenuation of Viruses During Percolation in Soils 1. Probabilistic Model the conceptual, theoretical, and mathematical foundations for a predictive screening model were presented. In this current volume we present a User's Guide for the computer mo...

Spectral theory and quantum mechanics mathematical foundations of quantum theories, symmetries and introduction to the algebraic formulation

CERN Document Server

Moretti, Valter

2017-01-01

This book discusses the mathematical foundations of quantum theories. It offers an introductory text on linear functional analysis with a focus on Hilbert spaces, highlighting the spectral theory features that are relevant in physics. After exploring physical phenomenology, it then turns its attention to the formal and logical aspects of the theory. Further, this Second Edition collects in one volume a number of useful rigorous results on the mathematical structure of quantum mechanics focusing in particular on von Neumann algebras, Superselection rules, the various notions of Quantum Symmetry and Symmetry Groups, and including a number of fundamental results on the algebraic formulation of quantum theories. Intended for Master's and PhD students, both in physics and mathematics, the material is designed to be self-contained: it includes a summary of point-set topology and abstract measure theory, together with an appendix on differential geometry. The book also benefits established researchers by organizing ...

Foundations of mathematical analysis

CERN Document Server

Johnsonbaugh, Richard

2010-01-01

This classroom-tested volume offers a definitive look at modern analysis, with views of applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. Upper-level undergraduate students with a background in calculus will benefit from its teachings, along with beginning graduate students seeking a firm grounding in modern analysis. A self-contained text, it presents the necessary background on the limit concept, and the first seven chapters could constitute a one-semester introduction to limits. Subsequent chapters discuss

Predictive factors of user acceptance on the primary educational mathematics aids product

Science.gov (United States)

Hidayah, I.; Margunani; Dwijanto

2018-03-01

Mathematics learning in primary schools requires instructional media. According to Piaget's theory, students are still in the concrete operational stage. For this reason, the development of the primary level mathematics aids is needed to support the development of successful mathematics learning. The stages of this research are the stages of commercialization with preparatory, marketing, and measurement analysis procedures. Promotion as part of marketing is done by doing a demonstration to the teacher. Measurements were performed to explore the predictive factors of user feasibility in adopting the product. Measurements were conducted using the concept of Technology Acceptance Model (TAM). Measurement variables include external variables, perceived usefulness, perceived ease of use, attitude, intention to use, and actual use. The result of this research shows that the contribution of predictive factors of mathematics teachers on the teaching aids product as follows: the external variable and perceived ease of use at 74%, perceived usefulness at 72%, intention to use (behavioral) at 58%, attitude at 52%, and the consequence factor (actual use) at 42%.

Towards an arithmetical logic the arithmetical foundations of logic

CERN Document Server

Gauthier, Yvon

2015-01-01

This book offers an original contribution to the foundations of logic and mathematics, and focuses on the internal logic of mathematical theories, from arithmetic or number theory to algebraic geometry. Arithmetical logic is the term used to refer to the internal logic of classical arithmetic, here called Fermat-Kronecker arithmetic, and combines Fermat’s method of infinite descent with Kronecker’s general arithmetic of homogeneous polynomials. The book also includes a treatment of theories in physics and mathematical physics to underscore the role of arithmetic from a constructivist viewpoint. The scope of the work intertwines historical, mathematical, logical and philosophical dimensions in a unified critical perspective; as such, it will appeal to a broad readership from mathematicians to logicians, to philosophers interested in foundational questions. Researchers and graduate students in the fields of philosophy and mathematics will benefit from the author’s critical approach to the foundations of l...

Early numerical foundations of young children's mathematical development.

Science.gov (United States)

Chu, Felicia W; vanMarle, Kristy; Geary, David C

2015-04-01

This study focused on the relative contributions of the acuity of the approximate number system (ANS) and knowledge of quantitative symbols to young children's early mathematical learning. At the beginning of preschool, 191 children (Mage=46 months) were administered tasks that assessed ANS acuity and explicit knowledge of the cardinal values represented by number words, and their mathematics achievement was assessed at the end of the school year. Children's executive functions, intelligence, and preliteracy skills and their parents' educational levels were also assessed and served as covariates. Both the ANS and cardinality tasks were significant predictors of end-of-year mathematics achievement with and without control of the covariates. As simultaneous predictors and with control of the covariates, cardinality remained significantly related to mathematics achievement, but ANS acuity did not. Mediation analyses revealed that the relation between ANS acuity and mathematics achievement was fully mediated by cardinality, suggesting that the ANS may facilitate children's explicit understanding of cardinal value and in this way may indirectly influence early mathematical learning. Copyright © 2015 Elsevier Inc. All rights reserved.

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:

Shells on elastic foundations

International Nuclear Information System (INIS)

Das, Y.C.; Kedia, K.K.

1977-01-01

No realistic analytical work in the area of Shells on Elastic Foundations has been reported in the literature. Various foundation models have been proposed by several authors. These models involve one or more than one parameters to characterise the foundation medium. Some of these models cannot be used to derive the basic equations governing the behaviour of shells on elastic foundations. In the present work, starting from an elastic continuum hypothesis, a mathematical model for foundation has been derived in curvilinear orthogonal coordinates by the help of principle of virtual displacements, treating one of the virtual displacements as known to satisfy certain given conditions at its edge surfaces. In this model, several foundation parameters can be considered and it can also be used for layered medium of both finite and infinite thickness. (Auth.)

The geometric phase in quantum systems foundations, mathematical concepts, and applications in molecular and condensed matter physics

CERN Document Server

Böhm, Arno; Koizumi, Hiroyasu; Niu, Qian; Zwanziger, Joseph

2003-01-01

Aimed at graduate physics and chemistry students, this is the first comprehensive monograph covering the concept of the geometric phase in quantum physics from its mathematical foundations to its physical applications and experimental manifestations It contains all the premises of the adiabatic Berry phase as well as the exact Anandan-Aharonov phase It discusses quantum systems in a classical time-independent environment (time dependent Hamiltonians) and quantum systems in a changing environment (gauge theory of molecular physics) The mathematical methods used are a combination of differential geometry and the theory of linear operators in Hilbert Space As a result, the monograph demonstrates how non-trivial gauge theories naturally arise and how the consequences can be experimentally observed Readers benefit by gaining a deep understanding of the long-ignored gauge theoretic effects of quantum mechanics and how to measure them

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.

Mathematics Competency Test: User's Manual.

Science.gov (United States)

Vernon, P. E.; And Others

The Mathematics Competency Test is a 46-question written test assessing mathematics achievement for groups or individuals aged 11 to adult. It is suitable for use with groups or individuals in school, college and workplace contexts. The questions are open-ended and require constructed responses rather than recognition of a correct answer in a…

Foundations of combinatorics with applications

CERN Document Server

Bender, Edward A

2006-01-01

This introduction to combinatorics, the foundation of the interaction between computer science and mathematics, is suitable for upper-level undergraduates and graduate students in engineering, science, and mathematics.The four-part treatment begins with a section on counting and listing that covers basic counting, functions, decision trees, and sieving methods. The following section addresses fundamental concepts in graph theory and a sampler of graph topics. The third part examines a variety of applications relevant to computer science and mathematics, including induction and recursion, sorti

Foundations of image science

CERN Document Server

Barrett, Harrison H

2013-01-01

Winner of the 2006 Joseph W. Goodman Book Writing Award! A comprehensive treatment of the principles, mathematics, and statistics of image science In today's visually oriented society, images play an important role in conveying messages. From seismic imaging to satellite images to medical images, our modern society would be lost without images to enhance our understanding of our health, our culture, and our world. Foundations of Image Science presents a comprehensive treatment of the principles, mathematics, and st

Mathematical foundations of transport theory

International Nuclear Information System (INIS)

Ershov, Yu.I.; Shikhov, S.B.

1985-01-01

Main items of application of the operator equations analyzing method in transport theory problems are considered. The mathematical theory of a reactor critical state is presented. Theorems of existence of positive solutions of non-linear non-stationary equations taking into account the temperature and xenon feedbacks are proved. Conditions for stability and asymptotic stability of steady-state regimes for different distributed models of a nuclear reactor are obtained on the basis of the modern operator perturbation theory, certain problems on control using an absorber are considered

General systems theory mathematical foundations

CERN Document Server

Mesarovic, Mihajlo D

1975-01-01

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank mat

Mathematics: Foundations for Business. Instructor's Guide.

Science.gov (United States)

Hopfe, Manfred W.; Bianci-Rossi, Larry

This is the instructor's guide to a text designed for the contemporary business student who frequently questions the need for studying mathematics. The text material is presented in a "building-block" fashion, with skills learned in earlier chapters organized to provide a smooth transition into more difficult topics. This guide consists…

78 FR 37590 - Advisory Committee for Mathematical and Physical Sciences #66; Notice of Meeting

Science.gov (United States)

2013-06-21

... Science Foundation and to provide advice and recommendations concerning research in mathematics and... NATIONAL SCIENCE FOUNDATION Advisory Committee for Mathematical and Physical Sciences 66; Notice... National Science Foundation announces the following meeting. Name: Advisory Committee for Mathematical and...

Utah's New Mathematics Core

Science.gov (United States)

Utah State Office of Education, 2011

2011-01-01

Utah has adopted more rigorous mathematics standards known as the Utah Mathematics Core Standards. They are the foundation of the mathematics curriculum for the State of Utah. The standards include the skills and understanding students need to succeed in college and careers. They include rigorous content and application of knowledge and reflect…

Mathematical Foundations of Quantum Information and Computation and Its Applications to Nano- and Bio-systems

CERN Document Server

Ohya, Masanori

2011-01-01

This monograph provides a mathematical foundation  to  the theory of quantum information and computation, with applications to various open systems including nano and bio systems. It includes introductory material on algorithm, functional analysis, probability theory, information theory, quantum mechanics and quantum field theory. Apart from standard material on quantum information like quantum algorithm and teleportation, the authors discuss findings on the theory of entropy in C*-dynamical systems, space-time dependence of quantum entangled states, entangling operators, adaptive dynamics, relativistic quantum information, and a new paradigm for quantum computation beyond the usual quantum Turing machine. Also, some important applications of information theory to genetics and life sciences, as well as recent experimental and theoretical discoveries in quantum photosynthesis are described.

Carl Stumpf's philosophy of mathematics

NARCIS (Netherlands)

Ierna, Carlo

2015-01-01

Like most of Franz Brentano's students, Carl Stumpf showed an interest in the philosophy of mathematics. In particular, Stumpf wrote his habilitation thesis On the Foundations of Mathematics, used mathematical examples in central parts of his lectures, and later returned to the topic in the

Modelling as a foundation for academic forming in mathematics education

NARCIS (Netherlands)

Perrenet, J.C.; Morsche, ter H.G.

2004-01-01

The Bachelor curriculum of Applied Mathematics in Eindhoven includes a series of modelling projects where pairs of students solve mathematical problems posed in non-mathematical language. Communication skills training is integrated with this track. Recently a new course has been added. The students

Driven by History: Mathematics Education Reform

Science.gov (United States)

Permuth, Steve; Dalzell, Nicole

2013-01-01

The advancement of modern societies is fueled by mathematics, and mathematics education provides the foundation upon which future scientists and engineers will build. Society dictates how mathematics will be taught through the development and implementation of mathematics standards. When examining the progression of these standards, it is…

Applying an alternative mathematics pedagogy for students with weak mathematics: meta-analysis of alternative pedagogies

Science.gov (United States)

Lake, Warren; Wallin, Margie; Woolcott, Geoff; Boyd, Wendy; Foster, Alan; Markopoulos, Christos; Boyd, William

2017-02-01

Student mathematics performance and the need for work-ready graduates to be mathematics-competent is a core issue for many universities. While both student and teacher are responsible for learning outcomes, there is a need to explicitly acknowledge the weak mathematics foundation of many university students. A systematic literature review was undertaken of identified innovations and/or interventions that may lead to improvement in student outcomes for university mathematics-based units of study. The review revealed the importance of understanding the foundations of student performance in higher education mathematics learning, especially in first year. Pre-university mathematics skills were identified as significant in student retention and mathematics success at university, and a specific focus on student pre-university mathematics skill level was found to be more effective in providing help, rather than simply focusing on a particular at-risk group. Diagnostics tools were found to be important in identifying (1) student background and (2) appropriate intervention. The studies highlighted the importance of appropriate and validated interventions in mathematics teaching and learning, and the need to improve the learning model for mathematics-based subjects, communication and technology innovations.

A mathematical structure for nuclei

International Nuclear Information System (INIS)

Fabre de la Ripelle, M

2012-01-01

The Shell Model was accepted even though it still lakes theoretical foundation [1]. A mathematical structure is proposed to give an answer to this statement and establish a needed foundation for this Model.

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

Binary Relations as a Foundation of Mathematics

NARCIS (Netherlands)

Kuper, Jan; Barendsen, E.; Capretta, V.; Geuvers, H.; Niqui, M.

2007-01-01

We describe a theory for binary relations in the Zermelo-Fraenkel style. We choose for ZFCU, a variant of ZFC Set theory in which the Axiom of Foundation is replaced by an axiom allowing for non-wellfounded sets. The theory of binary relations is shown to be equi-consistent ZFCU by constructing a

Foundations of the theory of probability

CERN Document Server

Kolmogorov, AN

2018-01-01

This famous little book remains a foundational text for the understanding of probability theory, important both to students beginning a serious study of probability and to historians of modern mathematics. 1956 second edition.

Using Digital Games to Learn Mathematics – What students think?

Directory of Open Access Journals (Sweden)

Su Ting Yong

2016-06-01

Full Text Available The aim of this study was to explore how university foundation students perceive the use of digital games in learning mathematics. Data was collected using an online questionnaire and 209 foundation university students participated in this study.  The questionnaire was used to explore students’ gaming experience and students’ attitude towards mathematics learning with digital games.  It was found that most of the university foundation students liked to play different types of digital games.  Males preferred playing digital games in more traditional male genres namely sport, racing, shooter, action adventure, role play and strategy games.  As for females, they generally preferred playing puzzle and simulation games.  Astonishingly, the foundation students were not very positive towards the use of digital games in learning mathematics, and their attitude was essentially influenced by their mathematics interest.  Students with greater interest in mathematics were more likely to support the use of digital games in learning. 

Mathematics in civilization

CERN Document Server

Resnikoff, Howard L

2015-01-01

Space flight, computers, lasers, and information technology ― these are but a few examples of the spectacular growth, development, and far-reaching applications of mathematics. But what of the field's past? Upon which intellectual milestones were the foundations of modern mathematics constructed? How has our comprehension of the physical universe, language, and the nature of thought itself been influenced and informed by the developments of mathematics through the ages?This lucid presentation examines how mathematics shaped and was shaped by the course of human events. In a format suited to co

The Mathematics Doctorate: A Time for Change? Carnegie Essays on the Doctorate: Mathematics.

Science.gov (United States)

Chan, Tony F.

The Carnegie Foundation commissioned a collection of essays as part of the Carnegie Initiative on the Doctorate (CID). Essays and essayists represent six disciplines that are part of the CID: chemistry, education, English, history, mathematics, and neuroscience. Intended to engender conversation about the conceptual foundation of doctoral…

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...

Kant's Schematism and the Foundations of Mathematics

DEFF Research Database (Denmark)

Jørgensen, Klaus Frovin

The theory of schematism was initiated by I. Kant, who, however, was never precise with respect to what he understood under this theory. I give---based on the theoretical works of Kant---an interpretation of the most important aspects of Kant's theory of schematism. In doing this I show how...... show that, contrary to Kant's own intentions, he was not up-to-date on mathematics. And in fact, it was because of this that it was possible for him to formulate his rather rigid theory concerning the unique characterizations of intuition and understanding. I show how phenomena in the mathematics...... of the time of Kant should have had an effect on him. He should have remained more critical towards his formulation and demarcation of intuition, understanding and reason. Finally I show how D. Hilbert in fact gives the necessary generalization of Kant's philosophy. This generalization provides us...

A user-friendly mathematical modelling web interface to assist local decision making in the fight against drug-resistant tuberculosis.

Science.gov (United States)

Ragonnet, Romain; Trauer, James M; Denholm, Justin T; Marais, Ben J; McBryde, Emma S

2017-05-30

Multidrug-resistant and rifampicin-resistant tuberculosis (MDR/RR-TB) represent an important challenge for global tuberculosis (TB) control. The high rates of MDR/RR-TB observed among re-treatment cases can arise from diverse pathways: de novo amplification during initial treatment, inappropriate treatment of undiagnosed MDR/RR-TB, relapse despite appropriate treatment, or reinfection with MDR/RR-TB. Mathematical modelling allows quantification of the contribution made by these pathways in different settings. This information provides valuable insights for TB policy-makers, allowing better contextualised solutions. However, mathematical modelling outputs need to consider local data and be easily accessible to decision makers in order to improve their usefulness. We present a user-friendly web-based modelling interface, which can be used by people without technical knowledge. Users can input their own parameter values and produce estimates for their specific setting. This innovative tool provides easy access to mathematical modelling outputs that are highly relevant to national TB control programs. In future, the same approach could be applied to a variety of modelling applications, enhancing local decision making.

Using Interactive Software to Teach Foundational Mathematical Skills

Directory of Open Access Journals (Sweden)

Larysa V Lysenko

2016-01-01

Full Text Available The pilot research presented here explores the classroom use of Emerging Literacy in Mathematics (ELM software, a research-based bilingual interactive multimedia instructional tool, and its potential to develop emerging numeracy skills. At the time of the study, a central theme of early mathematics curricula, Number Concept, was fully developed. It was broken down into five mathematical concepts including counting, comparing, adding, subtracting and decomposing. Each of these was further subdivided yielding 22 online activities, each building in a level of complexity and abstraction. In total, 234 grade one students from 12 classes participated in the two-group post-test study that lasted about seven weeks and for which students in the experimental group used ELM for about 30 minutes weekly. The results for the final sample of 186 students showed that ELM students scored higher on the standardized math test (Canadian Achievement Test, 2008 and reported less boredom and lower anxiety as measured on the Academic Emotions Questionnaire than their peers in the control group. This short duration pilot study of one ELM theme holds great promise for ELM’s continued development.

Foundations of mechanics

International Nuclear Information System (INIS)

Zorski, Henryk; Bazanski, Stanislaw; Gutowski, Roman; Slawianowski, Jan; Wilmanski, Krysztof; Wozniak, Czeslaw

1992-01-01

In the last 3 decades the field of mechanics has seen spectacular progress due to the demand for applications in problems of cosmology, thermonuclear fusion, metallurgy, etc. This book provides a broad and thorough overview on the foundations of mechanics. It discusses theoretical mechanics and continuum mechanics, as well as phenomenological thermodynamics, quantum mechanics and relativistic mechanics. Each chapter presents the basic physical facts of interest without going into details and derivations and without using advanced mathematical formalism. The first part constitutes a classical exposition of Lagrange's and Hamiltonian's analytical mechanics on which most of the continuum theory is based. The section on continuum mechanics focuses mainly on the axiomatic foundations, with many pointers for further research in this area. Special attention is given to modern continuum thermodynamics, both for the foundations and applications. A section on quantum mechanics is also included, since the phenomenological description of various quantum phenomena is becoming of increasing importance. refs.; figs.; tabs

Summer School Mathematical Foundations of Complex Networked Information Systems

CERN Document Server

Fosson, Sophie; Ravazzi, Chiara

2015-01-01

Introducing the reader to the mathematics beyond complex networked systems, these lecture notes investigate graph theory, graphical models, and methods from statistical physics. Complex networked systems play a fundamental role in our society, both in everyday life and in scientific research, with applications ranging from physics and biology to economics and finance. The book is self-contained, and requires only an undergraduate mathematical background.

Physical foundations of technical acoustics

CERN Document Server

Malecki, I

1969-01-01

Physical Foundations of Technical Acoustics discusses theoretical foundations of acoustical engineering. It is not so much a technical compendium as a systematic statement of physical laws so conceived that technologists might find in it all the information they need to become acquainted with the physical meaning and mathematical expression of phenomena they encounter in their work. To facilitate the acquirement of notions, which lie beyond a layman's grasp, the plan of narration adopted consists in beginning with the simplest idealized cases and then gradually moving on to the truest possibl

Proceedings – Mathematical Sciences | Indian Academy of Sciences

Indian Academy of Sciences (India)

Author Affiliations. Ali Reza Ashrafi1 Geetha Venkataraman1 2. Department of Mathematics, University of Kashan, Kashan, Iran; Department of Mathematics and Mathematical Sciences Foundation, St. Stephen's College, Delhi 110 007, India ...

Mathematical structures for computer graphics

CERN Document Server

Janke, Steven J

2014-01-01

A comprehensive exploration of the mathematics behind the modeling and rendering of computer graphics scenes Mathematical Structures for Computer Graphics presents an accessible and intuitive approach to the mathematical ideas and techniques necessary for two- and three-dimensional computer graphics. Focusing on the significant mathematical results, the book establishes key algorithms used to build complex graphics scenes. Written for readers with various levels of mathematical background, the book develops a solid foundation for graphics techniques and fills in relevant grap

Foundations of factor analysis

CERN Document Server

Mulaik, Stanley A

2009-01-01

Introduction Factor Analysis and Structural Theories Brief History of Factor Analysis as a Linear Model Example of Factor AnalysisMathematical Foundations for Factor Analysis Introduction Scalar AlgebraVectorsMatrix AlgebraDeterminants Treatment of Variables as Vectors Maxima and Minima of FunctionsComposite Variables and Linear Transformations Introduction Composite Variables Unweighted Composite VariablesDifferentially Weighted Composites Matrix EquationsMulti

Constructivism in mathematics

CERN Document Server

Troelstra, AS

1988-01-01

Studies in Logic and the Foundations of Mathematics, Volume 123: Constructivism in Mathematics: An Introduction, Vol. II focuses on various studies in mathematics and logic, including metric spaces, polynomial rings, and Heyting algebras.The publication first takes a look at the topology of metric spaces, algebra, and finite-type arithmetic and theories of operators. Discussions focus on intuitionistic finite-type arithmetic, theories of operators and classes, rings and modules, linear algebra, polynomial rings, fields and local rings, complete separable metric spaces, and located sets. The te

Quantum information theory mathematical foundation

CERN Document Server

Hayashi, Masahito

2017-01-01

This graduate textbook provides a unified view of quantum information theory. Clearly explaining the necessary mathematical basis, it merges key topics from both information-theoretic and quantum- mechanical viewpoints and provides lucid explanations of the basic results. Thanks to this unified approach, it makes accessible such advanced topics in quantum communication as quantum teleportation, superdense coding, quantum state transmission (quantum error-correction) and quantum encryption. Since the publication of the preceding book Quantum Information: An Introduction, there have been tremendous strides in the field of quantum information. In particular, the following topics – all of which are addressed here – made seen major advances: quantum state discrimination, quantum channel capacity, bipartite and multipartite entanglement, security analysis on quantum communication, reverse Shannon theorem and uncertainty relation. With regard to the analysis of quantum security, the present book employs an impro...

Positioning Mathematics Education Researchers to Influence Storylines

Science.gov (United States)

Herbel-Eisenmann, Beth; Sinclair, Nathalie; Chval, Kathryn B.; Clements, Douglas H.; Civil, Marta; Pape, Stephen J.; Stephan, Michelle; Wanko, Jeffrey J.; Wilkerson, Trena L.

2016-01-01

The NCTM Research Committee identifies key influences on mathematics education that are largely outside the domain of the academic world in which most mathematics education researchers live. The groups that are identified--including the media, companies and foundations, and other academic domains--affect the public's perception of mathematics and…

Using Digital Games to Learn Mathematics – What students think?

OpenAIRE

Su Ting Yong; Ian Harrison; Peter Gates

2016-01-01

The aim of this study was to explore how university foundation students perceive the use of digital games in learning mathematics. Data was collected using an online questionnaire and 209 foundation university students participated in this study.  The questionnaire was used to explore students’ gaming experience and students’ attitude towards mathematics learning with digital games.  It was found that most of the university foundation students liked to play different types of digital games.  ...

Mathematics and linguistics

Energy Technology Data Exchange (ETDEWEB)

Landauer, C.; Bellman, K.L.

1996-12-31

In this paper, we study foundational issues that we believe will help us develop a theoretically sound approach to constructing complex systems. The two theoretical approaches that have helped us understand and develop computational systems in the past are mathematics and linguistics. We describe some differences and strengths of the approaches, and propose a research program to combine the richness of linguistic reasoning with the precision of mathematics.

Assessing the Success of ICT¡¯s from a User Perspective: Case Study of Coffee Research Foundation, Kenya

OpenAIRE

Michael W. Makokha; Daniel O. Ochieng

2014-01-01

The study was conducted to validate the application of DeLone & McLean¡¯s Information System (IS) success model (2003) in a local setup in Kenya and to evaluate the success of an enterprise resource planning (ERP) system from a user perspective. It was carried out at Coffee Research Foundation (CRF) in Kenya. A number of past studies to measure the success of information systems in different settings were reviewed leading to the choice and use of the updated DeLone & McLean IS success model i...

The Carnegie Initiative on the Doctorate: The Case of Mathematics. Carnegie Essays on the Doctorate: Mathematics.

Science.gov (United States)

Bass, Hyman

The Carnegie Foundation commissioned a collection of essays as part of the Carnegie Initiative on the Doctorate (CID). Essays and essayists represent six disciplines that are part of the CID: chemistry, education, English, history, mathematics, and neuroscience. Intended to engender conversation about the conceptual foundation of doctoral…

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.

Advanced Training in Mathematics Schools

Indian Academy of Sciences (India)

Advanced Training in Mathematics Schools (ATM Schools) are a joint effort of more than. 50 active researchers across the country with support from the National Board for Higher. Mathematics. The objective of these schools is to impart basic knowledge in algebra, analysis and topology in the Annual Foundation School ...

Developing a Theoretical Framework to Inform the Design of a Teacher Professional Development Program to Enable Foundation to Year 2 Teachers of Mathematics to Build on Indigenous and Low-SES Students' Cultural Capital

Science.gov (United States)

Anderson, Robyn; Stütz, Alexander; Cooper, Tom; Nason, Rod

2017-01-01

This paper reports on the early stages of the conceptualisation and implementation of the Accelerated Inclusive Mathematics-Early Understandings (AIM EU) project, a project whose major goals are to advance theory and practice in the improvement of Foundation to Year 2 (F-2) teachers' capacity to teach mathematics and through this to enhance F-2…

Algorithmic foundation of multi-scale spatial representation

CERN Document Server

Li, Zhilin

2006-01-01

With the widespread use of GIS, multi-scale representation has become an important issue in the realm of spatial data handling. However, no book to date has systematically tackled the different aspects of this discipline. Emphasizing map generalization, Algorithmic Foundation of Multi-Scale Spatial Representation addresses the mathematical basis of multi-scale representation, specifically, the algorithmic foundation.Using easy-to-understand language, the author focuses on geometric transformations, with each chapter surveying a particular spatial feature. After an introduction to the essential operations required for geometric transformations as well as some mathematical and theoretical background, the book describes algorithms for a class of point features/clusters. It then examines algorithms for individual line features, such as the reduction of data points, smoothing (filtering), and scale-driven generalization, followed by a discussion of algorithms for a class of line features including contours, hydrog...

Mathematical Foundation Based Inter-Connectivity modelling of Thermal Image processing technique for Fire Protection

Directory of Open Access Journals (Sweden)

Sayantan Nath

2015-09-01

Full Text Available In this paper, integration between multiple functions of image processing and its statistical parameters for intelligent alarming series based fire detection system is presented. The proper inter-connectivity mapping between processing elements of imagery based on classification factor for temperature monitoring and multilevel intelligent alarm sequence is introduced by abstractive canonical approach. The flow of image processing components between core implementation of intelligent alarming system with temperature wise area segmentation as well as boundary detection technique is not yet fully explored in the present era of thermal imaging. In the light of analytical perspective of convolutive functionalism in thermal imaging, the abstract algebra based inter-mapping model between event-calculus supported DAGSVM classification for step-by-step generation of alarm series with gradual monitoring technique and segmentation of regions with its affected boundaries in thermographic image of coal with respect to temperature distinctions is discussed. The connectedness of the multifunctional operations of image processing based compatible fire protection system with proper monitoring sequence is presently investigated here. The mathematical models representing the relation between the temperature affected areas and its boundary in the obtained thermal image defined in partial derivative fashion is the core contribution of this study. The thermal image of coal sample is obtained in real-life scenario by self-assembled thermographic camera in this study. The amalgamation between area segmentation, boundary detection and alarm series are described in abstract algebra. The principal objective of this paper is to understand the dependency pattern and the principles of working of image processing components and structure an inter-connected modelling technique also for those components with the help of mathematical foundation.

A bridge to advanced mathematics

CERN Document Server

Sentilles, Dennis

2011-01-01

This helpful workbook-style ""bridge"" book introduces students to the foundations of advanced mathematics, spanning the gap between a practically oriented calculus sequence and subsequent courses in algebra and analysis with a more theoretical slant. Part 1 focuses on logic and number systems, providing the most basic tools, examples, and motivation for the manner, method, and concerns of higher mathematics. Part 2 covers sets, relations, functions, infinite sets, and mathematical proofs and reasoning. Author Dennis Sentilles also discusses the history and development of mathematics as well a

Bridging different perspectives of the physiological and mathematical disciplines.

Science.gov (United States)

Batzel, Jerry Joseph; Hinghofer-Szalkay, Helmut; Kappel, Franz; Schneditz, Daniel; Kenner, Thomas; Goswami, Nandu

2012-12-01

The goal of this report is to discuss educational approaches for bridging the different perspectives of the physiological and mathematical disciplines. These approaches can enhance the learning experience for physiology, medical, and mathematics students and simultaneously act to stimulate mathematical/physiological/clinical interdisciplinary research. While physiology education incorporates mathematics, via equations and formulas, it does not typically provide a foundation for interdisciplinary research linking mathematics and physiology. Here, we provide insights and ideas derived from interdisciplinary seminars involving mathematicians and physiologists that have been conducted over the last decade. The approaches described here can be used as templates for giving physiology and medical students insights into how sophisticated tools from mathematics can be applied and how the disciplines of mathematics and physiology can be integrated in research, thereby fostering a foundation for interdisciplinary collaboration. These templates are equally applicable to linking mathematical methods with other life and health sciences in the educational process.

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...

Smashing UX design foundations for designing online user experiences

CERN Document Server

Allen, Jesmond

2012-01-01

The ultimate guide to UX from the world's most popular resource for web designers and developers Smashing Magazine is the world's most popular resource for web designers and developers and with this book, the authors provide the pinnacle resource to becoming savvy with User Experience Design (UX). The authors first provide an overview of UX and chart its rise to becoming a valuable and necessary practice for narrowing the gap between Web sites, applications, and users in order to make a user's experience a happy, easy, and successful one.Examines the essential aspects of User Experience Design

Theoretical Foundations of Study of Cartography

Science.gov (United States)

Talhofer, Václav; Hošková-Mayerová, Šárka

2018-05-01

Cartography and geoinformatics are technical-based fields which deal with modelling and visualization of landscape in the form of a map. The theoretical foundation is necessary to obtain during study of cartography and geoinformatics based mainly on mathematics. For the given subjects, mathematics is necessary for understanding of many procedures that are connected to modelling of the Earth as a celestial body, to ways of its projection into a plane, to methods and procedures of modelling of landscape and phenomena in society and visualization of these models in the form of electronic as well as classic paper maps. Not only general mathematics, but also its extension of differential geometry of curves and surfaces, ways of approximation of lines and surfaces of functional surfaces, mathematical statistics and multi-criterial analyses seem to be suitable and necessary. Underestimation of the significance of mathematical education in cartography and geoinformatics is inappropriate and lowers competence of cartographers and professionals in geographic information science and technology to solve problems.

Addressing Priorities for Elementary School Mathematics

Science.gov (United States)

Venenciano, Linda; Dougherty, Barbara

2014-01-01

Findings from international assessments present an opportunity to reconsider mathematics education across the grades. If concepts taught in elementary grades lay the foundation for continued study, then children's introduction to school mathematics deserves particular attention. We consider Davydov's theory (1966), which sequences…

Technical Training: EMAG-2005 - Electromagnetic Design and Mathematical Optimization Methods in Magnet Technology

CERN Multimedia

Monique Duval

2005-01-01

CERN Technical Training 2005: Learning for the LHC! CERN Technical Training, in collaboration with the AT-MEL-EM section, is organising a new course series in the framework of the 2005 CERN Technical Training programme: EMAG-2005 - Electromagnetic Design and Mathematical Optimization Methods in Magnet Technology, composed of three-hour lectures in the morning and topical seminars in the afternoon. The EMAG-2005 course series will run at CERN from Monday April 4 until Thursday April 14 (no lectures on Friday 8). The course series, in English, will focus on the foundations of electromagnetism and the design of accelerator magnets, both normal conducting and superconducting, employing analytical and numerical field computations. Examples of the LHC magnet design using the CERN field computation program ROXIE will be presented. However, EMAG-2005 is not a ROXIE user course: it is rather a course for users or potential users of numerical field computation software, and for magnet designers. The course will be o...

What Is Our First Philosophy in Mathematics Education?

Science.gov (United States)

Ernest, Paul

2012-01-01

What are the theoretical foundations of mathematics education? Recently disciplines other than mathematics and psychology have grown in importance, including philosophy. But which branch of philosophy is the most fundamental for mathematics education? In this article, I consider the claims of five branches of philosophy to be our "first…

Designing Non-Cognitive Construct Measures That Improve Mathematics Achievement in Grade 5-6 Learners. A User-Centered Approach

Science.gov (United States)

Chatterji, Madhabi; Lin, Meiko

2018-01-01

Purpose: The purpose of this study was to design and iteratively improve the quality of survey-based measures of three non-cognitive constructs for Grade 5-6 students, keeping in mind information needs of users in education reform contexts. The constructs are: Mathematics-related Self-Efficacy, Self-Concept, and Anxiety (M-SE, M-SC, and M-ANX).…

Foundation Content Knowledge: What Do Pre-Service Teachers Need to Know?

Science.gov (United States)

Linsell, Chris; Anakin, Megan

2013-01-01

The mathematics content knowledge of pre-service teachers is a growing area of inquiry. This topic requires further theoretical development due to the limited applicability of current cognitive and practice-oriented frameworks of mathematics content knowledge to beginning pre-service teachers. Foundation content knowledge is an integrated,…

Pretend Play and the Cultural Foundations of Mathematics

Science.gov (United States)

Worthington, Maulfry; van Oers, Bert

2016-01-01

The aim of this study is to uncover the emergence of cultural mathematical understandings and communications in young children's spontaneous pretend play. It is based on Vygotskian cultural-historical perspectives and social-semiotic theory, informed by research into "funds of knowledge" and considers how children's informal knowledge of…

Development of a Multidisciplinary Middle School Mathematics Infusion Model

Science.gov (United States)

Russo, Maria; Hecht, Deborah; Burghardt, M. David; Hacker, Michael; Saxman, Laura

2011-01-01

The National Science Foundation (NSF) funded project "Mathematics, Science, and Technology Partnership" (MSTP) developed a multidisciplinary instructional model for connecting mathematics to science, technology and engineering content areas at the middle school level. Specifically, the model infused mathematics into middle school curriculum…

Professor Tony F. Chan Assistant Director for Mathematics and Physical Sciences National Science Foundation United States of America on 23rd May 2007. Here visiting ATLAS experiment with P. Jenni and M. Tuts.

CERN Multimedia

Maximilien Brice

2007-01-01

Professor Tony F. Chan Assistant Director for Mathematics and Physical Sciences National Science Foundation United States of America on 23rd May 2007. Here visiting ATLAS experiment with P. Jenni and M. Tuts.

STEM Education: What Does Mathematics Have to Offer?

Science.gov (United States)

Fitzallen, Noleine

2015-01-01

The emphasis on science, technology, engineering, and mathematics (STEM) education in recent times could be perceived as business as usual or as an opportunity for innovation and change in mathematics classrooms. Either option presents challenges for mathematics educators who are expected to contribute to the foundations of a STEM literate…

Continuum mechanics the birthplace of mathematical models

CERN Document Server

Allen, Myron B

2015-01-01

Continuum mechanics is a standard course in many graduate programs in engineering and applied mathematics as it provides the foundations for the various differential equations and mathematical models that are encountered in fluid mechanics, solid mechanics, and heat transfer.  This book successfully makes the topic more accessible to advanced undergraduate mathematics majors by aligning the mathematical notation and language with related courses in multivariable calculus, linear algebra, and differential equations; making connections with other areas of applied mathematics where parial differe

Foundation plate on the elastic half-space, deterministic and probabilistic approach

Directory of Open Access Journals (Sweden)

Tvrdá Katarína

2017-01-01

Full Text Available Interaction between the foundation plate and subgrade can be described by different mathematical - physical model. Elastic foundation can be modelled by different types of models, e.g. one-parametric model, two-parametric model and a comprehensive model - Boussinesque (elastic half-space had been used. The article deals with deterministic and probabilistic analysis of deflection of the foundation plate on the elastic half-space. Contact between the foundation plate and subsoil was modelled using contact elements node-node. At the end the obtained results are presented.

Foundations of mathematics and physics one century after Hilbert new perspectives

CERN Document Server

2018-01-01

This book explores the rich and deep interplay between mathematics and physics one century after David Hilbert’s works from 1891 to 1933, published by Springer in six volumes. The most prominent scientists in various domains of these disciplines contribute to this volume providing insight to their works, and analyzing the impact of the breakthrough and the perspectives of their own contributions. The result is a broad journey through the most recent developments in mathematical physics, such as string theory, quantum gravity, noncommutative geometry, twistor theory, Gauge and Quantum fields theories, just to mention a few. The reader, accompanied on this journey by some of the fathers of these theories, explores some far reaching interfaces where mathematics and theoretical physics interact profoundly and gets a broad and deep understanding of subjects which are at the core of recent developments in mathematical physics. The journey is not confined to the present state of the art, but sheds light on future ...

A First Course in Applied Mathematics

CERN Document Server

Rebaza, Jorge

2012-01-01

Explore real-world applications of selected mathematical theory, concepts, and methods Exploring related methods that can be utilized in various fields of practice from science and engineering to business, A First Course in Applied Mathematics details how applied mathematics involves predictions, interpretations, analysis, and mathematical modeling to solve real-world problems. Written at a level that is accessible to readers from a wide range of scientific and engineering fields, the book masterfully blends standard topics with modern areas of application and provides the needed foundation

International note: Are Emirati parents' attitudes toward mathematics linked to their adolescent children's attitudes toward mathematics and mathematics achievement?

Science.gov (United States)

Areepattamannil, Shaljan; Khine, Myint Swe; Melkonian, Michael; Welch, Anita G; Al Nuaimi, Samira Ahmed; Rashad, Fatimah F

2015-10-01

Drawing on data from the 2012 Program for International Student Assessment (PISA) and employing multilevel modeling as an analytic strategy, this study examined the relations of adolescent children's perceptions of their parents' attitudes towards mathematics to their own attitudes towards mathematics and mathematics achievement among a sample of 5116 adolescents from 384 schools in the United Arab Emirates. The results of this cross-sectional study revealed that adolescents who perceived that their parents liked mathematics and considered mathematics was important for their children not only to study but also for their career tended to report higher levels of intrinsic and instrumental motivation to learn mathematics, mathematics self-concept and self-efficacy, and mathematics work ethic. Moreover, adolescents who perceived that their parents liked mathematics and considered mathematics was important for their children's career tended to report positive intentions and behaviors toward mathematics. However, adolescents who perceived that their parents considered mathematics was important for their children's career tended to report higher levels of mathematics anxiety. Finally, adolescents who perceived that their parents considered mathematics was important for their children to study performed significantly better on the mathematics assessment than did their peers whose parents disregarded the importance of learning mathematics. Copyright © 2015 The Foundation for Professionals in Services for Adolescents. Published by Elsevier Ltd. All rights reserved.

DOE Fundamentals Handbook: Mathematics, Volume 1

International Nuclear Information System (INIS)

1992-06-01

The Mathematics Fundamentals Handbook was developed to assist nuclear facility operating contractors provide operators, maintenance personnel, and the technical staff with the necessary fundamentals training to ensure a basic understanding of mathematics and its application to facility operation. The handbook includes a review of introductory mathematics and the concepts and functional use of algebra, geometry, trigonometry, and calculus. Word problems, equations, calculations, and practical exercises that require the use of each of the mathematical concepts are also presented. This information will provide personnel with a foundation for understanding and performing basic mathematical calculations that are associated with various DOE nuclear facility operations

DOE Fundamentals Handbook: Mathematics, Volume 2

International Nuclear Information System (INIS)

1992-06-01

The Mathematics Fundamentals Handbook was developed to assist nuclear facility operating contractors provide operators, maintenance personnel, and the technical staff with the necessary fundamentals training to ensure a basic understanding of mathematics and its application to facility operation. The handbook includes a review of introductory mathematics and the concepts and functional use of algebra, geometry, trigonometry, and calculus. Word problems, equations, calculations, and practical exercises that require the use of each of the mathematical concepts are also presented. This information will provide personnel with a foundation for understanding and performing basic mathematical calculations that are associated with various DOE nuclear facility operations

A Foundation for Mobile User Experiences in Theme Parks

DEFF Research Database (Denmark)

Østergaard, Claus Møller

2013-01-01

Based on case studies, this paper proposes a theoretical understanding of three essential aspects, which affect mobile user experiences in theme parks. The aspect are (a) the controllability of the mobile content, (b) the balance in the hybrid space of proximate physical place and remote digital...... space, and (c) the social space. Furthermore, the social space is exceptionally important in understanding mobile user experiences in theme parks. Thus, this paper proposes to extract the social space from the physical place. This means, that mobile user experiences in theme parks can be understood...

Dr. William C. Harris, Director-General, Science Foundation Ireland

CERN Multimedia

Maximilien Brice

2002-01-01

Pictured with Robert Eisenstein, former assistant director for mathematical and physical sciences (MPS) at the US National Science Foundation (NSF), who is spending a year at CERN as a member of the ATLAS collaboration.

Frege, Dedekind, and Peano on the foundations of arithmetic

CERN Document Server

Gillies, Donald

2013-01-01

First published in 1982, this reissue contains a critical exposition of the views of Frege, Dedekind and Peano on the foundations of arithmetic. The last quarter of the 19th century witnessed a remarkable growth of interest in the foundations of arithmetic. This work analyses both the reasons for this growth of interest within both mathematics and philosophy and the ways in which this study of the foundations of arithmetic led to new insights in philosophy and striking advances in logic. This historical-critical study provides an excellent introduction to the problems of the philosop

Ancient Indian Leaps into Mathematics

CERN Document Server

Yadav, B S

2011-01-01

This book presents contributions of mathematicians covering topics from ancient India, placing them in the broader context of the history of mathematics. Although the translations of some Sanskrit mathematical texts are available in the literature, Indian contributions are rarely presented in major Western historical works. Yet some of the well-known and universally-accepted discoveries from India, including the concept of zero and the decimal representation of numbers, have made lasting contributions to the foundation of modern mathematics. Through a systematic approach, this book examines th

A College-Level Foundational Mathematics Course: Evaluation, Challenges, and Future Directions

Science.gov (United States)

Maciejewski, Wes

2012-01-01

Recently in Ontario, Canada, the College Math Project brought to light startling data on the achievement of students in Ontario's College of Applied Arts and Technology System related to their performance in first-year mathematics courses: one-third of the students had failed their first-year mathematics course or were at risk of not completing…

Evaluation of the "Foundations in Knowledge Translation" training initiative: preparing end users to practice KT.

Science.gov (United States)

Park, Jamie S; Moore, Julia E; Sayal, Radha; Holmes, Bev J; Scarrow, Gayle; Graham, Ian D; Jeffs, Lianne; Timmings, Caitlyn; Rashid, Shusmita; Johnson, Alekhya Mascarenhas; Straus, Sharon E

2018-04-25

Current knowledge translation (KT) training initiatives are primarily focused on preparing researchers to conduct KT research rather than on teaching KT practice to end users. Furthermore, training initiatives that focus on KT practice have not been rigorously evaluated and have focused on assessing short-term outcomes and participant satisfaction only. Thus, there is a need for longitudinal training evaluations that assess the sustainability of training outcomes and contextual factors that may influence outcomes. We evaluated the KT training initiative "Foundations in KT" using a mixed-methods longitudinal design. "Foundations in KT" provided training in KT practice and included three tailored in-person workshops, coaching, and an online platform for training materials and knowledge exchange. Two cohorts were included in the study (62 participants, including 46 "Foundations in KT" participants from 16 project teams and 16 decision-maker partners). Participants completed self-report questionnaires, focus groups, and interviews at baseline and at 6, 12, 18, and 24 months after the first workshop. Participant-level outcomes include survey results which indicated that participants' self-efficacy in evidence-based practice (F(1,8.9) = 23.7, p = 0.001, n = 45), KT activities (F(1,23.9) = 43.2, p training initiative helped participants achieve their KT project objectives, plan their projects, and solve problems over time. Contextual factors include teams with high self-reported organizational capacity and commitment to implement at the start of their project had buy-in from upper management that resulted in secured funding and resources for their project. Training initiative outcomes include participants who applied the KT knowledge and skills they learned to other projects by sharing their knowledge informally with coworkers. Sustained spread of KT practice was observed with five teams at 24 months. We completed a longitudinal evaluation of a KT

Primary Mathematics. A Saxon Teacher's Resource Booklet.

Science.gov (United States)

1997

Saxon's primary mathematics series is a "hands-on," success-oriented program which emphasizes manipulatives and mental math. The series addresses the multisensory approach to teaching. Its use enables all children to develop a solid foundation in the language and basic concepts of mathematics. Concepts are presented in carefully…

Why Husserl should have been a strong revisionist in mathematics

NARCIS (Netherlands)

Atten, M. van

Husserl repeatedly has claimed that (1) mathematics without a philosophical foundation is not a science but a mere technique; (2) philosophical considerations may lead to the rejection of parts of mathematical practice; but (3) they cannot lead to mathematical innovations. My thesis is that

Community Partnerships: Pathways to Meaningful Mathematics

Science.gov (United States)

Bush, Sarah B.; Karp, Karen S.; Lentz, Tova; Nadler, Jennifer

2013-01-01

This article showcases the benefits of the alliance the authors have established during the past two years with the Barnes Foundation to add more mathematics activities to their repertoire and to integrate more art into their mathematics lessons. Recently, they decided to focus on activities at the K-grade 2 level that could be used as an on-site…

Socioeconomic variation, number competence, and mathematics learning difficulties in young children.

Science.gov (United States)

Jordan, Nancy C; Levine, Susan C

2009-01-01

As a group, children from disadvantaged, low-income families perform substantially worse in mathematics than their counterparts from higher-income families. Minority children are disproportionately represented in low-income populations, resulting in significant racial and social-class disparities in mathematics learning linked to diminished learning opportunities. The consequences of poor mathematics achievement are serious for daily functioning and for career advancement. This article provides an overview of children's mathematics difficulties in relation to socioeconomic status (SES). We review foundations for early mathematics learning and key characteristics of mathematics learning difficulties. A particular focus is the delays or deficiencies in number competencies exhibited by low-income children entering school. Weaknesses in number competence can be reliably identified in early childhood, and there is good evidence that most children have the capacity to develop number competence that lays the foundation for later learning.

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.

Learning higher mathematics

CERN Document Server

Pontrjagin, Lev Semenovič

1984-01-01

Lev Semenovic Pontrjagin (1908) is one of the outstanding figures in 20th century mathematics. In a long career he has made fundamental con­ tributions to many branches of mathematics, both pure and applied. He has received every honor that a grateful government can bestow. Though in no way constrained to do so, he has through the years taught mathematics courses at Moscow State University. In the year 1975 he set himself the task of writing a series of books on secondary school and beginning university mathematics. In his own words, "I wished to set forth the foundations of higher mathematics in a form that would have been accessible to myself as a lad, but making use of all my experience as a scientist and a teacher, ac­ cumulated over many years. " The present volume is a translation of the first two out of four moderately sized volumes on this theme planned by Pro­ fessor Pontrjagin. The book begins at the beginning of modern mathematics, analytic ge­ ometry in the plane and 3-dimensional space. Refin...

Foundations of signal processing

CERN Document Server

Vetterli, Martin; Goyal, Vivek K

2014-01-01

This comprehensive and engaging textbook introduces the basic principles and techniques of signal processing, from the fundamental ideas of signals and systems theory to real-world applications. Students are introduced to the powerful foundations of modern signal processing, including the basic geometry of Hilbert space, the mathematics of Fourier transforms, and essentials of sampling, interpolation, approximation and compression. The authors discuss real-world issues and hurdles to using these tools, and ways of adapting them to overcome problems of finiteness and localisation, the limitations of uncertainty and computational costs. Standard engineering notation is used throughout, making mathematical examples easy for students to follow, understand and apply. It includes over 150 homework problems and over 180 worked examples, specifically designed to test and expand students' understanding of the fundamentals of signal processing, and is accompanied by extensive online materials designed to aid learning, ...

How we understand mathematics conceptual integration in the language of mathematical description

CERN Document Server

Woźny, Jacek

2018-01-01

This volume examines mathematics as a product of the human mind and analyzes the language of "pure mathematics" from various advanced-level sources. Through analysis of the foundational texts of mathematics, it is demonstrated that math is a complex literary creation, containing objects, actors, actions, projection, prediction, planning, explanation, evaluation, roles, image schemas, metonymy, conceptual blending, and, of course, (natural) language. The book follows the narrative of mathematics in a typical order of presentation for a standard university-level algebra course, beginning with analysis of set theory and mappings and continuing along a path of increasing complexity. At each stage, primary concepts, axioms, definitions, and proofs will be examined in an effort to unfold the tell-tale traces of the basic human cognitive patterns of story and conceptual blending. This book will be of interest to mathematicians, teachers of mathematics, cognitive scientists, cognitive linguists, and anyone interested...

Writing and mathematical problem solving in Grade 3

Directory of Open Access Journals (Sweden)

Belinda Petersen

2017-06-01

Full Text Available This article looks at writing tasks as a methodology to support learners’ mathematical problemsolving strategies in the South African Foundation Phase context. It is a qualitative case study and explores the relation between the use of writing in mathematics and development of learners’ problem-solving strategies and conceptual understanding. The research was conducted in a suburban Foundation Phase school in Cape Town with a class of Grade 3 learners involved in a writing and mathematics intervention. Writing tasks were modelled to learners and implemented by them while they were engaged in mathematical problem solving. Data were gathered from a sample of eight learners of different abilities and included written work, interviews, field notes and audio recordings of ability group discussions. The results revealed an improvement in the strategies and explanations learners used when solving mathematical problems compared to before the writing tasks were implemented. Learners were able to reflect critically on their thinking through their written strategies and explanations. The writing tasks appeared to support learners in providing opportunities to construct and apply mathematical knowledge and skills in their development of problem-solving strategies.

Foundations of Large-Scale Multimedia Information Management and Retrieval

CERN Document Server

Chang, Edward Y

2011-01-01

"Foundations of Large-Scale Multimedia Information Management and Retrieval - Mathematics of Perception" covers knowledge representation and semantic analysis of multimedia data and scalability in signal extraction, data mining, and indexing. The book is divided into two parts: Part I - Knowledge Representation and Semantic Analysis focuses on the key components of mathematics of perception as it applies to data management and retrieval. These include feature selection/reduction, knowledge representation, semantic analysis, distance function formulation for measuring similarity, and

MADS Users' Guide

Science.gov (United States)

Moerder, Daniel D.

2014-01-01

MADS (Minimization Assistant for Dynamical Systems) is a trajectory optimization code in which a user-specified performance measure is directly minimized, subject to constraints placed on a low-order discretization of user-supplied plant ordinary differential equations. This document describes the mathematical formulation of the set of trajectory optimization problems for which MADS is suitable, and describes the user interface. Usage examples are provided.

A history of mathematics

CERN Document Server

Boyer, Carl B

1989-01-01

"Boyer and Merzbach distill thousands of years of mathematics into this fascinating chronicle. From the Greeks to Godel, the mathematics is brilliant; the cast of characters is distinguished; the ebb and flow of ideas is everywhere evident. And, while tracing the development of European mathematics, the authors do not overlook the contributions of Chinese, Indian, and Arabic civilizations. Without doubt, this is--and will long remain--a classic one-volume history of mathematics and mathematicians who create it." --William Dunham Author, Journey Through Genius, The Great Theorems of Mathematics "When we read a book like A History of Mathematics, we get the picture of a mounting structure, ever taller and broader and more beautiful and magnificent--and with a foundation, moreover, that is as untainted and as functional now as it was when Thales worked out the first geometrical theorems nearly 26 centuries ago." --From the Foreword by Isaac Asimov "One of the most useful and comprehensive general introductions t...

Facilitating mathematics learning for students with upper extremity disabilities using touch-input system.

Science.gov (United States)

Choi, Kup-Sze; Chan, Tak-Yin

2015-03-01

To investigate the feasibility of using tablet device as user interface for students with upper extremity disabilities to input mathematics efficiently into computer. A touch-input system using tablet device as user interface was proposed to assist these students to write mathematics. User-switchable and context-specific keyboard layouts were designed to streamline the input process. The system could be integrated with conventional computer systems only with minor software setup. A two-week pre-post test study involving five participants was conducted to evaluate the performance of the system and collect user feedback. The mathematics input efficiency of the participants was found to improve during the experiment sessions. In particular, their performance in entering trigonometric expressions by using the touch-input system was significantly better than that by using conventional mathematics editing software with keyboard and mouse. The participants rated the touch-input system positively and were confident that they could operate at ease with more practice. The proposed touch-input system provides a convenient way for the students with hand impairment to write mathematics and has the potential to facilitate their mathematics learning. Implications for Rehabilitation Students with upper extremity disabilities often face barriers to learning mathematics which is largely based on handwriting. Conventional computer user interfaces are inefficient for them to input mathematics into computer. A touch-input system with context-specific and user-switchable keyboard layouts was designed to improve the efficiency of mathematics input. Experimental results and user feedback suggested that the system has the potential to facilitate mathematics learning for the students.

Mathematical phantoms for use in dose estimation of survivors in Hiroshima and Nagasaki

International Nuclear Information System (INIS)

Maruyama, Takashi

1990-01-01

The T65D (Tentative 1965 Dose) was recently revised on the basis of new scientific evidences which were available in accordance with the development of computer techniques and the accumulation of nuclear data. For the dose determinations of survivors in Hiroshima and Nagasaki, DS86 (Dosimetric System 1986) is a complete replacement of T65D for the Life Span Study (LSS) in RERF (Radiation Effects Research Foundation). In the DS86, depending on the input data for a survivor, various elements of several data bases are combined to provide the dosimetric variables requested by the user. The quantity finally desired for the LSS is absorbed dose in each organ. The calculation of quantities for converting incident fluence to absorbed dose in the target organ was carried out using Monte Carlo methods. For this calculation, mathematical phantoms were required. This paper describes the background data used for the construction of Japanese survivor phantoms and summarizes the mathematical phantoms employed in the DS86. (author)

An introduction to mathematical cryptography

CERN Document Server

Hoffstein, Jeffrey; Silverman, Joseph H

2014-01-01

This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems. Only basic linear algebra is required of the reader; techniques from algebra, number theory, and probability are introduced and developed as required. This text provides an ideal introduction for mathematics and computer science students to the mathematical foundations of modern cryptography. The book includes an extensive bibliography and index; supplementary materials are available online. The book covers a variety of topics that are considered central to mathematical cryptography. Key topics include: classical cryptographic constructions, such as Diffie–Hellmann key exchange, discrete logarithm-based cryptosystems, the RSA cryptosystem, and digital signatures; fundamental mathematical tools for cr...

Beyond Wittgenstein's remarks on the foundation of mathematics: Explication of Piaget's suggestion of a biological foundation

Science.gov (United States)

Carmesin, Hans-Otto

1992-06-01

Knowing about the axiomatic aspects of mathematics, Wittgenstein asked the more fundamental question: ‘But then what does the peculiar inexorability of mathematics consist in?’. He answers the question partially by saying: ‘Then do you want to say that “being true” means: being usable (or useful)? — No, not that; but that it can't be said of the series of natural numbers — any more than of our language —that it is true, but: that it is usable, and, above all, it is used’. Here it will be demonstrated that there is another aspect ‘to be said of the series of natural numbers’, besides the mere fact that they are used or usable, namely a biological one, as has been suggested, though not explicated, by Piaget.

The integration of Mathematics, Science and Technology in early childhood education and the foundation phase: The role of the formation of the professional identities of beginner teachers

Directory of Open Access Journals (Sweden)

Marie Botha

2015-02-01

Full Text Available This article focuses on the professional identity formation of six beginner teachers (three in early childhood education and three in the foundation phase, involved in the teaching of Mathematics, Science and Technology (MST. Attention is in particular being paid to the role of professional identity in how they applied innovative teaching methods such as enquiry-based teaching. The study is based on the personal narratives of the six teachers, regarding their own learning experiences in MST, the impact of their professional training at an institution of higher education, as well as their first experiences as MST teachers in the workplace. A qualitative research design was applied and data was obtained through visual (photo collages and written stories, observation and interviews. Whilst all the teachers held negative attitudes towards Mathematics, this situation was turned around during their university training. The three teachers in early childhood education experienced their entrance to the profession as positive, due mainly to the support of colleagues in their application of innovative teaching methods. Two teachers in the foundation phase, however, experienced the opposite. The findings emphasise the complex processes in the moulding of a professional teacher identity and how teaching practices are influenced by these processes.

The tools of mathematical reasoning

CERN Document Server

Lakins, Tamara J

2016-01-01

This accessible textbook gives beginning undergraduate mathematics students a first exposure to introductory logic, proofs, sets, functions, number theory, relations, finite and infinite sets, and the foundations of analysis. The book provides students with a quick path to writing proofs and a practical collection of tools that they can use in later mathematics courses such as abstract algebra and analysis. The importance of the logical structure of a mathematical statement as a framework for finding a proof of that statement, and the proper use of variables, is an early and consistent theme used throughout the book.

Teaching Preschoolers to Count: Effective Strategies for Achieving Early Mathematics Milestones

Science.gov (United States)

Jacobi-Vessels, Jill L.; Brown, E. Todd; Molfese, Victoria J.; Do, Ahn

2016-01-01

Attention to early childhood mathematics instructional strategies has sharpened due to the relatively poor mathematics performance of U.S. students in comparison to students from other countries and research evidence that early mathematics skills impact later achievement. Early Childhood counting skills form the foundation for subsequent…

The Identification, Implementation, and Evaluation of Critical User Interface Design Features of Computer-Assisted Instruction Programs in Mathematics for Students with Learning Disabilities

Science.gov (United States)

Seo, You-Jin; Woo, Honguk

2010-01-01

Critical user interface design features of computer-assisted instruction programs in mathematics for students with learning disabilities and corresponding implementation guidelines were identified in this study. Based on the identified features and guidelines, a multimedia computer-assisted instruction program, "Math Explorer", which delivers…

Digital Curriculum Resources in Mathematics Education: Foundations for Change

Science.gov (United States)

Pepin, Birgit; Choppin, Jeffrey; Ruthven, Kenneth; Sinclair, Nathalie

2017-01-01

In this conceptual review paper we draw on recent literature with respect to digital curriculum resources (DCR); we briefly outline and explain selected theoretical frames; and we discuss issues related to the design, and the use (by teachers and students) of digital curricula and e-textbooks in mathematics education. The results of our review…

Foundations of quantum theory from classical concepts to operator algebras

CERN Document Server

Landsman, Klaas

2017-01-01

This book studies the foundations of quantum theory through its relationship to classical physics. This idea goes back to the Copenhagen Interpretation (in the original version due to Bohr and Heisenberg), which the author relates to the mathematical formalism of operator algebras originally created by von Neumann. The book therefore includes comprehensive appendices on functional analysis and C*-algebras, as well as a briefer one on logic, category theory, and topos theory. Matters of foundational as well as mathematical interest that are covered in detail include symmetry (and its "spontaneous" breaking), the measurement problem, the Kochen-Specker, Free Will, and Bell Theorems, the Kadison-Singer conjecture, quantization, indistinguishable particles, the quantum theory of large systems, and quantum logic, the latter in connection with the topos approach to quantum theory. This book is Open Access under a CC BY licence.

Dynamic response of beams on elastic foundations to impact loading

International Nuclear Information System (INIS)

Prasad, B.B.; Sinha, B.P.

1987-01-01

The beam considered is a Timoshenko beam in which the effects of rotatory inertia and shear deformations are included and the foundation model consists of Winkler-Zimmermann type having Hookean linear elastic springs. The analysis is very useful for predicting the dynamic response of structural components of aircraft or nuclear reactors or even runways if that component may be mathematically idealized as a beam on elastic foundation. The effect of rotatory inertia and shear deformation is very much pronounced and hence should not be neglected in solving such impact problems. In general the effect of foundation modulus is to further increase the values of frequencies of vibrations. (orig./HP)

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…

Mathematical Modelling for Micropiles Embedded in Salt Rock

Directory of Open Access Journals (Sweden)

Rădan (Toader Georgiana

2016-03-01

Full Text Available This study presents the results of the mathematical modelling for the micropiles foundation of an investement objective located in Slanic, Prahova county. Three computing models were created and analyzed with software, based on Finite Element Method. With Plaxis 2D model was analyzed the isolated micropile and the three-dimensional analysis was made with Plaxis 3D model, for group of micropiles. For the micropiles foundation was used Midas GTS-NX model. The mathematical models were calibrated based with the in-situ tests results for axially loaded micropiles, embedded in salt rock. The paper presents the results obtained with the three software, the calibration and validation models.

The Native Language in Teaching Kindergarten Mathematics

Science.gov (United States)

Espada, Janet P.

2012-01-01

The use of the native language as a medium of instruction is believed to be the fastest and most natural route towards developing a strong foundation in mathematics literacy (Mimaropa, In D.O.No. 74, s.2009). This study examined the effect of using the native language in the teaching of kindergarten mathematics. A total of 34 five to six year old…

Theological Underpinnings of the Modern Philosophy of Mathematics.

Directory of Open Access Journals (Sweden)

Shaposhnikov Vladislav

2016-03-01

Full Text Available The study is focused on the relation between theology and mathematics in the situation of increasing secularization. My main concern in the second part of this paper is the early-twentieth-century foundational crisis of mathematics. The hypothesis that pure mathematics partially fulfilled the functions of theology at that time is tested on the views of the leading figures of the three main foundationalist programs: Russell, Hilbert and Brouwer.

Team Foundation Server 2013 customization

CERN Document Server

Beeming, Gordon

2014-01-01

This book utilizes a tutorial based approach, focused on the practical customization of key features of the Team Foundation Server for collaborative enterprise software projects.This practical guide is intended for those who want to extend TFS. This book is for intermediate users who have an understanding of TFS, and basic coding skills will be required for the more complex customizations.

The EMERGE Summer Program: Supporting Incoming Freshmen's Success in Mathematics Developmental Coursework

Science.gov (United States)

Bird, Katherine; Oppland-Cordell, Sarah; Hibdon, Joseph

2016-01-01

This paper describes the development, results, and future directions of the mathematics component of the EMERGE Summer Program at Northeastern Illinois University. Initiated summer 2014, EMERGE offered English and mathematics sessions for incoming freshmen. The mathematics session aimed to strengthen participants' mathematical foundations,…

"If I had to pick any subject, it wouldn't be maths": foundations for engagement with mathematics during the middle years

Science.gov (United States)

Attard, Catherine

2013-12-01

This article is a report on a longitudinal case study that investigated the problem of lowered engagement with mathematics and students' perspectives of the factors that influenced their engagement during the middle years of schooling. The article provides a synthesis of the entire study and a summary of its findings. In order to address the research question a group of 20 students from within the same school cohort participated in the study spanning three school years from their final year of primary school, to their second year of secondary school. Data was collected through interviews, focus group discussions, and classroom observations. A major finding of this study was that positive pedagogical relationships between teachers and their students must be developed as a foundation for sustained engagement.

Study on Dynamic Characteristics of Heavy Machine Tool-Composite Pile Foundation-Soil

Directory of Open Access Journals (Sweden)

CAI Li-Gang

2014-09-01

Full Text Available Heavy duty computer numerical control machine tools have characteristics of large self-weight, load and. The insufficiency of foundation bearing capacity leads to deformation of lathe bed, which effects machining accuracy. A combined-layer foundation model is created to describe the pile group foundation of multi-soil layer in this paper. Considering piles and soil in pile group as transversely isotropic material, equivalent constitutive relationship of composite foundation is constructed. A mathematical model is established by the introduction of boundary conditions, which is based on heavy duty computer numerical control machine tools-composite pile foundation-soil interaction system. And then, the response of different soil and pile depth is studied by a case. The model improves motion accuracy of machine tools.

Designing of Holistic Mathematic Education Model Based-"System Among" at Low Grade Elementary School

Science.gov (United States)

Hayati, R.; Fauzan, A.; Iswari, M.; Khaidir, A.

2018-04-01

The purpose of this study was to develop a model of Holistic Mathematics Education (HME) among systems based on low-grade primary school students so that students have a solid foundation when entering a higher behavior. This type of research is desaign research developed by Plomp to have three stages, namely the preliminary research, development or prototyping phase, and assessement Phase. This research resulted in a model Holistic Mathematics Education (HME) -based system is among the primary school students low grade consists of 10 stages, namely 1) Recap through the neighborhood, 2) Discussion groups by exploiting the environment, 3) Demonstration Group, 4) Exercise individuals, 5) mathematical modeling, 6) Demonstration of individuals, 7) Reflections, 8) impressions and messages, and giving meaning, 9) Celebrations and 10) A thorough assessment. Furthermore, this model also produces 7 important components that should be developed teacher, namely 1) constructivism, 2) the nature of nature, 3) independence, 4) parable, 5) inquiry, 6) cooperation, and 7) strengthening. This model will produce a model in the form of books, student books and teacher's guide book as a support system that can help users in its application.

National Science Foundation Assistant Director for Mathematics and Physical Sciences Tony Chan (USA) visiting LHCb experiment on 23rd May 2007 with Spokesperson T. Nakada, Advisor to CERN Director-General J. Ellis and I. Belyaev of Syracuse

CERN Multimedia

Maximilien Brice

2007-01-01

National Science Foundation Assistant Director for Mathematics and Physical Sciences Tony Chan (USA) visiting LHCb experiment on 23rd May 2007 with Spokesperson T. Nakada, Advisor to CERN Director-General J. Ellis and I. Belyaev of Syracuse

Quality of life among lower limb prosthesis users attending Artificial Limb Center of Fauji Foundation Hospital Rawalpindi

International Nuclear Information System (INIS)

Kalsoom, U.; Bairam, S.

2018-01-01

To assess quality of life and the influencing factors as perceived by lower limb prosthesis users. Study Design: Cross sectional study. Place and Duration of Study: Artificial Limb Centre, Fauji Foundation Hospital Rawalpindi, 11 months (Jan to Nov 2014). Material and Methods: A sample of 50 patients with lower limb amputations and using lower limb prosthesis were recruited by applying inclusion criteria. Responses were recorded on demographic variables, reasons for amputation, time of provision of prosthesis, employment status etc. by the investigator on a structured pretested questionnaire after their consent. A p-value of <0.05 was taken as significant. Quality of life was interpreted on 5 point Likert scale. Data was analyzed in SPSS version 21. Result: Majority of respondents i.e. 17 (34%) were in 51-60 years age group with mean age 46 +- 14 years while 33 (66%) were males and 27 (54%) illiterate, 33 (66%) could afford a prosthesis. Trauma 28 (56%) was the most prevalent cause of lower limb amputation and among them 15 (53%) had road accident injuries. Various factors influenced quality of life as perceived by the respondents and in 10 (20%), 16 (32%), 25 (50%) social, family life and emotional status was affected respectively, while 14 (28%) of the prosthesis user were unemployed. Prosthesis were provided after 2 years in 18 (36%) and in 37 (74%) prosthesis were provided by the health care facility. Good quality of life was perceived in 40 (80%) respondents. Conclusion: Perceived Quality of life was good in majority of the prosthesis users but others can't be ignored. It can be improved by early provision of prosthesis which can help in better employment opportunities. (author)

From quantum foundations to applications and back.

Science.gov (United States)

Gisin, Nicolas; Fröwis, Florian

2018-07-13

Quantum non-locality has been an extremely fruitful subject of research, leading the scientific revolution towards quantum information science, in particular, to device-independent quantum information processing. We argue that the time is ripe to work on another basic problem in the foundations of quantum physics, the quantum measurement problem, which should produce good physics in theoretical, mathematical, experimental and applied physics. We briefly review how quantum non-locality contributed to physics (including some outstanding open problems) and suggest ways in which questions around macroscopic quantumness could equally contribute to all aspects of physics.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'. © 2018 The Author(s).

A foundation for translating user interaction designs into OSF/Motif-based software

OpenAIRE

Hinson, Kenneth Paul

1994-01-01

The user interface development process occurs in a behavioral domain and in a constructional domain. The development process in the behavioral domain focuses on the "look and feel" of the user interface and its behavior in response to user actions. The development process in the constructional domain focuses on developing software to implement the user interface. Although one may attempt to design a user interface from a constructional view, it is important to concentrate desig...

Perceptions of user studies as a foundation for public programming ...

African Journals Online (AJOL)

The purpose of this study was to examine the role of user studies and the evaluation of services in the development of effective public programming initiatives by the public archives of east and southern Africa. Users of the archives are the backbone of effective archival services. Sadly, it appears that the records are more ...

Mathematical methods for cancer evolution

CERN Document Server

Suzuki, Takashi

2017-01-01

The purpose of this monograph is to describe recent developments in mathematical modeling and mathematical analysis of certain problems arising from cell biology. Cancer cells and their growth via several stages are of particular interest. To describe these events, multi-scale models are applied, involving continuously distributed environment variables and several components related to particles. Hybrid simulations are also carried out, using discretization of environment variables and the Monte Carlo method for the principal particle variables. Rigorous mathematical foundations are the bases of these tools. The monograph is composed of four chapters. The first three chapters are concerned with modeling, while the last one is devoted to mathematical analysis. The first chapter deals with molecular dynamics occurring at the early stage of cancer invasion. A pathway network model based on a biological scenario is constructed, and then its mathematical structures are determined. In the second chapter mathematica...

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

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.

Elementary School Mathematics Priorities

Science.gov (United States)

Wilson, W. Stephen

2009-01-01

This article first describes some of the basic skills and knowledge that a solid elementary school mathematics foundation requires. It then elaborates on several points germane to these practices. These are then followed with a discussion and conclude with final comments and suggestions for future research. The article sets out the five…

Mathematics of the quantum informatics. An introduction; Mathematik der Quanteninformatik. Eine Einfuehrung

Energy Technology Data Exchange (ETDEWEB)

Scherer, Wolfgang

2016-07-01

Starting from the physical foundations all mathematics required for the quantum informatics are introduced and explained. The essential aspects of the quantum informatics are mathematically formulated. All statements made are also proved in the book.

Essays on the Foundations of Mathematics by Moritz Pasch

CERN Document Server

Pollard, Stephen

2010-01-01

Moritz Pasch (1843-1930) is justly celebrated as a key figure in the history of axiomatic geometry. Less well known are his contributions to other areas of foundational research. This volume features English translations of 14 papers Pasch published in the decade 1917-1926. In them, Pasch argues that geometry and, more surprisingly, number theory are branches of empirical science; he provides axioms for the combinatorial reasoning essential to Hilbert's program of consistency proofs; he explores 'implicit definition' (a generalization of definition by abstraction) and indicates how this techni

Digital curriculum resources in mathematics education: foundations for change

OpenAIRE

Pepin, B.; Choppin, J.; Ruthven, K.; Sinclair, N.

2017-01-01

In this conceptual review paper we draw on recent literature with respect to digital curriculum resources (DCR); we briefly outline and explain selected theoretical frames; and we discuss issues related to the design, and the use (by teachers and students) of digital curricula and e-textbooks in mathematics education. The results of our review show the following. Firstly, whilst there are some contrasting tendencies between research on instructional technology and research on DCR, these studi...

Logical foundation of quantum mechanics

International Nuclear Information System (INIS)

Stachow, E.W.

1980-01-01

The subject of this article is the reconstruction of quantum mechanics on the basis of a formal language of quantum mechanical propositions. During recent years, research in the foundations of the language of science has given rise to a dialogic semantics that is adequate in the case of a formal language for quantum physics. The system of sequential logic which is comprised by the language is more general than classical logic; it includes the classical system as a special case. Although the system of sequential logic can be founded without reference to the empirical content of quantum physical propositions, it establishes an essential part of the structure of the mathematical formalism used in quantum mechanics. It is the purpose of this paper to demonstrate the connection between the formal language of quantum physics and its representation by mathematical structures in a self-contained way. (author)

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...

Special relativity - the foundation of macroscopic physics

International Nuclear Information System (INIS)

Dixon, W.G.

1978-01-01

This book aims to show that an understanding of the basic laws of macroscopic systems can be gained more easily within relativistic physics than within Newtonian physics. The unity of dynamics, thermodynamics and electromagnetism under the umbrella of special relativity is examined under chapter headings entitled: the physics of space and time, affine spaces in mathematics and physics, foundations of dynamics, relativistic simple fluids, and, electrodynamics of polarizable fluids. (U.K.)

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.

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...

Designing for user engagement

CERN Document Server

Geisler, Cheryl

2013-01-01

Designing for User Engagement on the Web: 10 Basic Principles is concerned with making user experience engaging. The cascade of social web applications we are now familiar with - blogs, consumer reviews, wikis, and social networking - are all engaging experiences. But engagement is an increasingly common goal in business and productivity environments as well. This book provides a foundation for all those seeking to design engaging user experiences rich in communication and interaction. Combining a handbook on basic principles with case studies, it provides readers with a ric

The Applied Mathematics for Power Systems (AMPS)

Energy Technology Data Exchange (ETDEWEB)

Chertkov, Michael [Los Alamos National Laboratory

2012-07-24

Increased deployment of new technologies, e.g., renewable generation and electric vehicles, is rapidly transforming electrical power networks by crossing previously distinct spatiotemporal scales and invalidating many traditional approaches for designing, analyzing, and operating power grids. This trend is expected to accelerate over the coming years, bringing the disruptive challenge of complexity, but also opportunities to deliver unprecedented efficiency and reliability. Our Applied Mathematics for Power Systems (AMPS) Center will discover, enable, and solve emerging mathematics challenges arising in power systems and, more generally, in complex engineered networks. We will develop foundational applied mathematics resulting in rigorous algorithms and simulation toolboxes for modern and future engineered networks. The AMPS Center deconstruction/reconstruction approach 'deconstructs' complex networks into sub-problems within non-separable spatiotemporal scales, a missing step in 20th century modeling of engineered networks. These sub-problems are addressed within the appropriate AMPS foundational pillar - complex systems, control theory, and optimization theory - and merged or 'reconstructed' at their boundaries into more general mathematical descriptions of complex engineered networks where important new questions are formulated and attacked. These two steps, iterated multiple times, will bridge the growing chasm between the legacy power grid and its future as a complex engineered network.

Opening inquiry mathematics to parents: Can they be engaged as teachers’ partners in mathematical work?

Directory of Open Access Journals (Sweden)

Ioannis Papadopoulos

2017-12-01

Full Text Available This paper presents a two-stage project designed to develop the partnership between teacher and parents. The project began with a workshop constructed to motivate parents to be interested in doing mathematics in a way that is different from the one they experienced as students and, as a result, to be eager to become involved in the co-production of didactic materials for classroom use. Parents were engaged in real, collaborative, high-level mathematical work as a first step in engaging them as partners in mathematical work with their children.  During this first stage, parents were familiarized with inquiry mathematics tasks to provide them with the foundation necessary to become partners and co-producers during the second. The findings give evidence that the learning of reform math tasks and their co-creation supported teacher and parents’ partnership and that parents were moved mathematically and personally by the experience.

International note: exploring differences in native and immigrant adolescents' mathematics achievement and dispositions towards mathematics in Qatar.

Science.gov (United States)

Areepattamannil, Shaljan; Melkonian, Michael; Khine, Myint Swe

2015-04-01

The burgeoning immigrant population in major immigrant-receiving countries in North America and Europe has necessitated researchers and policymakers in these countries to examine the academic success of children of immigration and the factors contributing to their academic success. However, there is sparse research on the academic trajectories of children of immigration in other continents, such as Asia. Hence, the purpose of the present study was to examine first- and second-generation immigrant adolescents' mathematics achievement and dispositions towards mathematics in comparison to their native peers in one of the Middle Eastern countries in Asia, Qatar. The results of the study indicated that both first- and second-generation immigrant adolescents tended to have higher mathematics achievement, intrinsic motivation to learn mathematics, instrumental motivation to learn mathematics, mathematics self-efficacy, and mathematics self-concept than did their native counterparts. Moreover, immigrant adolescents tended to have lower mathematics anxiety than did their native peers. The study also revealed significant differences between first- and second-generation immigrant adolescents with respect to their mathematics achievement and dispositions towards mathematics. Copyright © 2015 The Foundation for Professionals in Services for Adolescents. Published by Elsevier Ltd. All rights reserved.

Impact loads on beams on elastic foundations

International Nuclear Information System (INIS)

Kameswara Rao, N.S.V.; Prasad, B.B.

1975-01-01

Quite often, complex structural components are idealised as beams in engineering analysis and design. Also, equations governing the responses of shallow shells are mathematically equivalent to the equations governing the responses of beams on elastic foundations. Hence with possible applications in several technical disciplines, the behaviour of beams on elastic foundations subjected to impact loads is studied in detail in the present investigation both analytically and experimentally. The analytical methods include analysis and energy method. The effect of foundation parameters (stiffness, and damping constants) on the dynamic responses of the beam-foundation system has been analysed. In modal analysis, the free-vibration equation has been solved by replacing the applied impulse by suitable initial conditions and the solution has been obtained as the linear combination of an infinite sequence of discrete eigen-vectors. In the energy method, the beam-foundation system is treated to be under forced vibrations and the forcing function has been obtained using the Hertz's law of impact. In the case of free-free end conditions of the beam, the rigid body modes and the elastic modes have been superposed to obtain the total response. The responses predicted using modal analysis are higher than those obtained using energy method. From the present study it is observed that model analysis is preferable to energy method. (Auth.)

Mathematics and art a cultural history

CERN Document Server

Gamwell, Lynn

2016-01-01

This is a cultural history of mathematics and art, from antiquity to the present. Mathematicians and artists have long been on a quest to understand the physical world they see before them and the abstract objects they know by thought alone. Taking readers on a tour of the practice of mathematics and the philosophical ideas that drive the discipline, Lynn Gamwell points out the important ways mathematical concepts have been expressed by artists. Sumptuous illustrations of artworks and cogent math diagrams are featured in Gamwell’s comprehensive exploration. Gamwell begins by describing mathematics from antiquity to the Enlightenment, including Greek, Islamic, and Asian mathematics. Then focusing on modern culture, Gamwell traces mathematicians’ search for the foundations of their science, such as David Hilbert’s conception of mathematics as an arrangement of meaning-free signs, as well as artists’ search for the essence of their craft, such as Aleksandr Rodchenko’s monochrome paintings. She shows t...

Socially Response-Able Mathematics Education: Implications of an Ethical Approach

Science.gov (United States)

Atweh, Bill; Brady, Kate

2009-01-01

This paper discusses an approach to mathematics education based on the concept of ethical responsibility. It argues that an ethical approach to mathematics teaching lays the theoretical foundations for social justice concerns in the discipline. The paper develops a particular understanding of ethical responsibility based on the writings of Emanuel…

Partial differential equations of mathematical physics

CERN Document Server

Sobolev, S L

1964-01-01

Partial Differential Equations of Mathematical Physics emphasizes the study of second-order partial differential equations of mathematical physics, which is deemed as the foundation of investigations into waves, heat conduction, hydrodynamics, and other physical problems. The book discusses in detail a wide spectrum of topics related to partial differential equations, such as the theories of sets and of Lebesgue integration, integral equations, Green's function, and the proof of the Fourier method. Theoretical physicists, experimental physicists, mathematicians engaged in pure and applied math

User Frustrations as Opportunities

Directory of Open Access Journals (Sweden)

Michael Weiss

2012-04-01

Full Text Available User frustrations are an excellent source of new product ideas. Starting with this observation, this article describes an approach that entrepreneurs can use to discover business opportunities. Opportunity discovery starts with a problem that the user has, but may not be able to articulate. User-centered design techniques can help elicit those latent needs. The entrepreneur should then try to understand how users are solving their problem today, before proposing a solution that draws on the unique skills and technical capabilities available to the entrepreneur. Finally, an in-depth understanding of the user allows the entrepreneur to hone in on the points of difference and resonance that are the foundation of a strong customer value proposition.

Mathematical games, abstract games

CERN Document Server

Neto, Joao Pedro

2013-01-01

User-friendly, visually appealing collection offers both new and classic strategic board games. Includes abstract games for two and three players and mathematical games such as Nim and games on graphs.

Applied mathematics and condensed matter; Mathematiques appliquees et matiere condensee

Energy Technology Data Exchange (ETDEWEB)

Bouche, D.; Jollet, F. [CEA Bruyeres-le-Chatel, 91 (France)

2011-01-15

Applied mathematics have always been a key tool in computing the structure of condensed matter. In this paper, we present the most widely used methods, and show the importance of mathematics in their genesis and evolution. After a brief survey of quantum Monte Carlo methods, which try to compute the N electrons wave function, the paper describes the theoretical foundations of N independent particle approximations. We mainly focus on density functional theory (DFT). This theory associated with advanced numerical methods, and high performance computing, has produced significant achievements in the field. This paper presents the foundations of the theory, as well as different numerical methods used to solve DFT equations. (authors)

Universics: a Theory of Universes of Discourse for Metamathematics and Foundations

Directory of Open Access Journals (Sweden)

Ioachim Drugus

2016-04-01

Full Text Available A new type of structures called ``universes'' is introduced to subsume the ``von Neumann universe'', ``Grothendieck universes'' and ``universes of discourse'' of various theories. Theories are also treated as universes, ``universes of ideas'', where ``idea" is a common term for assertions and terms. A dualism between induction and deduction and their treatment on a common basis is provided. The described approach referenced as ``universics'' is expected to be useful for metamathematical analysis and to serve as a foundation for mathematics. As a motivation for this research served the Harvey Friedman's desideratum to develop a foundational theory based on ``induction construction'', possibly comprising set theory. This desideratum emerged due to ``foundational incompleteness'' of set theory. The main results of this paper are an explication of the notion ``foundational completeness'', and a generalization of well-founded-ness.

Which kind of mathematics was known and referred to by those who wanted to integrate mathematics in «Wisdom»

DEFF Research Database (Denmark)

Høyrup, Jens

2016-01-01

Plato, so the story goes, held mathematics in high esteem, and those philosopher-kings that ought to rule his republic should have a thorough foundation in mathematics. This may well be true – but an observation made by Aristotle suggests that the mathematics which Plato intends is not the one...... based on theorems and proofs which we normally identify with “Greek mathematics”. Most other ancient writers who speak of mathematics as a road toward Wisdom also appear to be blissfully ignorant of the mathematics of Euclid, Archimedes, Apollonios, etc. – though not necessarily of their names. The aim...... of the paper is to identify the kinds of mathematics which were available as external sources for this current (on the whole leaving out of consideration Liberal-Arts mathematics as not properly external). A number of borrowings can be traced to various practitioners' traditions – but always as bits borrowed...

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.

The influence of gender on performance in mathematics in in the ...

African Journals Online (AJOL)

The influence of gender on performance in mathematics in in the foundation phase: the perceptions of selected teachers in a specific school. ... Again, the study has suggested strategies to encourage girls to do mathematics so as to improve their chances of following career options in engineering, accounting, medicine, ...

Online handwritten mathematical expression recognition

Science.gov (United States)

Büyükbayrak, Hakan; Yanikoglu, Berrin; Erçil, Aytül

2007-01-01

We describe a system for recognizing online, handwritten mathematical expressions. The system is designed with a user-interface for writing scientific articles, supporting the recognition of basic mathematical expressions as well as integrals, summations, matrices etc. A feed-forward neural network recognizes symbols which are assumed to be single-stroke and a recursive algorithm parses the expression by combining neural network output and the structure of the expression. Preliminary results show that writer-dependent recognition rates are very high (99.8%) while writer-independent symbol recognition rates are lower (75%). The interface associated with the proposed system integrates the built-in recognition capabilities of the Microsoft's Tablet PC API for recognizing textual input and supports conversion of hand-drawn figures into PNG format. This enables the user to enter text, mathematics and draw figures in a single interface. After recognition, all output is combined into one LATEX code and compiled into a PDF file.

Topics in the Foundations of General Relativity and Newtonian Gravitation Theory

CERN Document Server

Malament, David B

2012-01-01

In Topics in the Foundations of General Relativity and Newtonian Gravitation Theory, David B. Malament presents the basic logical-mathematical structure of general relativity and considers a number of special topics concerning the foundations of general relativity and its relation to Newtonian gravitation theory. These special topics include the geometrized formulation of Newtonian theory (also known as Newton-Cartan theory), the concept of rotation in general relativity, and Gödel spacetime. One of the highlights of the book is a no-go theorem that can be understood to show that there is

Developing a Multi-Dimensional Early Elementary Mathematics Screener and Diagnostic Tool: The Primary Mathematics Assessment.

Science.gov (United States)

Brendefur, Jonathan L; Johnson, Evelyn S; Thiede, Keith W; Strother, Sam; Severson, Herb H

2018-01-01

There is a critical need to identify primary level students experiencing difficulties in mathematics to provide immediate and targeted instruction that remediates their deficits. However, most early math screening instruments focus only on the concept of number, resulting in inadequate and incomplete information for teachers to design intervention efforts. We propose a mathematics assessment that screens and provides diagnostic information in six domains that are important to building a strong foundation in mathematics. This article describes the conceptual framework and psychometric qualities of a web-based assessment tool, the Primary Math Assessment (PMA). The PMA includes a screener to identify students at risk for poor math outcomes and a diagnostic tool to provide a more in-depth profile of children's specific strengths and weaknesses in mathematics. The PMA allows teachers and school personnel to make better instructional decisions by providing more targeted analyses.

The road to Maxwell's demon conceptual foundations of statistical mechanics

CERN Document Server

Hemmo, Meir

2012-01-01

Time asymmetric phenomena are successfully predicted by statistical mechanics. Yet the foundations of this theory are surprisingly shaky. Its explanation for the ease of mixing milk with coffee is incomplete, and even implies that un-mixing them should be just as easy. In this book the authors develop a new conceptual foundation for statistical mechanics that addresses this difficulty. Explaining the notions of macrostates, probability, measurement, memory, and the arrow of time in statistical mechanics, they reach the startling conclusion that Maxwell's Demon, the famous perpetuum mobile, is consistent with the fundamental physical laws. Mathematical treatments are avoided where possible, and instead the authors use novel diagrams to illustrate the text. This is a fascinating book for graduate students and researchers interested in the foundations and philosophy of physics.

Mathematics education and the information society

NARCIS (Netherlands)

Gravemeijer, K.P.E.; Damlamian, A.; Rodigues, J.F.; Sträßer, R.

2013-01-01

Starting point for this chapter is that societal changes ask for adaptations of a foundational mathematics curriculum for all. This chapter especially looks at the effects of information technology and globalization on the job market and employability with an eye on its consequences for the goals of

Dr Math gets MUDDY: the "dirt" on how to attract teenagers to Mathematics and Science by using multi-user dungeon games over Mxit on cell phones

CSIR Research Space (South Africa)

Butgereit, L

2010-05-01

Full Text Available -user dungeon games (MUDs) with a science and mathematical twist were deployed using Mxit (a popular instant messaging system in South Africa) on cell phones to encourage teenagers to learn more about math and science to practice math and science skills...

Quantum mechanics by walking 1. Foundations

International Nuclear Information System (INIS)

Pade, Jochen

2012-01-01

Quantum mechanics by walking introduces to the foundations of non-relativistic quantum mechanics. This book applies to studyings of teaching physics as well as all studyings of physics, who look for an appropriate, easy, fresh, and modern approach to the field. In the present first volume the essential principles of quantum mechanics are worked out. in order to be able to develop their mathematical formulation as fastly and clearly as possible, systematically between wave mechanics and algebraic presentation is changed. Beside themes, which are traditionally in textbooks of quantum mechanics, extensively actual aspects like interaction-free quantum measurement, neutrino oscillations, or quantum cryptography are considered as well as fundamental problems and epistemological questions discussed, as they occur in connection with the measurement process. The list of the postulates of quantum mechanics closes this volume; they form the framework for the extensions and applications, which are discussed in the second volume. The required mathematical aids are introduced step by step. In the appendix the most important mathematical tools are compactly collected, so that supplementing literature can be far reachingly abandoned. Furthermore in the appendix supplementing themes are deepened as for instance the Quantum Zeno effect or delayed-choice experiments.

Mathematical Perspectives

Energy Technology Data Exchange (ETDEWEB)

Glimm, J.

2009-10-14

Progress for the past decade or so has been extraordinary. The solution of Fermat's Last Theorem [11] and of the Poincare Conjecture [1] have resolved two of the most outstanding challenges to mathematics. For both cases, deep and advanced theories and whole subfields of mathematics came into play and were developed further as part of the solutions. And still the future is wide open. Six of the original seven problems from the Clay Foundation challenge remain open, the 23 DARPA challenge problems are open. Entire new branches of mathematics have been developed, including financial mathematics and the connection between geometry and string theory, proposed to solve the problems of quantized gravity. New solutions of the Einstein equations, inspired by shock wave theory, suggest a cosmology model which fits accelerating expansion of the universe possibly eliminating assumptions of 'dark matter'. Intellectual challenges and opportunities for mathematics are greater than ever. The role of mathematics in society continues to grow; with this growth comes new opportunities and some growing pains; each will be analyzed here. We see a broadening of the intellectual and professional opportunities and responsibilities for mathematicians. These trends are also occuring across all of science. The response can be at the level of the professional societies, which can work to deepen their interactions, not only within the mathematical sciences, but also with other scientific societies. At a deeper level, the choices to be made will come from individual mathematicians. Here, of course, the individual choices will be varied, and we argue for respect and support for this diversity of responses. In such a manner, we hope to preserve the best of the present while welcoming the best of the new.

Telling Mathematical Stories with Live Editing

Science.gov (United States)

Thomson, Ian

2017-01-01

Using "live editing" it is possible to write code that can be run a section at a time. This makes it easier to spot and correct errors. It can also be used to create an interactive mathematical story. This brief article shows how MATLAB software can be used to take the user on a mathematical journey with historical connections.

Interdisciplinary Biomathematics: Engaging Undergraduates in Research on the Fringe of Mathematical Biology

Science.gov (United States)

Fowler, Kathleen; Luttman, Aaron; Mondal, Sumona

2013-01-01

The US National Science Foundation's (NSF's) Undergraduate Biology and Mathematics (UBM) program significantly increased undergraduate research in the biomathematical sciences. We discuss three UBM-funded student research projects at Clarkson University that lie at the intersection of not just mathematics and biology, but also other fields. The…

Theoretical foundations of functional data analysis, with an introduction to linear operators

CERN Document Server

Hsing, Tailen

2015-01-01

Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators provides a uniquely broad compendium of the key mathematical concepts and results that are relevant for the theoretical development of functional data analysis (FDA).The self-contained treatment of selected topics of functional analysis and operator theory includes reproducing kernel Hilbert spaces, singular value decomposition of compact operators on Hilbert spaces and perturbation theory for both self-adjoint and non self-adjoint operators. The probabilistic foundation for FDA is described from the

Early Foundations for Mathematics Learning and Their Relations to Learning Disabilities.

Science.gov (United States)

Geary, David C

2013-02-01

Children's quantitative competencies upon entry into school can have lifelong consequences. Children who start behind generally stay behind, and mathematical skills at school completion influence employment prospects and wages in adulthood. I review the current debate over whether early quantitative learning is supported by (a) an inherent system for representing approximate magnitudes, (b) an attentional-control system that enables explicit processing of quantitative symbols, such as Arabic numerals, or (c) the logical problem-solving abilities that facilitate learning of the relations among numerals. Studies of children with mathematical learning disabilities and difficulties have suggested that each of these competencies may be involved, but to different degrees and at different points in the learning process. Clarifying how and when these competencies facilitate early quantitative learning and developing interventions to address their impact on children have the potential to yield substantial benefits for individuals and for society.

Mathematics for natural scientists fundamentals and basics

CERN Document Server

Kantorovich, Lev

2016-01-01

This book, the first in a two part series, covers a course of mathematics tailored specifically for physics, engineering and chemistry students at the undergraduate level. It is unique in that it begins with logical concepts of mathematics first encountered at A-level and covers them in thorough detail, filling in the gaps in students' knowledge and reasoning. Then the book aids the leap between A-level and university-level mathematics, with complete proofs provided throughout and all complex mathematical concepts and techniques presented in a clear and transparent manner. Numerous examples and problems (with answers) are given for each section and, where appropriate, mathematical concepts are illustrated in a physics context. This text gives an invaluable foundation to students and a comprehensive aid to lecturers. Mathematics for Natural Scientists: Fundamentals and Basics is the first of two volumes. Advanced topics and their applications in physics are covered in the second volume.

Mathematical Foundation for Plane Covering Using Hexagons

Science.gov (United States)

Johnson, Gordon G.

1999-01-01

This work is to indicate the development and mathematical underpinnings of the algorithms previously developed for covering the plane and the addressing of the elements of the covering. The algorithms are of interest in that they provides a simple systematic way of increasing or decreasing resolution, in the sense that if we have the covering in place and there is an image superimposed upon the covering, then we may view the image in a rough form or in a very detailed form with minimal effort. Such ability allows for quick searches of crude forms to determine a class in which to make a detailed search. In addition, the addressing algorithms provide an efficient way to process large data sets that have related subsets. The algorithms produced were based in part upon the work of D. Lucas "A Multiplication in N Space" which suggested a set of three vectors, any two of which would serve as a bases for the plane and also that the hexagon is the natural geometric object to be used in a covering with a suggested bases. The second portion is a refinement of the eyeball vision system, the globular viewer.

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

Mathematical methods for physicists

CERN Document Server

Arfken, George B

2005-01-01

This best-selling title provides in one handy volume the essential mathematical tools and techniques used to solve problems in physics. It is a vital addition to the bookshelf of any serious student of physics or research professional in the field. The authors have put considerable effort into revamping this new edition.* Updates the leading graduate-level text in mathematical physics* Provides comprehensive coverage of the mathematics necessary for advanced study in physics and engineering* Focuses on problem-solving skills and offers a vast array of exercises * Clearly illustrates and proves mathematical relationsNew in the Sixth Edition:* Updated content throughout, based on users'' feedback * More advanced sections, including differential forms and the elegant forms of Maxwell''s equations* A new chapter on probability and statistics* More elementary sections have been deleted

Which kind of mathematics was known by and referred to by those who wanted to integrate mathematics in «Wisdom» - Neopythagoreans and others?

DEFF Research Database (Denmark)

Høyrup, Jens

Plato, so the story goes, held mathematics in high esteem, and those philosopher-kings that ought to rule his republic should have a thorough foundation in mathematics. This may well be true - but an observation made by Aristotle suggests that the mathematics which Plato intends is not the one...... based on theorems and proofs which we normally identify with "Greek mathematics". Most other ancient writers who speak of mathematics as a road towardWisdom also appear to be blissfully ignorant of the mathematics of Euclid, Archimedes, Apollonios, etc. The aim of the paper is to identify the kinds...... of mathematics which were available as external sources for this current (on the whole leaving out of consideration Liberal-Arts mathematics as not properly external). A number of borrowings can be traced to various practitioners' traditions - but always as bits borrowed out of context....

A Mathematical Approach to Establishing Constitutive Models for Geomaterials

Directory of Open Access Journals (Sweden)

Guang-hua Yang

2013-01-01

Full Text Available The mathematical foundation of the traditional elastoplastic constitutive theory for geomaterials is presented from the mathematical point of view, that is, the expression of stress-strain relationship in principal stress/strain space being transformed to the expression in six-dimensional space. A new framework is then established according to the mathematical theory of vectors and tensors, which is applicable to establishing elastoplastic models both in strain space and in stress space. Traditional constitutive theories can be considered as its special cases. The framework also enables modification of traditional constitutive models.

Clarification of some mathematical misunderstandings about Savage's foundations of statistics, 1954

NARCIS (Netherlands)

P.P. Wakker (Peter)

1993-01-01

textabstractThis note discusses some mathematical misunderstandings about Savage (1954). It is shown that in his model the probability measure cannot be countably additive, that the set of events must be a σ-algebra and not just an algebra, that Savage did not characterize all atomless finitely

Quantum theory informational foundations and foils

CERN Document Server

Spekkens, Robert

2016-01-01

This book provides the first unified overview of the burgeoning research area at the interface between Quantum Foundations and Quantum Information.  Topics include: operational alternatives to quantum theory, information-theoretic reconstructions of the quantum formalism, mathematical frameworks for operational theories, and device-independent features of the set of quantum correlations. Powered by the injection of fresh ideas from the field of Quantum Information and Computation, the foundations of Quantum Mechanics are in the midst of a renaissance. The last two decades have seen an explosion of new results and research directions, attracting broad interest in the scientific community. The variety and number of different approaches, however, makes it challenging for a newcomer to obtain a big picture of the field and of its high-level goals. Here, fourteen original contributions from leading experts in the field cover some of the most promising research directions that have emerged in the new wave of quant...

Supporting NPD teams in innovation : Structuring user data on the foundations of empathy

NARCIS (Netherlands)

Alkaya, M.; Sleeswijk Visser, F.; de Lille, C.S.H.

2012-01-01

Gathering and analyzing user data in new product development (NPD), both qualitative and quantitative, can be a strong driver for innovation in companies. While ideally user data should be obtained through direct interactions between NPD departments and targeted users, time and cost restrictions

A Critical Discourse Analysis of Practical Problems in a Foundation Mathematics Course at a South African University

Science.gov (United States)

le Roux, Kate; Adler, Jill

2016-01-01

Mathematical problems that make links to the everyday and to disciplines other than mathematics--variously referred to as practical, realistic, real-world or applied problems in the literature--feature in school and undergraduate mathematics reforms aimed at increasing mathematics participation in contexts of inequity and diversity. In this…

A Reflective Journey through Theory and Research in Mathematical Learning and Development

Science.gov (United States)

Belbase, Shashidhar

2010-01-01

This paper is an attempt to reflect on class sessions during the fall 2010 in a course "Theory and Research in Mathematical Learning and Development". This reflection as a learning journey portrays discussions based on foundational perspectives (FP), historical highlights (HH), and guiding questions (GQ) related to mathematics learning and…

Mathematical physics a modern introduction to its foundations

CERN Document Server

Hassani, Sadri

2013-01-01

The goal of this book is to expose the reader to the indispensable role that mathematics---often very abstract---plays in modern physics. Starting with the notion of vector spaces, the first half of the book develops topics as diverse as algebras, classical orthogonal polynomials, Fourier analysis, complex analysis, differential and integral equations, operator theory, and multi-dimensional Green's functions. The second half of the book introduces groups, manifolds, Lie groups and their representations, Clifford algebras and their representations, and fiber bundles and their applications to differential geometry and gauge theories. This second edition is a substantial revision of the first one with a complete rewriting of many chapters and the addition of new ones, including chapters on algebras, representation of Clifford algebras and spinors, fiber bundles, and gauge theories. The spirit of the first edition, namely the balance between rigor and physical application, has been maintained, as is the abundance...

Lectures on Mathematical Foundation of Turbulent Viscous Flows

CERN Document Server

Miyakawa, Tetsuro

2006-01-01

Five leading specialists reflect on different and complementary approaches to fundamental questions in the study of the Fluid Mechanics and Gas Dynamics equations. Constantin presents the Euler equations of ideal incompressible fluids and discusses the blow-up problem for the Navier-Stokes equations of viscous fluids, describing some of the major mathematical questions of turbulence theory. These questions are connected to the Caffarelli-Kohn-Nirenberg theory of singularities for the incompressible Navier-Stokes equations that is explained in Gallavotti's lectures. Kazhikhov introduces the theory of strong approximation of weak limits via the method of averaging, applied to Navier-Stokes equations. Y. Meyer focuses on several nonlinear evolution equations - in particular Navier-Stokes - and some related unexpected cancellation properties, either imposed on the initial condition, or satisfied by the solution itself, whenever it is localized in space or in time variable. Ukai presents the asymptotic analysis th...

Quantum information theory. Mathematical foundation. 2. ed.

Energy Technology Data Exchange (ETDEWEB)

Hayashi, Masahito [Nagoya Univ. (Japan). Graduate School of Mathematics

2017-07-01

This graduate textbook provides a unified view of quantum information theory. Clearly explaining the necessary mathematical basis, it merges key topics from both information-theoretic and quantum- mechanical viewpoints and provides lucid explanations of the basic results. Thanks to this unified approach, it makes accessible such advanced topics in quantum communication as quantum teleportation, superdense coding, quantum state transmission (quantum error-correction) and quantum encryption. Since the publication of the preceding book Quantum Information: An Introduction, there have been tremendous strides in the field of quantum information. In particular, the following topics - all of which are addressed here - made seen major advances: quantum state discrimination, quantum channel capacity, bipartite and multipartite entanglement, security analysis on quantum communication, reverse Shannon theorem and uncertainty relation. With regard to the analysis of quantum security, the present book employs an improved method for the evaluation of leaked information and identifies a remarkable relation between quantum security and quantum coherence. Taken together, these two improvements allow a better analysis of quantum state transmission. In addition, various types of the newly discovered uncertainty relation are explained. Presenting a wealth of new developments, the book introduces readers to the latest advances and challenges in quantum information. To aid in understanding, each chapter is accompanied by a set of exercises and solutions.

Quantum information theory. Mathematical foundation. 2. ed.

International Nuclear Information System (INIS)

Hayashi, Masahito

2017-01-01

This graduate textbook provides a unified view of quantum information theory. Clearly explaining the necessary mathematical basis, it merges key topics from both information-theoretic and quantum- mechanical viewpoints and provides lucid explanations of the basic results. Thanks to this unified approach, it makes accessible such advanced topics in quantum communication as quantum teleportation, superdense coding, quantum state transmission (quantum error-correction) and quantum encryption. Since the publication of the preceding book Quantum Information: An Introduction, there have been tremendous strides in the field of quantum information. In particular, the following topics - all of which are addressed here - made seen major advances: quantum state discrimination, quantum channel capacity, bipartite and multipartite entanglement, security analysis on quantum communication, reverse Shannon theorem and uncertainty relation. With regard to the analysis of quantum security, the present book employs an improved method for the evaluation of leaked information and identifies a remarkable relation between quantum security and quantum coherence. Taken together, these two improvements allow a better analysis of quantum state transmission. In addition, various types of the newly discovered uncertainty relation are explained. Presenting a wealth of new developments, the book introduces readers to the latest advances and challenges in quantum information. To aid in understanding, each chapter is accompanied by a set of exercises and solutions.

Geometric Transformations in Middle School Mathematics Textbooks

Science.gov (United States)

Zorin, Barbara

2011-01-01

This study analyzed treatment of geometric transformations in presently available middle grades (6, 7, 8) student mathematics textbooks. Fourteen textbooks from four widely used textbook series were evaluated: two mainline publisher series, Pearson (Prentice Hall) and Glencoe (Math Connects); one National Science Foundation (NSF) funded curriculum…

An introduction to mathematical modeling a course in mechanics

CERN Document Server

Oden, Tinsley J

2011-01-01

A modern approach to mathematical modeling, featuring unique applications from the field of mechanics An Introduction to Mathematical Modeling: A Course in Mechanics is designed to survey the mathematical models that form the foundations of modern science and incorporates examples that illustrate how the most successful models arise from basic principles in modern and classical mathematical physics. Written by a world authority on mathematical theory and computational mechanics, the book presents an account of continuum mechanics, electromagnetic field theory, quantum mechanics, and statistical mechanics for readers with varied backgrounds in engineering, computer science, mathematics, and physics. The author streamlines a comprehensive understanding of the topic in three clearly organized sections: Nonlinear Continuum Mechanics introduces kinematics as well as force and stress in deformable bodies; mass and momentum; balance of linear and angular momentum; conservation of energy; and constitutive equation...

Java Foundation Classes in a Nutshell Desktop Quick Reference

CERN Document Server

Flanagan, David

1999-01-01

Java Foundation Classes in a Nutshell is an indispensable quick reference for Java programmers who are writing applications that use graphics or graphical user interfaces. The author of the bestsellingJava in a Nutshell has written fast-paced introductions to the Java APIs that comprise the Java Foundation Classes (JFC), such as the Swing GUI components and Java 2D, so that you can start using these exciting new technologies right away. This book also includes O'Reilly's classic-style, quick-reference material for all of the classes in the javax.swing and java.awt packages and their numerous

Partial Support of Meeting of the Board on Mathematical Sciences and Their Applications

Energy Technology Data Exchange (ETDEWEB)

Weidman, Scott [National Academy of Sciences, Washington DC (United States)

2014-08-31

During the performance period, BMSA released the following major reports: Transforming Combustion Research through Cyberinfrastructure (2011); Assessing the Reliability of Complex Models: Mathematical and Statistical Foundations of Verification, Validation, and Uncertainty Quantification (2012); Fueling Innovation and Discovery: The Mathematical Sciences in the 21st Century (2012); Aging and the Macroeconomy: Long-Term Implications of an Older Population (2012); The Mathematical Sciences in 2025 (2013); Frontiers in Massive Data Analysis (2013); and Developing a 21st Century Global Library for Mathematics Research (2014).

Proceedings of the Third International Workshop on Mathematical Foundations of Computational Anatomy

DEFF Research Database (Denmark)

the mathematical community around shapes and the MICCAI community in view of computational anatomy applications. It targets more particularly researchers investigating the combination of statistical and geometrical aspects in the modeling of the variability of biological shapes. The workshop is a forum...... of the workshop: statistics on manifolds and diff eomorphisms for surface or longitudinal registration. One session gathers papers exploring new mathematical structures beyond Riemannian geometry while the last oral session deals with the emerging theme of statistics on graphs and trees. Finally, a poster session......Computational anatomy is an emerging discipline at the interface of geometry, statistics and image analysis which aims at modeling and analyzing the biological shape of tissues and organs. The goal is to estimate representative organ anatomies across diseases, populations, species or ages, to model...

Deep foundation rebound instrumentation at the Grand Gulf Nuclear Power Station

International Nuclear Information System (INIS)

Blendy, M.M.; Boisen, B.P.

1978-01-01

Removing an extensive amount of overburden can initiate adjustments in the foundation mass. Rebound adjustments induced by this removal include, in addition to elastic response, elements of visco-elastic and plastic response which have to be taken into account when the foundation is loaded by subsequent construction. The accurate measurement of foundation response can be important in the design and construction of deep foundations and can be essential in the construction of very deep foundations. In 1974, a large foundation excavation was undertaken for the two unit Grand Gulf Nuclear Station. Overburden removal ranged in depth from 65 feet in the turbine area to 110 feet in the containment area. Very long, rod-type Multiple Position Borehole Extensometers measured the rebound. The design of the extensometers, and the dimensions of the installed instruments, are discussed. Graphs are included which show the adjustments measured by each extensometer during the deepening of the excavation. The measured rebound for each transducer package of each extensometer is summarized. The data are compared to predicted values based on a mathematical model developed using laboratory test results and empirical methods. The resulting information forms part of the permanent record of construction for the nuclear power station

EULER - A Real Virtual Library for Mathematics

CERN Document Server

Jost, Michael

2004-01-01

The EULER project completed its work in November 2002. It forms the last part of a very successful project in the specialized but global discipline of mathematics. After a successful RTD project had created the technology, a take-up project has effectively exploited it to the point where its future is assured through a not-for-profit consortium. EULER is a European based, world class, real virtual library for mathematics with up-to-date technological solutions, well accepted by users. In particular, EULER provides a world reference and delivery service, transparent to the end user and offering full coverage of the mathematics literature world-wide, including bibliographic data, peer reviews and/or abstracts, indexing, classification and search, transparent access to library services, co-operation with commercial information providers (publishers, bookstores). The EULER services provide a gateway to the electronic catalogues and repositories of participating institutions, while the latter retain complete respo...

Noted astrophysicist Michael S. Turner to Head NSF'S mathematical and physical sciences directorate

CERN Multimedia

2003-01-01

"The National Science Foundation has named celebrated astrophysicist Michael S. Turner of the University of Chicago as Assistant Director for Mathematical and Physical Sciences. He will head a $1 billion directorate that supports research in mathematics, physics, chemistry, materials and astronomy, as well as multidisciplinary programs and education" (1/2 page).

Brain Functors: A Mathematical Model of Intentional Perception and Action

OpenAIRE

David Ellerman

2016-01-01

Category theory has foundational importance because it provides conceptual lenses to characterize what is important and universal in mathematics - with adjunctions being the primary lens. If adjunctions are so important in mathematics, then perhaps they will isolate concepts of some importance in the empirical sciences. But the applications of adjunctions have been hampered by an overly restrictive formulation that avoids heteromorphisms or hets. By reformulating an adjunction using hets, it ...

Mathematics Programming on the Apple II and IBM PC.

Science.gov (United States)

Myers, Roy E.; Schneider, David I.

1987-01-01

Details the features of BASIC used in mathematics programming and provides the information needed to translate between the Apple II and IBM PC computers. Discusses inputing a user-defined function, setting scroll windows, displaying subscripts and exponents, variable names, mathematical characters and special symbols. (TW)

Bruteau's philosophy of spiritual evolution and consciousness: foundation for a nursing cosmology.

Science.gov (United States)

McCarthy, M Patrice

2011-01-01

The ontological foundation of the modern world view based on irreconcilable dichotomies has held hegemonic status since the dawn of the scientific revolution. The post-modern critique has exposed the inadequacies of the modern perspective and challenged the potential for any narrative to adequately ground a vision for the future. This paper proposes that the philosophy of Beatrice Bruteau can support a foundation for a visionary world view consistent with nursing's respect for human dignity and societal health. The author discusses the key concepts of Bruteau's perspective on societal evolution based on an integrated study of science, mathematics, religion, and philosophy. This perspective is discussed as a foundation to move beyond the dichotomous influence of the modern world view and the deconstructive critique of the post-modern perspective. The author suggests spiritual evolution and a participatory consciousness as an ontological foundation for a cosmology congruent with nursing's social mandate. © 2010 Blackwell Publishing Ltd.

A Multifaceted Mathematical Approach for Complex Systems

Energy Technology Data Exchange (ETDEWEB)

Alexander, F.; Anitescu, M.; Bell, J.; Brown, D.; Ferris, M.; Luskin, M.; Mehrotra, S.; Moser, B.; Pinar, A.; Tartakovsky, A.; Willcox, K.; Wright, S.; Zavala, V.

2012-03-07

Applied mathematics has an important role to play in developing the tools needed for the analysis, simulation, and optimization of complex problems. These efforts require the development of the mathematical foundations for scientific discovery, engineering design, and risk analysis based on a sound integrated approach for the understanding of complex systems. However, maximizing the impact of applied mathematics on these challenges requires a novel perspective on approaching the mathematical enterprise. Previous reports that have surveyed the DOE's research needs in applied mathematics have played a key role in defining research directions with the community. Although these reports have had significant impact, accurately assessing current research needs requires an evaluation of today's challenges against the backdrop of recent advances in applied mathematics and computing. To address these needs, the DOE Applied Mathematics Program sponsored a Workshop for Mathematics for the Analysis, Simulation and Optimization of Complex Systems on September 13-14, 2011. The workshop had approximately 50 participants from both the national labs and academia. The goal of the workshop was to identify new research areas in applied mathematics that will complement and enhance the existing DOE ASCR Applied Mathematics Program efforts that are needed to address problems associated with complex systems. This report describes recommendations from the workshop and subsequent analysis of the workshop findings by the organizing committee.

Semi-automatic scene generation using the Digital Anatomist Foundational Model.

Science.gov (United States)

Wong, B A; Rosse, C; Brinkley, J F

1999-01-01

A recent survey shows that a major impediment to more widespread use of computers in anatomy education is the inability to directly manipulate 3-D models, and to relate these to corresponding textual information. In the University of Washington Digital Anatomist Project we have developed a prototype Web-based scene generation program that combines the symbolic Foundational Model of Anatomy with 3-D models. A Web user can browse the Foundational Model (FM), then click to request that a 3-D scene be created of an object and its parts or branches. The scene is rendered by a graphics server, and a snapshot is sent to the Web client. The user can then manipulate the scene, adding new structures, deleting structures, rotating the scene, zooming, and saving the scene as a VRML file. Applications such as this, when fully realized with fast rendering and more anatomical content, have the potential to significantly change the way computers are used in anatomy education.

Characteristic of critical and creative thinking of students of mathematics education study program

Science.gov (United States)

Rochmad; Agoestanto, A.; Kharis, M.

2018-03-01

Critical and creative thinking give important role in learning matematics for mathematics education students. This research to explored the characteristic of critical and creative thinking of students of mathematics study program in mathematics department. Critical thinking and creative thinking can be illustrated as two sides of a coin, which one is associated to the other. In elementary linear algebra courses, however, critical thinking can be seen as a foundation to build students’ creative thinking.

Teachers' Understanding of Mathematical Cognition in Childhood: Towards a Shift in Pedagogical Content Knowledge?

Science.gov (United States)

Henning, Elizabeth

2013-01-01

This article about the discourse of pedagogy as related to child cognition in mathematics addresses the issue of what constitutes the main disciplinary content and the pedagogical content knowledge (PCK) of foundation-phase teachers. I argue that, unless child cognition itself is the primary disciplinary content of foundation-phase teacher's…

The role of a posteriori mathematics in physics

Science.gov (United States)

MacKinnon, Edward

2018-05-01

The calculus that co-evolved with classical mechanics relied on definitions of functions and differentials that accommodated physical intuitions. In the early nineteenth century mathematicians began the rigorous reformulation of calculus and eventually succeeded in putting almost all of mathematics on a set-theoretic foundation. Physicists traditionally ignore this rigorous mathematics. Physicists often rely on a posteriori math, a practice of using physical considerations to determine mathematical formulations. This is illustrated by examples from classical and quantum physics. A justification of such practice stems from a consideration of the role of phenomenological theories in classical physics and effective theories in contemporary physics. This relates to the larger question of how physical theories should be interpreted.

User's guide to the Sandia Mathematical Program Library at Livermore

Energy Technology Data Exchange (ETDEWEB)

Huddleston, R.E.; Jefferson, T.H.

1976-03-01

The Sandia Mathematical Program Library is a collection of general-purpose mathematical subroutines which are maintained within Sandia on a quick service basis. This document is intended to be a reference guide for using the library at Sandia Laboratories, Livermore. (auth)

Does Knowing More Advanced Mathematics Ensure Effectiveness of Working towards Demonstrating Specialised Mathematical Content Knowledge of Second-Year Pre-Service Teachers?

Science.gov (United States)

Livy, Sharyn

2012-01-01

The theoretical understanding that underpins a teacher's foundation knowledge draws on their common content knowledge (CCK) and influences their mathematics' teaching (Rowland, Turner, Thwaites, & Huckstep, 2009). Teachers who have specialised content knowledge (SCK) demonstrate a unique kind of content knowledge which is more than knowing the…

Petr Hájek on mathematical fuzzy logic

CERN Document Server

Montagna, Franco

2014-01-01

This volume celebrates the work of Petr Hájek on mathematical fuzzy logic and presents how his efforts have influenced prominent logicians who are continuing his work. The book opens with a discussion on Hájek's contribution to mathematical fuzzy logic and with a scientific biography of him, progresses to include two articles with a foundation flavour, that demonstrate some important aspects of Hájek's production, namely, a paper on the development of fuzzy sets and another paper on some fuzzy versions of set theory and arithmetic. Articles in the volume also focus on the treatment of vague

Intangible heritage for sustainable future: mathematics in the paddy field

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Dewanto, Stanley P.; Kusuma, Dianne A.; Nurani Ruchjana, Budi; Setiawan Abdullah, Atje

2017-10-01

Mathematics, as the only general language, can describe all phenomena on earth. Mathematics not only helps us to understand these phenomena, but it also can sustain human activities, consequently ensure that the future development is sustainable. Indonesia, with high cultural diversity, should aware to have its understanding, skills, and philosophies developed by certain societies, with long histories of interaction with their natural surroundings, which will provide a foundation for locally appropriate sustainable development. This paper discussed the condition and situation on certain area in Cigugur, Indonesia, and what skills, knowledge, and concept can be transmitted, regarding simple mathematics (arithmetic). Some examples are provided.

Remote access to mathematical software

International Nuclear Information System (INIS)

Dolan, E.; Hovland, P.; More, J.; Norris, B.; Smith, B.

2001-01-01

The network-oriented application services paradigm is becoming increasingly common for scientific computing. The popularity of this approach can be attributed to the numerous advantages to both user and developer provided by network-enabled mathematical software. The burden of installing and maintaining complex systems is lifted from the user, while enabling developers to provide frequent updates without disrupting service. Access to software with similar functionality can be unified under the same interface. Remote servers can utilize potentially more powerful computing resources than may be available locally. We discuss some of the application services developed by the Mathematics and Computer Science Division at Argonne National Laboratory, including the Network Enabled Optimization System (NEOS) Server and the Automatic Differentiation of C (ADIC) Server, as well as preliminary work on Web access to the Portable Extensible Toolkit for Scientific Computing (PETSc). We also provide a brief survey of related work

Mathematical Properties Relevant to Geomagnetic Field Modeling

DEFF Research Database (Denmark)

Sabaka, Terence J.; Hulot, Gauthier; Olsen, Nils

2010-01-01

be directly measured. In this chapter, the mathematical foundation of global (as opposed to regional) geomagnetic field modeling is reviewed, and the spatial modeling of the field in spherical coordinates is focussed. Time can be dealt with as an independent variable and is not explicitly considered......Geomagnetic field modeling consists in converting large numbers of magnetic observations into a linear combination of elementary mathematical functions that best describes those observations.The set of numerical coefficients defining this linear combination is then what one refers.......The relevant elementary mathematical functions are introduced, their properties are reviewed, and how they can be used to describe the magnetic field in a source-free (such as the Earth’s neutral atmosphere) or source-dense (such as the ionosphere) environment is explained. Completeness and uniqueness...

Mathematical Properties Relevant to Geomagnetic Field Modeling

DEFF Research Database (Denmark)

Sabaka, Terence J.; Hulot, Gauthier; Olsen, Nils

2014-01-01

be directly measured. In this chapter, the mathematical foundation of global (as opposed to regional) geomagnetic field modeling is reviewed, and the spatial modeling of the field in spherical coordinates is focused. Time can be dealt with as an independent variable and is not explicitly considered......Geomagnetic field modeling consists in converting large numbers of magnetic observations into a linear combination of elementary mathematical functions that best describes those observations. The set of numerical coefficients defining this linear combination is then what one refers....... The relevant elementary mathematical functions are introduced, their properties are reviewed, and how they can be used to describe the magnetic field in a source-free (such as the Earth’s neutral atmosphere) or source-dense (such as the ionosphere) environment is explained. Completeness and uniqueness...

Strategies to Recruit and Retain Students in Physical Science and Mathematics on a Diverse College Campus

Science.gov (United States)

Chang, Jen-Mei; Kwon, Chuhee; Stevens, Lora; Buonora, Paul

2016-01-01

This article presents implementation details and findings of a National Science Foundation Scholarship in Science, Technology, Engineering, and Mathematics Program (S-STEM) consisting of many high-impact practices to recruit and retain students in the physical sciences and mathematics programs, particularly first-generation and underrepresented…

Bending of a nonlinear beam reposing on an unilateral foundation

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Machalová J.

2011-06-01

Full Text Available This article is going to deal with bending of a nonlinear beam whose mathematical model was proposed by D. Y. Gao in (Gao, D. Y., Nonlinear elastic beam theory with application in contact problems and variational approaches,Mech. Research Communication, 23 (1 1996. The model is based on the Euler-Bernoulli hypothesis and under assumption of nonzero lateral stress component enables moderately large deflections but with small strains. This is here extended by the unilateralWinkler foundation. The attribution unilateral means that the foundation is not connected with the beam. For this problem we demonstrate a mathematical formulation resulting from its natural decomposition which leads to a saddle-point problem with a proper Lagrangian. Next we are concerned with methods of solution for our problem by means of the finite element method as the paper (Gao, D. Y., Nonlinear elastic beam theory with application in contact problems and variational approaches, Mech. Research Communication, 23 (1 1996 has no mention of it. The main alternatives are here the solution of a system of nonlinear nondifferentiable equations or finding of a saddle point through the use of the augmented Lagrangian method. This is illustrated by an example in the final part of the article.

Working memory and language: skill-specific or domain-general relations to mathematics?

Science.gov (United States)

Purpura, David J; Ganley, Colleen M

2014-06-01

Children's early mathematics skills develop in a cumulative fashion; foundational skills form a basis for the acquisition of later skills. However, non-mathematical factors such as working memory and language skills have also been linked to mathematical development at a broad level. Unfortunately, little research has been conducted to evaluate the specific relations of these two non-mathematical factors to individual aspects of early mathematics. Thus, the focus of this study was to determine whether working memory and language were related to only individual aspects of early mathematics or related to many components of early mathematics skills. A total of 199 4- to 6-year-old preschool and kindergarten children were assessed on a battery of early mathematics tasks as well as measures of working memory and language. Results indicated that working memory has a specific relation to only a few-but critically important-early mathematics skills and language has a broad relation to nearly all early mathematics skills. Copyright © 2014 Elsevier Inc. All rights reserved.

Mathematical model for spreading dynamics of social network worms

International Nuclear Information System (INIS)

Sun, Xin; Liu, Yan-Heng; Han, Jia-Wei; Liu, Xue-Jie; Li, Bin; Li, Jin

2012-01-01

In this paper, a mathematical model for social network worm spreading is presented from the viewpoint of social engineering. This model consists of two submodels. Firstly, a human behavior model based on game theory is suggested for modeling and predicting the expected behaviors of a network user encountering malicious messages. The game situation models the actions of a user under the condition that the system may be infected at the time of opening a malicious message. Secondly, a social network accessing model is proposed to characterize the dynamics of network users, by which the number of online susceptible users can be determined at each time step. Several simulation experiments are carried out on artificial social networks. The results show that (1) the proposed mathematical model can well describe the spreading dynamics of social network worms; (2) weighted network topology greatly affects the spread of worms; (3) worms spread even faster on hybrid social networks

Building on the foundation for an engineering career

Science.gov (United States)

White, Susan; White, Ruth

1994-01-01

A predictable and preventable hurdle stops a majority of young women from entering the scientific and technical fields. This cuts down the individual's career possibilities and cuts in half the pool of potential U.S. engineers later available to industry. The waste of talent does not advance our country's competitive position. The typical American adolescent girl has acquired all the basic mathematical skills needed to pursue science and math, but, from adolescence on, she does not build the foundation of science and math courses that she would need later in life to work in engineering. Several questions are addressed: Why are some young women stopped cold in their mathematical tracks during adolescence? What is the influence of psychology, including discussion of the personality traits quantifiably shared by women in technical fields? and How should the school system adapt to keep their female charges learning math and science?

Philosophy of mathematics and deductive structure in Euclid's elements

CERN Document Server

Mueller, Ian

2006-01-01

A survey of Euclid's Elements, this text provides an understanding of the classical Greek conception of mathematics. It offers a well-rounded perspective, examining similarities to modern views as well as differences. Rather than focusing strictly on historical and mathematical issues, the book examines philosophical, foundational, and logical questions.Although comprehensive in its treatment, this study represents a less cumbersome, more streamlined approach than the classic three-volume reference by Sir Thomas L. Heath (also available from Dover Publications). To make reading easier and to f

CATO--A Guided User Interface for Different CAS

Science.gov (United States)

Janetzko, Hans-Dieter

2017-01-01

CATO is a new user interface, written in Java and developed by the author as a response to the significant difficulties faced by students who only sporadically use computer algebra systems (CAS). The usage of CAS in mathematical lectures should be an integral part of mathematical instruction. However, difficulties arise for those students who have…

INFORMATIONAL-METHODICAL SUPPORT OF THE COURSE «MATHEMATICAL LOGIC AND THEORY OF ALGORITHMS»

Directory of Open Access Journals (Sweden)

Y. I. Sinko

2010-06-01

Full Text Available In this article the basic principles of training technique of future teachers of mathematics to foundations of mathematical logic and theory of algorithms in the Kherson State University with the use of information technologies are examined. General description of functioning of the methodical system of learning of mathematical logic with the use of information technologies, in that variant, when information technologies are presented by the integrated specialized programmatic environment of the educational purpose «MatLog» is given.

Early Learning Foundations. Indiana's Early Learning Development Framework Aligned to the Indiana Academic Standards, 2014

Science.gov (United States)

Indiana Department of Education, 2015

2015-01-01

The "Foundations" (English/language arts, mathematics, social emotional skills, approaches to play and learning, science, social studies, creative arts, and physical health and growth) are Indiana's early learning development framework and are aligned to the 2014 Indiana Academic Standards. This framework provides core elements that…

Second Differences: A Mathematical Bridge between Two Projects

Science.gov (United States)

Fischer, Joyce; Wayment, Stanley; Johnson, Christopher

2010-01-01

Making connections is one of the most important foundations involved in learning mathematics. Two projects are presented in this article: one involving Newton's Second Law of Motion and the other involving the determination of star numbers, a type of figurate number. The two invoke seemingly different modalities for students at different levels of…

A Study of Visualization for Mathematics Education

Science.gov (United States)

Daugherty, Sarah C.

2008-01-01

Graphical representations such as figures, illustrations, and diagrams play a critical role in mathematics and they are equally important in mathematics education. However, graphical representations in mathematics textbooks are static, Le. they are used to illustrate only a specific example or a limited set. of examples. By using computer software to visualize mathematical principles, virtually there is no limit to the number of specific cases and examples that can be demonstrated. However, we have not seen widespread adoption of visualization software in mathematics education. There are currently a number of software packages that provide visualization of mathematics for research and also software packages specifically developed for mathematics education. We conducted a survey of mathematics visualization software packages, summarized their features and user bases, and analyzed their limitations. In this survey, we focused on evaluating the software packages for their use with mathematical subjects adopted by institutions of secondary education in the United States (middle schools and high schools), including algebra, geometry, trigonometry, and calculus. We found that cost, complexity, and lack of flexibility are the major factors that hinder the widespread use of mathematics visualization software in education.

God created the integers the mathematical breakthroughs that changed history

CERN Document Server

2007-01-01

Bestselling author and physicist Stephen Hawking explores the "masterpieces" of mathematics, 25 landmarks spanning 2,500 years and representing the work of 15 mathematicians, including Augustin Cauchy, Bernard Riemann, and Alan Turing. This extensive anthology allows readers to peer into the mind of genius by providing them with excerpts from the original mathematical proofs and results. It also helps them understand the progression of mathematical thought, and the very foundations of our present-day technologies. Each chapter begins with a biography of the featured mathematician, clearly explaining the significance of the result, followed by the full proof of the work, reproduced from the original publication.

Interactions Between Mathematics and Physics: The History of the Concept of Function—Teaching with and About Nature of Mathematics

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Kjeldsen, Tinne Hoff; Lützen, Jesper

2015-07-01

In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined it as a variable that depends in an arbitrary manner on another variable. The change was required when mathematicians discovered that analytic expressions were not sufficient to represent physical phenomena such as the vibration of a string (Euler) and heat conduction (Fourier and Dirichlet). The introduction of generalized functions or distributions is shown to stem partly from the development of new theories of physics such as electrical engineering and quantum mechanics that led to the use of improper functions such as the delta function that demanded a proper foundation. We argue that the development of student understanding of mathematics and its nature is enhanced by embedding mathematical concepts and theories, within an explicit-reflective framework, into a rich historical context emphasizing its interaction with other disciplines such as physics. Students recognize and become engaged with meta-discursive rules governing mathematics. Mathematics teachers can thereby teach inquiry in mathematics as it occurs in the sciences, as mathematical practice aimed at obtaining new mathematical knowledge. We illustrate such a historical teaching and learning of mathematics within an explicit and reflective framework by two examples of student-directed, problem-oriented project work following the Roskilde Model, in which the connection to physics is explicit and provides a learning space where the nature of mathematics and mathematical practices are linked to natural science.

Does Math Achievement "h'APP'en" when iPads and Game-Based Learning Are Incorporated into Fifth-Grade Mathematics Instruction?

Science.gov (United States)

Carr, Jennie M.

2012-01-01

After 10 years of No Child Left Behind standards-focused education, mathematics scores have improved only marginally for elementary-aged students. Students who developed a solid conceptual mathematics foundation at the elementary level succeeded later in higher-level mathematics courses; thus, educators have sought ways to increase mathematics…

Two Theories of "Theory" in Mathematics Education: Using Kuhn and Lakatos to Examine Four Foundational Issues.

Science.gov (United States)

Orton, Robert E.

1988-01-01

The ideas of Kuhn and Lakatos are used to study four issues in mathematics education related to values, units of analysis, theory of mind, and nature of mathematical entities. The goal is to determine whether differences between the assumptions are best understood in Kuhnian or Lakatosian terms. (MNS)

Determination of p-y Curves using Finite Element Modelling for Bucket Foundation in Undrained Soft and Medium Clay

DEFF Research Database (Denmark)

Hvidberg, Mogens Bonde; Ibsen, Lars Bo

In many years the types of foundation, such as monopiles and bucket foundation which are used in the offshore wind turbine industry, have been analysed analytically with formulations that are based on much slender piles, than are used today. Because of that, the analytical calculation...... is not describing the connection between the horizontal bearing capacity of the soil and the displacement of the foundation accurate, in particular for the bucket foundation because of the much smaller slenderness of the profile. Numerical modelling is used to examine that bearing capacity the bucket foundation has...... in soft and medium clay at different dimensions of the bucket, to a horizontal displacement. After that a mathematical formulation is determined, based on (Reese et al, 1975), so it is possible to get a more accurate result in an analytical calculation....

On the Origin of Symbolic Mathematics and Its Significance for Wittgenstein’s Thought

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Sören Stenlund

2015-07-01

However, the nature of symbolic mathematics has been concealed and confused due to the strong influence of the heritage from the Euclidean and Aristotelian traditions. This essay sheds some light on what has been concealed by approaching some of the crucial issues from a historical perspective. Furthermore, I argue that the conception of modern mathematics as symbolic mathematics was essential to Wittgenstein’s approach to the foundations and nature of mathematics. This connection between Wittgenstein’s thought and symbolic mathematics provides the resources for countering the still prevalent view that he defended an uttrely idiosyncratic conception, disconnected from the progress of serious science. Instead, his project can be seen as clarifying ideas that have been crucial to the development of mathematics since early modernity.

Hydroelastic Oscillations of a Circular Plate, Resting on Winkler Foundation

Science.gov (United States)

Kondratov, D. V.; Mogilevich, L. I.; Popov, V. S.; Popova, A. A.

2018-01-01

The forced hydroelastic oscillations of a circular plate resting on elastic foundation are investigated. The oscillations are caused by a stamp vibration under interaction with a plate through a thin layer of viscous incompressible liquid. The axis-symmetric problem for the regime of the steady-state harmonic oscillations is considered. On the basis of hydroelasticity problem solution the laws of plate deflection and pressure in the liquid are found. The functions of the amplitudes deflection distribution and liquid pressure along the plate are constructed. The presented mathematical model provides for investigating viscous liquid layer interaction dynamics with a circular plate resting on an elastic foundation. The above-mentioned model makes it possible to define the plate oscillations resonance frequencies and the corresponding amplitudes of deflection and liquid pressure, as well.

Performance Analysis of Diversity-Controlled Multi-User Superposition Transmission for 5G Wireless Networks.

Science.gov (United States)

Yeom, Jeong Seon; Chu, Eunmi; Jung, Bang Chul; Jin, Hu

2018-02-10

In this paper, we propose a novel low-complexity multi-user superposition transmission (MUST) technique for 5G downlink networks, which allows multiple cell-edge users to be multiplexed with a single cell-center user. We call the proposed technique diversity-controlled MUST technique since the cell-center user enjoys the frequency diversity effect via signal repetition over multiple orthogonal frequency division multiplexing (OFDM) sub-carriers. We assume that a base station is equipped with a single antenna but users are equipped with multiple antennas. In addition, we assume that the quadrature phase shift keying (QPSK) modulation is used for users. We mathematically analyze the bit error rate (BER) of both cell-edge users and cell-center users, which is the first theoretical result in the literature to the best of our knowledge. The mathematical analysis is validated through extensive link-level simulations.

Problem solving in foundation engineering using foundationPro

CERN Document Server

Yamin, Mohammad

2016-01-01

This book is at once a supplement to traditional foundation engineering textbooks and an independent problem-solving learning tool. The book is written primarily for university students majoring in civil or construction engineering taking foundation analysis and design courses to encourage them to solve design problems. Its main aim is to stimulate problem solving capability and foster self-directed learning. It also explains the use of the foundationPro software, available at no cost, and includes a set of foundation engineering applications. Taking a unique approach, Dr. Yamin summarizes the general step-by-step procedure to solve various foundation engineering problems, illustrates traditional applications of these steps with longhand solutions, and presents the foundationPro solutions. The special structure of the book allows it to be used in undergraduate and graduate foundation design and analysis courses in civil and construction engineering. The book stands as valuable resource for students, faculty, ...

Engineering Mathematics in Context

DEFF Research Database (Denmark)

Ravn, Ole; Henriksen, Lars Bo

2017-01-01

A theory-based approach to scientific research has an inherent tendency to become secluded from the ongoing problems and discussions of the surrounding society. A problem-based approach to research immediately involves this context of problems and discussions from the outset. In this article, we ...... argue that education in university engineering mathematics should take its outset in contextual problems in order to provide a foundation for the skills and capabilities engineers need in their future job settings, whether it be research or development activities....

Game Design and Development as Mathematical Activities

DEFF Research Database (Denmark)

Jensen, Erik Ottar; Hanghøj, Thorkild; Misfeldt, Morten

2016-01-01

education which have mostly been tied to students making learning games involving specific mathematical content. Game design activities are reported to have a motivational pull for students. A challenge seems to be that the students are mostly motivated by the game design or the programming activities...... between user and goal through the computational artifacts being used. The framework serves as a lens for making sense of computer game design as a context for learning mathematics....

Genomic similarity and kernel methods I: advancements by building on mathematical and statistical foundations.

Science.gov (United States)

Schaid, Daniel J

2010-01-01

Measures of genomic similarity are the basis of many statistical analytic methods. We review the mathematical and statistical basis of similarity methods, particularly based on kernel methods. A kernel function converts information for a pair of subjects to a quantitative value representing either similarity (larger values meaning more similar) or distance (smaller values meaning more similar), with the requirement that it must create a positive semidefinite matrix when applied to all pairs of subjects. This review emphasizes the wide range of statistical methods and software that can be used when similarity is based on kernel methods, such as nonparametric regression, linear mixed models and generalized linear mixed models, hierarchical models, score statistics, and support vector machines. The mathematical rigor for these methods is summarized, as is the mathematical framework for making kernels. This review provides a framework to move from intuitive and heuristic approaches to define genomic similarities to more rigorous methods that can take advantage of powerful statistical modeling and existing software. A companion paper reviews novel approaches to creating kernels that might be useful for genomic analyses, providing insights with examples [1]. Copyright © 2010 S. Karger AG, Basel.

Mathematical theories of classical particle channeling in perfect crystals

International Nuclear Information System (INIS)

Dumas, H. Scott

2005-01-01

We present an overview of our work on rigorous mathematical theories of channeling for highly energetic positive particles moving in classical perfect crystal potentials. Developed over the last two decades, these theories include: (i) a comprehensive, highly mathematical theory based on Nekhoroshev's theorem which embraces both axial and planar channeling as well as certain non-channeling particle motions (ii) a theory of axial channeling for relativistic particles based on a single-phase averaging method for ordinary differential equations and (iii) a theory of planar channeling for relativistic particles based on a two-phase averaging method for ordinary differential equations. Here we touch briefly on (i) and (ii), then focus on (iii). Together these theories place Lindhard's continuum model approximations on a firm mathematical foundation, and should serve as the starting point for more refined mathematical treatments of channeling

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

Discovering Mathematics with Magma Reducing the Abstract to the Concrete

CERN Document Server

Bosma, Wieb

2006-01-01

With a design based on the ontology and semantics of algebra, Magma enables users to rapidly formulate and perform calculations in the more abstract parts of mathematics. This book introduces the role Magma plays in advanced mathematical research through 14 case studies which, in most cases, describe computations underpinning theoretical results.

Classroom-Based Professional Expertise: A Mathematics Teacher's Practice with Technology

Science.gov (United States)

Bozkurt, Gulay; Ruthven, Kenneth

2017-01-01

This study examines the classroom practice and craft knowledge underpinning one teacher's integration of the use of GeoGebra software into mathematics teaching. The chosen teacher worked in an English secondary school and was professionally well regarded as an accomplished user of digital technology in mathematics teaching. Designed in accordance…

International Conference on Mathematics and Computing

CERN Document Server

Giri, Debasis; Saxena, P; Srivastava, P

2014-01-01

This book discusses recent developments and contemporary research in mathematics, statistics and their applications in computing. All contributing authors are eminent academicians, scientists, researchers and scholars in their respective fields, hailing from around the world. The conference has emerged as a powerful forum, offering researchers a venue to discuss, interact and collaborate, and stimulating the advancement of mathematics and its applications in computer science. The book will allow aspiring researchers to update their knowledge of cryptography, algebra, frame theory, optimizations, stochastic processes, compressive sensing, functional analysis, complex variables, etc. Educating future consumers, users, producers, developers and researchers in mathematics and computing is a challenging task and essential to the development of modern society. Hence, mathematics and its applications in computer science are of vital importance to a broad range of communities, including mathematicians and computing p...

Social media for health promotion: What messages are women receiving about cardiovascular disease risk by the Canadian Heart and Stroke Foundation?

Science.gov (United States)

Gonsalves, Christine A; McGannon, Kerry R; Schinke, Robert J

2017-11-01

The aim of this study was to explore the meanings of women's cardiovascular disease constructed within the Canadian Heart and Stroke Foundation Facebook page. Posts from Heart and Stroke Foundation and public user comments surrounding the launch of the Heart and Stroke Foundation re-branding were of interest. Ethnographic content analysis was employed to analyse text ( n = 40), images ( n = 32), videos ( n = 6), user comments and replies ( n = 42) from November 2016 to March 2017. Constructions (re)presented on Facebook of 'typical' women at risk and risk reduction were problematic as women most at risk were excluded through the use of consumerist, medicalized identities which also excluded promotion of healthy behaviour changes.

Drug use trajectory patterns among older drug users

Directory of Open Access Journals (Sweden)

Tyndall B

2011-05-01

Full Text Available Miriam Boeri, Thor Whalen, Benjamin Tyndall, Ellen BallardKennesaw State University, Department of Sociology and Criminal Justice, Kennesaw GA, USAAbstract: To better understand patterns of drug use trajectories over time, it is essential to have standard measures of change. Our goal here is to introduce measures we developed to quantify change in drug use behaviors. A secondary goal is to provide effective visualizations of these trajectories for applied use. We analyzed data from a sample of 92 older drug users (ages 45 to 65 to identify transition patterns in drug use trajectories across the life course. Data were collected for every year since birth using a mixed methods design. The community-drawn sample of active and former users were 40% female, 50% African American, and 60% reporting some college or greater. Their life histories provided retrospective longitudinal data on the diversity of paths taken throughout the life course and changes in drug use patterns that occurred over time. Bayesian analysis was used to model drug trajectories displayed by innovative computer graphics. The mathematical techniques and visualizations presented here provide the foundation for future models using Bayesian analysis. In this paper we introduce the concepts of transition counts, transition rates and relapse/remission rates, and we describe how these measures can help us better understand drug use trajectories. Depicted through these visual tools, measurements of discontinuous patterns provide a succinct view of individual drug use trajectories. The measures we use on drug use data will be further developed to incorporate contextual influences on the drug trajectory and build predictive models that inform rehabilitation efforts for drug users. Although the measures developed here were conceived to better examine drug use trajectories, the applications of these measures can be used with other longitudinal datasets.Keywords: drug use, trajectory patterns

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.

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.

Foundations of quantum gravity

CERN Document Server

Lindesay, James

2013-01-01

Exploring how the subtleties of quantum coherence can be consistently incorporated into Einstein’s theory of gravitation, this book is ideal for researchers interested in the foundations of relativity and quantum physics. The book examines those properties of coherent gravitating systems that are most closely connected to experimental observations. Examples of consistent co-gravitating quantum systems whose overall effects upon the geometry are independent of the coherence state of each constituent are provided, and the properties of the trapping regions of non-singular black objects, black holes, and a dynamic de Sitter cosmology are discussed analytically, numerically, and diagrammatically. The extensive use of diagrams to summarise the results of the mathematics enables readers to bypass the need for a detailed understanding of the steps involved. Assuming some knowledge of quantum physics and relativity, the book provides textboxes featuring supplementary information for readers particularly interested ...

E-Learning and Affective Student’s Profile in Mathematics

Directory of Open Access Journals (Sweden)

Giovannina Albano

2008-12-01

Full Text Available This paper is concerned with the personalisation of teaching/learning paths in mathematics education. Such personalisation would exploit the research results on the connection between the affective experience of the student learning mathematics and his/her success or failure in mathematics, which produces the learner’s attitude towards mathematics. We present a model for the learner’s affective profile in mathematics, which would extend the current user profile in an e-learning platform taking into account the learner’s attitude, to be used in order to offer and manage a Unit of Learning in mathematics better tailored on the global student’ needs. Tools for the implementation of the model in an e-learning platform have been devised. Activities templates suitable to various attitudes towards mathematics have been designed and their experimentation is in progress.

A Good Foundation for Number Learning for Five-Year-Olds? An Evaluation of the English Early Learning "Numbers" Goal in the Light of Research

Science.gov (United States)

Gifford, Sue

2014-01-01

This article sets out to evaluate the English Early Years Foundation Stage Goal for Numbers, in relation to research evidence. The Goal, which sets out to provide "a good foundation in mathematics", has greater breadth of content and higher levels of difficulty than previous versions. Research suggests that the additional expectations…

Mathematical concepts of quantum mechanics. 2. ed.

International Nuclear Information System (INIS)

Gustafson, Stephen J.; Sigal, Israel Michael

2011-01-01

The book gives a streamlined introduction to quantum mechanics while describing the basic mathematical structures underpinning this discipline. Starting with an overview of key physical experiments illustrating the origin of the physical foundations, the book proceeds with a description of the basic notions of quantum mechanics and their mathematical content. It then makes its way to topics of current interest, specifically those in which mathematics plays an important role. The more advanced topics presented include many-body systems, modern perturbation theory, path integrals, the theory of resonances, quantum statistics, mean-field theory, second quantization, the theory of radiation (non-relativistic quantum electrodynamics), and the renormalization group. With different selections of chapters, the book can serve as a text for an introductory, intermediate, or advanced course in quantum mechanics. The last four chapters could also serve as an introductory course in quantum field theory. (orig.)

The Role of Cognitive Processes, Foundational Math Skill, and Calculation Accuracy and Fluency in Word-Problem Solving versus Pre-Algebraic Knowledge

Science.gov (United States)

Fuchs, Lynn S.; Gilbert, Jennifer K.; Powell, Sarah R.; Cirino, Paul T.; Fuchs, Douglas; Hamlett, Carol L.; Seethaler, Pamela M.; Tolar, Tammy D.

2016-01-01

The purpose of this study was to examine child-level pathways in development of pre-algebraic knowledge versus word-problem solving, while evaluating the contribution of calculation accuracy and fluency as mediators of foundational skills/processes. Children (n = 962; mean 7.60 years) were assessed on general cognitive processes and early calculation, word-problem, and number knowledge at start of grade 2; calculation accuracy and calculation fluency at end of grade 2; and pre-algebraic knowledge and word-problem solving at end of grade 4. Important similarities in pathways were identified, but path analysis also indicated that language comprehension is more critical for later word-problem solving than pre-algebraic knowledge. We conclude that pathways in development of these forms of 4th-grade mathematics performance are more alike than different, but demonstrate the need to fine-tune instruction for strands of the mathematics curriculum in ways that address individual students’ foundational mathematics skills or cognitive processes. PMID:27786534

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.

Mathematical principles of signal processing Fourier and wavelet analysis

CERN Document Server

Brémaud, Pierre

2002-01-01

Fourier analysis is one of the most useful tools in many applied sciences. The recent developments of wavelet analysis indicates that in spite of its long history and well-established applications, the field is still one of active research. This text bridges the gap between engineering and mathematics, providing a rigorously mathematical introduction of Fourier analysis, wavelet analysis and related mathematical methods, while emphasizing their uses in signal processing and other applications in communications engineering. The interplay between Fourier series and Fourier transforms is at the heart of signal processing, which is couched most naturally in terms of the Dirac delta function and Lebesgue integrals. The exposition is organized into four parts. The first is a discussion of one-dimensional Fourier theory, including the classical results on convergence and the Poisson sum formula. The second part is devoted to the mathematical foundations of signal processing - sampling, filtering, digital signal proc...

Mathematics of quantum mechanics. Foundations, examples, problems, solutions; Mathematik der Quantenmechanik. Grundlagen, Beispiele, Aufgaben, Loesungen

Energy Technology Data Exchange (ETDEWEB)

Korsch, Hans Juergen

2013-07-01

This book mediates the fundamental terms and methods, which are necessary for an understanding of quantum mechanics. It shows, how mathematics can contribute to the understanding of quantum mechanics. The presented quantum-mechanical problems aim at the illustration and exercise of the most important mathematical methods. Because of the clear and understandable presentation and the numerous completely calculated examples and problems this book is suited for the self-study, for the accompanying of courses on quantum physics, for the accomplishment of exercise problems, and for the preparation on examinations.

Glogs as Non-Routine Problem Solving Tools in Mathematics

Science.gov (United States)

Devine, Matthew T.

2013-01-01

In mathematical problem solving, American students are falling behind their global peers because of a lack of foundational and reasoning skills. A specific area of difficulty with problem solving is working non-routine, heuristic-based problems. Many students are not provided with effective instruction and often grow frustrated and dislike math.…

Constructing Contracts: Making Discrete Mathematics Relevant to Beginning Programmers

Science.gov (United States)

Gegg-Harrison, Timothy S.

2005-01-01

Although computer scientists understand the importance of discrete mathematics to the foundations of their field, computer science (CS) students do not always see the relevance. Thus, it is important to find a way to show students its relevance. The concept of program correctness is generally taught as an activity independent of the programming…

Blessing of dimensionality: mathematical foundations of the statistical physics of data.

Science.gov (United States)

Gorban, A N; Tyukin, I Y

2018-04-28

The concentrations of measure phenomena were discovered as the mathematical background to statistical mechanics at the end of the nineteenth/beginning of the twentieth century and have been explored in mathematics ever since. At the beginning of the twenty-first century, it became clear that the proper utilization of these phenomena in machine learning might transform the curse of dimensionality into the blessing of dimensionality This paper summarizes recently discovered phenomena of measure concentration which drastically simplify some machine learning problems in high dimension, and allow us to correct legacy artificial intelligence systems. The classical concentration of measure theorems state that i.i.d. random points are concentrated in a thin layer near a surface (a sphere or equators of a sphere, an average or median-level set of energy or another Lipschitz function, etc.). The new stochastic separation theorems describe the thin structure of these thin layers: the random points are not only concentrated in a thin layer but are all linearly separable from the rest of the set, even for exponentially large random sets. The linear functionals for separation of points can be selected in the form of the linear Fisher's discriminant. All artificial intelligence systems make errors. Non-destructive correction requires separation of the situations (samples) with errors from the samples corresponding to correct behaviour by a simple and robust classifier. The stochastic separation theorems provide us with such classifiers and determine a non-iterative (one-shot) procedure for their construction.This article is part of the theme issue 'Hilbert's sixth problem'. © 2018 The Author(s).

Blessing of dimensionality: mathematical foundations of the statistical physics of data

Science.gov (United States)

Gorban, A. N.; Tyukin, I. Y.

2018-04-01

The concentrations of measure phenomena were discovered as the mathematical background to statistical mechanics at the end of the nineteenth/beginning of the twentieth century and have been explored in mathematics ever since. At the beginning of the twenty-first century, it became clear that the proper utilization of these phenomena in machine learning might transform the curse of dimensionality into the blessing of dimensionality. This paper summarizes recently discovered phenomena of measure concentration which drastically simplify some machine learning problems in high dimension, and allow us to correct legacy artificial intelligence systems. The classical concentration of measure theorems state that i.i.d. random points are concentrated in a thin layer near a surface (a sphere or equators of a sphere, an average or median-level set of energy or another Lipschitz function, etc.). The new stochastic separation theorems describe the thin structure of these thin layers: the random points are not only concentrated in a thin layer but are all linearly separable from the rest of the set, even for exponentially large random sets. The linear functionals for separation of points can be selected in the form of the linear Fisher's discriminant. All artificial intelligence systems make errors. Non-destructive correction requires separation of the situations (samples) with errors from the samples corresponding to correct behaviour by a simple and robust classifier. The stochastic separation theorems provide us with such classifiers and determine a non-iterative (one-shot) procedure for their construction. This article is part of the theme issue `Hilbert's sixth problem'.

A mobile design lab for user-driven innovation

DEFF Research Database (Denmark)

Christiansen, Ellen; Kanstrup, Anne Marie

2007-01-01

The paper presents the history and conceptual foundation for the Mobile Design Lab, ment to support both designers and users in the acts of user-driven innovation. The Mobile Design Lab is based on Vygotsky's theory of tool- and language-mediation, and was created in 2004 to support research...... and teaching of user driven innovation. Being itself an example of user-driven innovation it has taken shape of HCI design research projekcts, in which we have been involved since 2004. The first challenge was to get 'out of the lab', the next to get 'out of the head', and finally we are currently working...

The Mathematical Foundations of 3D Compton Scatter Emission Imaging

Directory of Open Access Journals (Sweden)

T. T. Truong

2007-01-01

Full Text Available The mathematical principles of tomographic imaging using detected (unscattered X- or gamma-rays are based on the two-dimensional Radon transform and many of its variants. In this paper, we show that two new generalizations, called conical Radon transforms, are related to three-dimensional imaging processes based on detected Compton scattered radiation. The first class of conical Radon transform has been introduced recently to support imaging principles of collimated detector systems. The second class is new and is closely related to the Compton camera imaging principles and invertible under special conditions. As they are poised to play a major role in future designs of biomedical imaging systems, we present an account of their most important properties which may be relevant for active researchers in the field.

Theoretical investigation of interaction between a rectangular plate and fractional viscoelastic foundation

Directory of Open Access Journals (Sweden)

Chengcheng Zhang

2014-08-01

Full Text Available The interaction between plates and foundations is a typical problem encountered in geotechnical engineering. The long-term plate performance is highly dependent on the rheological characteristics of ground soil. Compared with conventional linear rheology, the fractional calculus-based theory is a more powerful mathematical tool that can address this issue. This paper proposes a fractional Merchant model (FMM to investigate the time-dependent behavior of a simply supported rectangular plate on viscoelastic foundation. The correspondence principle involving Laplace transforms was employed to derive the closed-form solutions of plate response under uniformly distributed load. The plate deflection, bending moment, and foundation reaction calculated using the FMM were compared with the results obtained from the analogous elastic model (EM and the standard Merchant model (SMM. It is shown that the upper and lower bound solutions of the FMM can be determined using the EM. In addition, a parametric study was performed to examine the influences of the model parameters on the time-dependent behavior of the plate–foundation interaction problem. The results indicate that a small fractional differential order corresponds to a plate resting on a sandy soil foundation, while the fractional differential order value should be increased for a clayey soil foundation. The long-term performance of a foundation plate can be accurately simulated by varying the values of the fractional differential order and the viscosity coefficient. The observations from this study reveal that the proposed fractional model has the capability to capture the variation of plate deflection over many decades of time.

Mathematical foundations of the dendritic growth models.

Science.gov (United States)

Villacorta, José A; Castro, Jorge; Negredo, Pilar; Avendaño, Carlos

2007-11-01

At present two growth models describe successfully the distribution of size and topological complexity in populations of dendritic trees with considerable accuracy and simplicity, the BE model (Van Pelt et al. in J. Comp. Neurol. 387:325-340, 1997) and the S model (Van Pelt and Verwer in Bull. Math. Biol. 48:197-211, 1986). This paper discusses the mathematical basis of these models and analyzes quantitatively the relationship between the BE model and the S model assumed in the literature by developing a new explicit equation describing the BES model (a dendritic growth model integrating the features of both preceding models; Van Pelt et al. in J. Comp. Neurol. 387:325-340, 1997). In numerous studies it is implicitly presupposed that the S model is conditionally linked to the BE model (Granato and Van Pelt in Brain Res. Dev. Brain Res. 142:223-227, 2003; Uylings and Van Pelt in Network 13:397-414, 2002; Van Pelt, Dityatev and Uylings in J. Comp. Neurol. 387:325-340, 1997; Van Pelt and Schierwagen in Math. Biosci. 188:147-155, 2004; Van Pelt and Uylings in Network. 13:261-281, 2002; Van Pelt, Van Ooyen and Uylings in Modeling Dendritic Geometry and the Development of Nerve Connections, pp 179, 2000). In this paper we prove the non-exactness of this assumption, quantify involved errors and determine the conditions under which the BE and S models can be separately used instead of the BES model, which is more exact but considerably more difficult to apply. This study leads to a novel expression describing the BE model in an analytical closed form, much more efficient than the traditional iterative equation (Van Pelt et al. in J. Comp. Neurol. 387:325-340, 1997) in many neuronal classes. Finally we propose a new algorithm in order to obtain the values of the parameters of the BE model when this growth model is matched to experimental data, and discuss its advantages and improvements over the more commonly used procedures.

The Research on Subsidence Prediction of Soils Around Deep Foundation Pit

Directory of Open Access Journals (Sweden)

Ge LIU

2014-12-01

Full Text Available Deep foundation pit will cause settlement of surround buildings in the process of excavation. When the settlement is excessive, it will give rise to safety issues. Subsidence monitoring has become an important measure to ensure the safety of deep foundation pits. But in current subsidence monitoring engineering, the costs of wiring, unwiring and installation are particularly high. This paper proposes a portable wireless data transmission device in forecasting and early warning of settlement deformation of soils around deep foundation pits. We solve the problem by adopting the means of wireless communication to replace the cable transmission link part. The device does not rely on any personal computers. Instead, it can directly deal with the collected data through grey prediction GM (1, 1 mathematical model, neural network and interpolation model to give short-term, medium- term and long-term forecasts, respectively. Additionally it is able to set a threshold value. Once the forecast data reach the threshold, the device can issue alert and achieve the target of reminding technicians, so as to provide reliable basis to prevent and reduce disasters.

Substance and Dynamics: Two Elements of Aristotelian-Thomistic Philosophy of Nature in the Foundation of Mathematics in Physics

Directory of Open Access Journals (Sweden)

Rudolf Larenz

2017-09-01

Full Text Available The article aims at proposing a way of solution to the problem why mathematics is efficient in physics. Its strategy consists in, first, identifying servere reductionisms performed on physical processes in order to have them correspond to mathematics. As this makes it impossible to understand the real relationship between matter and mathematics, a necessary step on the way to an understanding is to abandon the reductionisms from the very outset. Consequently, one is faced with the need of searching for mathematical elements in nature, as if there never had been any successful mathematics in physics. And for this search, one has to rely on experience alone. To this end, the article takes its inspiration from two pillars of Aristotelian philosophy of nature, the notions of ‘substance’ and ‘dynamics’, together with a careful examination of the treasure of accumulated experience in physics. Upon this basis, the hylomorphic structure of elementary particles, which are considered to be at the basis of all material substances, is the source for the most common features of the dynamical order of material things in general. This dynamical order, in turn, is quite likely to be reflected in mathematical terms. This is a novel approach because, at present, the most common framework for dealing with the question of mathematics in physics is Scientific Realism. It addresses the question why the existent physico-mathematical theories are successful. In order to find an answer, it starts from these theories and some methodological considerations, but does not address the question of where these theories stem from. In particular, it does not consider the possibility that these theories might, at least in part, stem from the material things they are referring to. The latter approach is what is suggested here. It is that of Natural Realism, of which Aristotle is an eminent representative.

Colloquy on Minority Males in Science, Technology, Engineering, and Mathematics

Science.gov (United States)

Didion, Catherine; Fortenberry, Norman L.; Cady, Elizabeth

2012-01-01

On August 8-12, 2010 the National Academy of Engineering (NAE), with funding from the National Science Foundation (NSF), convened the Colloquy on Minority Males in Science, Technology, Engineering, and Mathematics (STEM), following the release of several reports highlighting the educational challenges facing minority males. The NSF recognized the…

The MATH--Open Source Application for Easier Learning of Numerical Mathematics

Science.gov (United States)

Glaser-Opitz, Henrich; Budajová, Kristina

2016-01-01

The article introduces a software application (MATH) supporting an education of Applied Mathematics, with focus on Numerical Mathematics. The MATH is an easy to use tool supporting various numerical methods calculations with graphical user interface and integrated plotting tool for graphical representation written in Qt with extensive use of Qwt…

Cultivating Mathematics in an International Space: Roles of Gösta Mittag-Leffler in the Development and Internationalization of Mathematics in Sweden and Beyond, 1880-1920

DEFF Research Database (Denmark)

Turner, Laura

2011-01-01

This thesis aims to investigate several areas of mathematical activity undertaken by the Swedish mathematician Gösta Mittag-Leffler (1846-1927). These not only markedly impacted the development of mathematics in Stockholm, where they were centred, but transformed, by virtue of their roots in both...... the foundation of the Scandinavian Congress of Mathematicians (1909) according to a belief that cultural solidarity would both enrich each country involved and afford a united group more clout than could be gained by each of the small nations alone. By analyzing Mittag-Leffler's strategies and tactics...

2nd International Conference on Mathematics and Computing

CERN Document Server

Chowdhury, Dipanwita; Giri, Debasis

2015-01-01

This book discusses recent developments and contemporary research in mathematics, statistics and their applications in computing. All contributing authors are eminent academicians, scientists, researchers and scholars in their respective fields, hailing from around the world. This is the second conference on mathematics and computing organized at Haldia Institute of Technology, India. The conference has emerged as a powerful forum, offering researchers a venue to discuss, interact and collaborate, and stimulating the advancement of mathematics and its applications in computer science. The book will allow aspiring researchers to update their knowledge of cryptography, algebra, frame theory, optimizations, stochastic processes, compressive sensing, functional analysis, complex variables, etc. Educating future consumers, users, producers, developers and researchers in mathematics and computing is a challenging task and essential to the development of modern society. Hence, mathematics and its applications in com...

Proceedings – Mathematical Sciences | Indian Academy of Sciences

Indian Academy of Sciences (India)

Special issue devoted to advances in specific areas of mathematics and proceedings of selected high quality conferences are also published. ... Editorial Manager is a user-friendly online submission and review management system. Authors ...

Approaches to teaching primary level mathematics

Directory of Open Access Journals (Sweden)

Caroline Long

2014-12-01

Full Text Available In this article we explore approaches to curriculum in the primary school in order to map and manage the omissions implicit in the current unfolding of the Curriculum and Assessment Policy Statement for mathematics. The focus of school-based research has been on curriculum coverage and cognitive depth. To address the challenges of teaching mathematics from the perspective of the learner, we ask whether the learners engage with the subject in such a way that they build foundations for more advanced mathematics. We firstly discuss three approaches that inform the teaching of mathematics in the primary school and which may be taken singly or in conjunction into organising the curriculum: the topics approach, the process approach, and the conceptual fields approach. Each of the approaches is described and evaluated by presenting both their advantages and disadvantages. We then expand on the conceptual fields approach by means of an illustrative example. The planning of an instructional design integrates both a topics and a process approach into a conceptual fields approach. To address conceptual depth within this approach, we draw on five dimensions required for understanding a mathematical concept. In conclusion, we reflect on an approach to curriculum development that draws on the integrated theory of conceptual fields to support teachers and learners in the quest for improved teaching and learning.

The Generalized Principle of the Golden Section and its applications in mathematics, science, and engineering

International Nuclear Information System (INIS)

Stakhov, A.P.

2005-01-01

The 'Dichotomy Principle' and the classical 'Golden Section Principle' are two of the most important principles of Nature, Science and also Art. The Generalized Principle of the Golden Section that follows from studying the diagonal sums of the Pascal triangle is a sweeping generalization of these important principles. This underlies the foundation of 'Harmony Mathematics', a new proposed mathematical direction. Harmony Mathematics includes a number of new mathematical theories: an algorithmic measurement theory, a new number theory, a new theory of hyperbolic functions based on Fibonacci and Lucas numbers, and a theory of the Fibonacci and 'Golden' matrices. These mathematical theories are the source of many new ideas in mathematics, philosophy, botanic and biology, electrical and computer science and engineering, communication systems, mathematical education as well as theoretical physics and physics of high energy particles

Mathematics of large eddy simulation of turbulent flows

Energy Technology Data Exchange (ETDEWEB)

Berselli, L.C. [Pisa Univ. (Italy). Dept. of Applied Mathematics ' ' U. Dini' ' ; Iliescu, T. [Virginia Polytechnic Inst. and State Univ., Blacksburg, VA (United States). Dept. of Mathematics; Layton, W.J. [Pittsburgh Univ., PA (United States). Dept. of Mathematics

2006-07-01

Large eddy simulation (LES) is a method of scientific computation seeking to predict the dynamics of organized structures in turbulent flows by approximating local, spatial averages of the flow. Since its birth in 1970, LES has undergone an explosive development and has matured into a highly-developed computational technology. It uses the tools of turbulence theory and the experience gained from practical computation. This book focuses on the mathematical foundations of LES and its models and provides a connection between the powerful tools of applied mathematics, partial differential equations and LES. Thus, it is concerned with fundamental aspects not treated so deeply in the other books in the field, aspects such as well-posedness of the models, their energy balance and the connection to the Leray theory of weak solutions of the Navier-Stokes equations. The authors give a mathematically informed and detailed treatment of an interesting selection of models, focusing on issues connected with understanding and expanding the correctness and universality of LES. This volume offers a useful entry point into the field for PhD students in applied mathematics, computational mathematics and partial differential equations. Non-mathematicians will appreciate it as a reference that introduces them to current tools and advances in the mathematical theory of LES. (orig.)

A Mathematical Theory of System Information Flow

Science.gov (United States)

2016-06-27

i.i.d. is usually quite involved. There are numerous experiments , often using photons, to test Bell’s Inequality recorded in the literature, but the...classical setting. Peter focused on non-locality as an alternative theory and experiments using the CHSH inequality , and devised a statistical procedure...761 (2014). 7. BIERHORST, P., A new loophole in recent Bell test experiments , arXiv:1311.4488, (2014). 8. BIERHORST, P., A Mathematical Foundation

HTGR Cost Model Users' Manual

International Nuclear Information System (INIS)

Gandrik, A.M.

2012-01-01

The High Temperature Gas-Cooler Reactor (HTGR) Cost Model was developed at the Idaho National Laboratory for the Next Generation Nuclear Plant Project. The HTGR Cost Model calculates an estimate of the capital costs, annual operating and maintenance costs, and decommissioning costs for a high-temperature gas-cooled reactor. The user can generate these costs for multiple reactor outlet temperatures; with and without power cycles, including either a Brayton or Rankine cycle; for the demonstration plant, first of a kind, or nth of a kind project phases; for a single or four-pack configuration; and for a reactor size of 350 or 600 MWt. This users manual contains the mathematical models and operating instructions for the HTGR Cost Model. Instructions, screenshots, and examples are provided to guide the user through the HTGR Cost Model. This model was design for users who are familiar with the HTGR design and Excel. Modification of the HTGR Cost Model should only be performed by users familiar with Excel and Visual Basic.

Education Foundation Pouk Tomang Website Using Macromedia Dreamweaver Mx

OpenAIRE

Ramses Sitorus; Cut Asiana Gemawaty, Skom., MMSi

2003-01-01

Everything has been more rapid because of technological developments, one of the Internet. Internet has made it easier - especially for ease of profitable Internet service users. Information is now so easy to obtain thanks to the Internet, education can use this technology for entering the competition in providing information about schools and education quality in it. With the proposed project, expected Tomang POUK Education Foundation which is engaged in education can also benefit.

Using Assessment for Learning Mathematics with Mobile Tablet Based Solutions

Directory of Open Access Journals (Sweden)

Ghislain Maurice Norbert Isabwe

2014-03-01

Full Text Available This article discusses assessment for learning in mathematics subjects. Teachers of large classes face the challenge of regularly assessing studentsཿ ongoing mathematical learning achievements. Taking the complexity of assessment and feedback for learning as a background, we have developed a new approach to the assessment for learning mathematics at university level. We devised mobile tablet technology supported assessment processes, and we carried out user studies in both Rwanda and Norway. Results of our study indicated that students found it fruitful to be involved in assessing other studentsཿ mathematics work, i.e. assessing fellow studentsཿ answers to mathematical tasks. By being involved in the assessment process, the students expected mathematical learning gains. Their providing and obtaining of feedback to/from their fellow students using technology supported tools were highly appreciated as regards their own mathematical learning process.

On foundational and geometric critical aspects of quantum electrodynamics

International Nuclear Information System (INIS)

Prugovecki, E.

1994-01-01

The foundational difficulties encountered by the conventional formulation of quantum electrodynamics, and the criticism by Dirac Schwinger, Rohrlich, and others, aimed at some of the physical and mathematical premises underlying that formulation, are reviewed and discussed. The basic failings of the conventional methods of quantization of the electromagnetic field are pointed out, especially with regard to the issue of local (anti) commutativity of quantum fields as an embodiment of relativistic microcausality. A brief description is given of a recently advanced new type of approach to quantum electrodynamics, and to quantum field theory in general, which is epistemically based on intrinsically quantum ideas about the physical nature of spacetime, and is mathematically based on a fiber theoretical formulation of quantum geometries, aimed in part at removing the aforementioned difficulties and inconsistencies. It is shown that these ideas can be traced to a conceptualization of spacetime outlined by Einstein in the last edition of his well-known semipopular exposition of relativity theory. 57 refs

Mathematical foundations of the Burrus techniques for spectral unfolding

International Nuclear Information System (INIS)

Rust, B.W.

1976-01-01

This paper treats the numerical solution of the first kind Fredholm integral equation in the case where the normal nonuniqueness and ill-conditioning problems are further aggravated by the presence of stochastic measuring errors. The basic ideas, due originally to Walter R. Burrus, of the techniques described are to seek statistical confidence interval estimates for the solution and to make the intervals as small as possible by using physically motivated a priori information to constrain the size of the set of permissible solutions. When these constraints are added to the classical linear regression model, the resulting interval estimation problems can be formulated in terms of parametric quadratic programming, but the solution of such problems is difficult and costly. Two more practicable methods have been developed which give suboptimal bounds, i.e., intervals which are somewhat wider than the optimally narrow ones that would be obtained from the quadratic programming procedure. One method uses various linear programming approximations while the other uses a constrained least squares procedure reminiscent of the Phillips-Twomey-Tikonov smoothing and regularizing techniques. Both methods are illustrated by mathematical and physically motivated examples

The Effects of a Tier 3 Intervention on the Mathematics Performance of Second Grade Students With Severe Mathematics Difficulties.

Science.gov (United States)

Bryant, Brian R; Bryant, Diane Pedrotty; Porterfield, Jennifer; Dennis, Minyi Shih; Falcomata, Terry; Valentine, Courtney; Brewer, Chelsea; Bell, Kathy

2016-01-01

The purpose of this study was to determine the effectiveness of a systematic, explicit, intensive Tier 3 (tertiary) intervention on the mathematics performance of students in second grade with severe mathematics difficulties. A multiple-baseline design across groups of participants showed improved mathematics performance on number and operations concepts and procedures, which are the foundation for later mathematics success. In the previous year, 12 participants had experienced two doses (first and second semesters) of a Tier 2 intervention. In second grade, the participants continued to demonstrate low performance, falling below the 10th percentile on a researcher-designed universal screener and below the 16th percentile on a distal measure, thus qualifying for the intensive intervention. A project interventionist, who met with the students 5 days a week for 10 weeks (9 weeks for one group), conducted the intensive intervention. The intervention employed more intensive instructional design features than the previous Tier 2 secondary instruction, and also included weekly games to reinforce concepts and skills from the lessons. Spring results showed significantly improved mathematics performance (scoring at or above the 25th percentile) for most of the students, thus making them eligible to exit the Tier 3 intervention. © Hammill Institute on Disabilities 2014.

Corporate Foundations

DEFF Research Database (Denmark)

Herlin, Heidi; Thusgaard Pedersen, Janni

2013-01-01

action between business and NGOs through convening, translation, collaboration, and mediation. Our study provides valuable insights into the tri-part relationship of company foundation NGO by discussing the implications of corporate foundations taking an active role in the realm of corporate social...... responsibility (CSR). The paper hence illuminates the fascinating and overlooked role of corporate foundations as potential bridges between business and civil society. It also informs theory on boundary organizations by clarifying challenges and limits of such institutions.......This paper aims to explore the potential of Danish corporate foundations as boundary organizations facilitating relationships between their founding companies and non-governmental organizations (NGOs). Hitherto, research has been silent about the role of corporate foundations in relation to cross...

User's Manual MCnest - Markov Chain Nest Productivity Model Version 2.0

Science.gov (United States)

The Markov chain nest productivity model, or MCnest, is a set of algorithms for integrating the results of avian toxicity tests with reproductive life-history data to project the relative magnitude of chemical effects on avian reproduction. The mathematical foundation of MCnest i...

Gender Stereotypes among Road Users

Directory of Open Access Journals (Sweden)

Kabalevskaya, Alexandra I.

2013-09-01

Full Text Available This article analyzes the mechanism of stereotyping as exemplified by gender stereotypes of road users. Gender stereotypes are not only viewed as an a priori image of a percept, but also examined ‘in action’ — at the very moment of their actualization with road users. In the paper we have identified the content of road users’ gender stereotypes; analyzed the behaviour of male and female drivers, pinpointing a number of gender-specific behavioural features; demonstrated that male and female driving differ from each other in terms of speed, intensity and roughness; and identified the conditions and mechanisms underlying the actualization of gender stereotypes. Based on video and audio materials, we have found that drivers’ gender-specific behavioural features are perceivable to road users: such features trigger the actualization of gender stereotypes as attributive schemes, which determine the interaction between road users, while also laying the foundation for gender stereotypes.

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.

Variational data assimilation: mathematical foundations and one application Assimilação variacional de dados: fundamentos matemáticos e uma aplicação

Directory of Open Access Journals (Sweden)

Paulo S. D. da Silva

2011-09-01

Full Text Available Variational Data Assimilation and Adjoint Equation Method are presented here as a general methodology designed to improve the quality of computational simulation when are given the dynamics and a set of observation of the system under study. The mathematical foundations the procedures to obtain the adjoint of a given computational program, a fundamental task in order to apply the methodology, are carefully examined.A Assimilação Variacional de Dados e o método das Equações Adjuntas são aqui apresentados como uma metodologia geral, desenvolvida para melhorar a qualidade das simulações computacionais, quando a dinâmica e um conjunto de observações do sistema em estudo são conhecidos. Os fundamentos matemáticos e os procedimentos para se obter o adjunto de um dado programa computacional, uma tarefa fundamental para a aplicação da metodologia, são cuidadosamente examinados.

National Science Foundation Assistant Director for Mathematics and Physical Sciences Tony Chan (USA) visiting CMS experiment on 23rd May 2007 with Spokesperson T. Virdee, Deputy Spokesperson R. Cousins, Advisor to CERN Director-General J. Ellis, US CMS Research Program Deputy Manager D. Marlow and FNAL D. Green

CERN Multimedia

Maximilien Brice

2007-01-01

National Science Foundation Assistant Director for Mathematics and Physical Sciences Tony Chan (USA) visiting CMS experiment on 23rd May 2007 with Spokesperson T. Virdee, Deputy Spokesperson R. Cousins, Advisor to CERN Director-General J. Ellis, US CMS Research Program Deputy Manager D. Marlow and FNAL D. Green

TEDS-M 2008 User Guide for the International Database. Supplement 4: TEDS-M Released Mathematics and Mathematics Pedagogy Knowledge Assessment Items

Science.gov (United States)

Brese, Falk, Ed.

2012-01-01

The goal for selecting the released set of test items was to have approximately 25% of each of the full item sets for mathematics content knowledge (MCK) and mathematics pedagogical content knowledge (MPCK) that would represent the full range of difficulty, content, and item format used in the TEDS-M study. The initial step in the selection was to…

Evaluation of NSF's Program of Grants and Vertical Integration of Research and Education in the Mathematical Sciences (VIGRE)

Science.gov (United States)

National Academies Press, 2009

2009-01-01

In 1998, the National Science Foundation (NSF) launched a program of Grants for Vertical Integration of Research and Education in the Mathematical Sciences (VIGRE). These grants were designed for institutions with PhD-granting departments in the mathematical sciences, for the purpose of developing high-quality education programs, at all levels,…

Multi-User GeoGebra for Virtual Math Teams

Directory of Open Access Journals (Sweden)

Gerry Stahl

2010-05-01

Full Text Available The Math Forum is an online resource center for pre-algebra, algebra, geometry and pre-calculus. Its Virtual Math Teams (VMT service provides an integrated web-based environment for small teams to discuss mathematics. The VMT collaboration environment now includes the dynamic mathematics application, GeoGebra. It offers a multi-user version of GeoGebra, which can be used in concert with VMT’s chat, web browsers, curricula and wiki repository.

The Generalized Principle of the Golden Section and its applications in mathematics, science, and engineering

Energy Technology Data Exchange (ETDEWEB)

Stakhov, A.P. [International Club of the Golden Section, 6 McCreary Trail, Bolton, ON, L7E 2C8 (Canada)] e-mail: goldenmuseum@rogers.com

2005-10-01

The 'Dichotomy Principle' and the classical 'Golden Section Principle' are two of the most important principles of Nature, Science and also Art. The Generalized Principle of the Golden Section that follows from studying the diagonal sums of the Pascal triangle is a sweeping generalization of these important principles. This underlies the foundation of 'Harmony Mathematics', a new proposed mathematical direction. Harmony Mathematics includes a number of new mathematical theories: an algorithmic measurement theory, a new number theory, a new theory of hyperbolic functions based on Fibonacci and Lucas numbers, and a theory of the Fibonacci and 'Golden' matrices. These mathematical theories are the source of many new ideas in mathematics, philosophy, botanic and biology, electrical and computer science and engineering, communication systems, mathematical education as well as theoretical physics and physics of high energy particles.

Culturally Responsive Teaching in the Context of Mathematics: A Grounded Theory Case Study

Science.gov (United States)

Bonner, Emily P.; Adams, Thomasenia L.

2012-01-01

In this grounded theory case study, four interconnected, foundational cornerstones of culturally responsive mathematics teaching (CRMT), communication, knowledge, trust/relationships, and constant reflection/revision, were systematically unearthed to develop an initial working theory of CRMT that directly informs classroom practice. These…

Leibniz on the parallel postulate and the foundations of geometry the unpublished manuscripts

CERN Document Server

De Risi, Vincenzo

2016-01-01

This book offers a general introduction to the geometrical studies of Gottfried Wilhelm Leibniz (1646-1716) and his mathematical epistemology. In particular, it focuses on his theory of parallel lines and his attempts to prove the famous Parallel Postulate. Furthermore it explains the role that Leibniz’s work played in the development of non-Euclidean geometry. The first part is an overview of his epistemology of geometry and a few of his geometrical findings, which puts them in the context of the seventeenth-century studies on the foundations of geometry. It also provides a detailed mathematical and philosophical commentary on his writings on the theory of parallels, and discusses how they were received in the eighteenth century as well as their relevance for the non-Euclidean revolution in mathematics. The second part offers a collection of Leibniz’s essays on the theory of parallels and an English translation of them. While a few of these papers have already been published (in Latin) in the standard Le...

Ethnophysics, Mathematical Modeling, Geometry... All in the same Manzuá

Directory of Open Access Journals (Sweden)

Ednilson Sergio Ramalho de Souza

2013-06-01

Full Text Available The objective this is paper is to show partial results of research for project of doctorate whose intention is to analyze the Ethnophysics of the amazon fisherman end to develop innovative didactic resources for the conceptual approach in Physics and Mathematics in the classroom of the high school and higher education in environment of Mathematical Modeling. The research question was: How the build the Manzuá can contextualize lessons of Physics and Mathematics in high school? The methodology used was ethnographicresearch. The theoretical foundations were Ethnomathematics (D’AMBROSIO, 2008, Mental Models (JONHSON-LAIRD, 1983, Mathematical Modeling (CHAVES e ESPÍRITO SANTO, 2008 end Conceptual Field ((VERGNAUD, 2007. The initial results suggest which the traditional physical knowledge is strongly related to mental models formed in function long years practice in the construction of the Manzuá end the operational invariants take part in the mental models. The situations lived during the construction of the Manzuá can base situations-problem in the classes of Physics and Mathematics in environment of Mathematical Modeling. We can, therefore, develop didactics resources that relate the traditional knowledge to the school knowledge

The use of isiXhosa children’s poetry as a tool to integrate literacy, mathematics and life skills in Foundation Phase: Grade R-3

Directory of Open Access Journals (Sweden)

Nozuko Gxekwa

2017-12-01

Full Text Available Literature helps us understand and make sense of the world around us. It is a part of education, which broadens one’s mind about how to understand, transfer knowledge and provide meaningful and authentic learning. Thus, this article aims to highlight how some elements of isiXhosa children’s poetry can be used to help pre-service teachers to teach and integrate mathematics and life skills with literacy in Foundation Phase (FP. This approach of using poems for integration strengthens concepts and skills in more than one subject area. The theoretical framework that informed the article is integrative learning. The data in this article were generated through non-participant classroom observations and non-structured interviews with the participants of the study and the researchers adopted the interpretative phenomenological analysis method for data analysis. This article was prompted by findings of lack of understanding of integrative teaching and learning and lack of teaching resources in isiXhosa to enhance integrative teaching and learning in FP intervention undertaken with 25 first year isiXhosa-speaking FP students.

Mathematical foundation of the application of modal analysis to the investigation of space-time reactor behaviour

International Nuclear Information System (INIS)

Obradovic, D.M.

1970-01-01

In recent years investigations in the field of kinetics and dynamics of nuclear reactors have been directed towards overcoming an insufficiently accurate point reactor model. For that purpose different mathematical approaches have been used. This thesis is devoted to modal analysis because, from the practical point of view, it is a very promising and, from the mathematical and physical point of view, a very interesting method. Some fundamental mathematical problems connected with the application of modal analysis to the investigations of the reactor space-time behaviour are still unsolved and accordingly our purpose is to solve some of these problems. The spectral properties of the diffusion and P 1 operators are studied in some detail applying the Krein-Rutman theory of the K-positive operators, the Krasnosel'skii theory of u 0 operators, and the Keldis theory of the operator families. The formal solution to the initial value problem (as an abstract Cauchy problem), associated with the diffusion and P 1 operators is also studied. Modal analysis is identified as a set of methods in the mathematical literature known as the Galerkin methods (or projection methods). Following this idea (using the results of the mathematical investigations of the Galerkin methods) and using our results of the investigations of the properties of the diffusion and P 1 operators, the applicability of modal analysis to the approximate solution of the diffusion and P 1 equations and of the eigenvalue problems associated with the diffusion and P 1 operators is established. As an example of the application of modal analysis the Bubnov and Galerkin method is applied to a multiregion thermal nuclear reactor for the determination of: (i) frequency response, (ii) eigenvalues and eigenvectors of the stationary diffusion operator, (iii) eigenvalues and eigenvectors of the non-stationary diffusion operators. On the basis of the expressions obtained the corresponding computer programmes for radial

Perceptions and Impact of Mandatory eLearning for Foundation Trainee Doctors: A Qualitative Evaluation.

Science.gov (United States)

Brooks, Hannah L; Pontefract, Sarah K; Vallance, Hannah K; Hirsch, Christine A; Hughes, Elizabeth; Ferner, Robin E; Marriott, John F; Coleman, Jamie J

2016-01-01

Junior doctors in the UK must complete various educational components during their two year Foundation training programme. It is important that mandatory learning is informative and engaging. The aim of this study was to evaluate trainee doctors' perceptions of a Technology Enhanced Learning (TEL) programme developed to improve prescribing competency. Focus groups and interviews were conducted at three hospital sites in the West Midlands. Codes, sub-themes and themes were determined using deductive and inductive thematic analysis. Data were collected from 38 Foundation trainee doctors. Results revealed major themes relating to prescribing education, the user experience and user engagement. Key findings included the positive impact of preparedness following undergraduate education on the user experience of the TEL programme at the postgraduate level; the impact of content, structure, and individual learning needs and styles on the user experience; and the impact of motivation and time on engagement. Most trainees engaged with the programme owing to its mandatory nature; however, some trainees also used the programme voluntarily, for example, to acquire knowledge prior to starting a new placement. It is important to ensure that learners are willing to engage with mandatory TEL, and that they have the time and motivation to do so. It is also important to ensure that learners have a positive user experience and that in designing TEL individual differences in learning styles and needs are taken into account. These findings have implications for educators and system developers in the construction and design of mandatory eLearning programmes.

Variational analysis and aerospace engineering mathematical challenges for the aerospace of the future

CERN Document Server

Mohammadi, Bijan; Pironneau, Olivier; Cipolla, Vittorio

2016-01-01

This book presents papers surrounding the extensive discussions that took place from the ‘Variational Analysis and Aerospace Engineering’ workshop held at the Ettore Majorana Foundation and Centre for Scientific Culture in 2015. Contributions to this volume focus on advanced mathematical methods in aerospace engineering and industrial engineering such as computational fluid dynamics methods, optimization methods in aerodynamics, optimum controls, dynamic systems, the theory of structures, space missions, flight mechanics, control theory, algebraic geometry for CAD applications, and variational methods and applications. Advanced graduate students, researchers, and professionals in mathematics and engineering will find this volume useful as it illustrates current collaborative research projects in applied mathematics and aerospace engineering.

[The ethics of care, the users' perspective].

Science.gov (United States)

Desclerc-Dulac, Danièle; Paris, Marc

2017-09-01

The user's perspective on the notion of nursing ethics is essential, in a context where the health democracy is becoming increasingly important. However, at a time when treatment is becoming cross-disciplinary, the user is right to reflect on the existence of distinct codes of ethics for each profession. To take into account the interest of the patient, a core foundation common to all the different professions could be envisaged, from the point of view of the ethics of care. Copyright © 2017. Published by Elsevier Masson SAS.

The future of mathematical communication. Final technical report

Energy Technology Data Exchange (ETDEWEB)

Christy, J.

1994-12-31

One of the first fruits of cooperation with LBL was the use of the MBone (Multi-Cast Backbone) to broadcast the Conference on the Future of Mathematical Communication, held at MSRI November 30--December 3, 1994. Late last fall, MSRI brought together more than 150 mathematicians, librarians, software developers, representatives of scholarly societies, and both commercial and not-for-profit publishers to discuss the revolution in scholarly communication brought about by digital technology. The conference was funded by the Department of Energy, the National Science Foundation, and the Paul and Gabriella Rosenbaum Foundation. It focused on the impact of the technological revolution on mathematics, but necessarily included issues of a much wider scope. There were talks on electronic publishing, collaboration across the Internet, economic and intellectual property issues, and various new technologies which promise to carry the revolution forward. There were panel discussions of electronic documents in mathematics, the unique nature of electronic journals, technological tools, and the role of scholarly societies. There were focus groups on Developing Countries, K-12 Education, Libraries, and Te{sub X}. The meeting also embodied the promises of the revolution; it was multicast over the MBone channel of the Internet to hundreds of sites around the world and much information on the conference will be available on their World Wide Web server at the URL http://www.msri.org/fmc. The authors have received many comments about the meeting indicating that it has had a profound impact on how the community thinks about how scientists can communicate and make their work public.

Pemrograman Graphical User Interface (GUI) Dengan Matlab Untuk Mendesain Alat Bantu Opersai Matematika

OpenAIRE

Butar Butar, Ronisah Putra

2011-01-01

Graphical User Interface ( GUI) is a application program orient visual which woke up with graphical obyek in the place of comand of text for the user interaction. Graphical User Interface ( GUI) in MATLAB embraced in a application of GUIDE ( Graphical User Interface Builder). In this paper will be discuss about how disagning a appliance assist mathematics operation with program of Graphical User Interface ( GUI) with MATLAB with aim to as one of the appliance alternative assist...

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.

Truth, possibility and probability new logical foundations of probability and statistical inference

CERN Document Server

Chuaqui, R

1991-01-01

Anyone involved in the philosophy of science is naturally drawn into the study of the foundations of probability. Different interpretations of probability, based on competing philosophical ideas, lead to different statistical techniques, and frequently to mutually contradictory consequences. This unique book presents a new interpretation of probability, rooted in the traditional interpretation that was current in the 17th and 18th centuries. Mathematical models are constructed based on this interpretation, and statistical inference and decision theory are applied, including some examples in artificial intelligence, solving the main foundational problems. Nonstandard analysis is extensively developed for the construction of the models and in some of the proofs. Many nonstandard theorems are proved, some of them new, in particular, a representation theorem that asserts that any stochastic process can be approximated by a process defined over a space with equiprobable outcomes.

Quantum mechanics by walking 1. Foundations; Quantenmechanik zu Fuss 1. Grundlagen

Energy Technology Data Exchange (ETDEWEB)

Pade, Jochen [Oldenburg Univ. (Germany)

2012-11-01

Quantum mechanics by walking introduces to the foundations of non-relativistic quantum mechanics. This book applies to studyings of teaching physics as well as all studyings of physics, who look for an appropriate, easy, fresh, and modern approach to the field. In the present first volume the essential principles of quantum mechanics are worked out. in order to be able to develop their mathematical formulation as fastly and clearly as possible, systematically between wave mechanics and algebraic presentation is changed. Beside themes, which are traditionally in textbooks of quantum mechanics, extensively actual aspects like interaction-free quantum measurement, neutrino oscillations, or quantum cryptography are considered as well as fundamental problems and epistemological questions discussed, as they occur in connection with the measurement process. The list of the postulates of quantum mechanics closes this volume; they form the framework for the extensions and applications, which are discussed in the second volume. The required mathematical aids are introduced step by step. In the appendix the most important mathematical tools are compactly collected, so that supplementing literature can be far reachingly abandoned. Furthermore in the appendix supplementing themes are deepened as for instance the Quantum Zeno effect or delayed-choice experiments.

Tensor analysis methods for activity characterization in spatiotemporal data

Energy Technology Data Exchange (ETDEWEB)

Haass, Michael Joseph; Van Benthem, Mark Hilary; Ochoa, Edward M

2014-03-01

Tensor (multiway array) factorization and decomposition offers unique advantages for activity characterization in spatio-temporal datasets because these methods are compatible with sparse matrices and maintain multiway structure that is otherwise lost in collapsing for regular matrix factorization. This report describes our research as part of the PANTHER LDRD Grand Challenge to develop a foundational basis of mathematical techniques and visualizations that enable unsophisticated users (e.g. users who are not steeped in the mathematical details of matrix algebra and mulitway computations) to discover hidden patterns in large spatiotemporal data sets.

The Reflective Foundation

DEFF Research Database (Denmark)

Lunde Jørgensen, Ida

Private foundations and cultural philanthropy by élites is viewed with increasing skepticism in recent years, begging the question of the extent to which foundations reflect on their role vis a vis wider societal norms. Through the prism of the New Carlsberg Foundation, financed by the brewery...... Carlsberg A/S, the paper seeks to elucidate the way in which one culturally significant foundation from Denmark has reflected on - and legitimated - its work and investments at critical moments in the past decades. The paper indicates a foundation with a high degree of reflection on the wider societal...

Edwin B. Wilson and the rise of mathematical economics in America, 1920-1940

OpenAIRE

Carvajalino, Juan

2017-01-01

In the paper, Edwin B. Wilson's influence on the rise of mathematical economics in America between the 1920s and 1940s is explored. The focus is laid on showing how on the grounds of his foundational ideas about science Wilson worked at the organizational and educational fronts to modernize economics, at this at three levels. First, the paper shows the ways in which around 1930 Wilson was key, at the nationwide level, in the constitution of the first organized community of American mathematic...

Matrix Mathematics Theory, Facts, and Formulas (Second Edition)

CERN Document Server

Bernstein, Dennis S

2011-01-01

When first published in 2005, Matrix Mathematics quickly became the essential reference book for users of matrices in all branches of engineering, science, and applied mathematics. In this fully updated and expanded edition, the author brings together the latest results on matrix theory to make this the most complete, current, and easy-to-use book on matrices. Each chapter describes relevant background theory followed by specialized results. Hundreds of identities, inequalities, and matrix facts are stated clearly and rigorously with cross references, citations to the literature, and illuminat

Toward User Interfaces and Data Visualization Criteria for Learning Design of Digital Textbooks

Science.gov (United States)

Railean, Elena

2014-01-01

User interface and data visualisation criteria are central issues in digital textbooks design. However, when applying mathematical modelling of learning process to the analysis of the possible solutions, it could be observed that results differ. Mathematical learning views cognition in on the base on statistics and probability theory, graph…

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…

Downlink Error Rates of Half-duplex Users in Full-duplex Networks over a Laplacian Inter-User Interference Limited and EGK fading

KAUST Repository

Soury, Hamza; Elsawy, Hesham; Alouini, Mohamed-Slim

2017-01-01

This paper develops a mathematical framework to study downlink error rates and throughput for half-duplex (HD) terminals served by a full-duplex (FD) base station (BS). The developed model is used to motivate long term pairing for users that have

Think3d!: Improving mathematics learning through embodied spatial training.

Science.gov (United States)

Burte, Heather; Gardony, Aaron L; Hutton, Allyson; Taylor, Holly A

2017-01-01

Spatial thinking skills positively relate to Science, Technology, Engineering, and Math (STEM) outcomes, but spatial training is largely absent in elementary school. Elementary school is a time when children develop foundational cognitive skills that will support STEM learning throughout their education. Spatial thinking should be considered a foundational cognitive skill. The present research examined the impact of an embodied spatial training program on elementary students' spatial and mathematical thinking. Students in rural elementary schools completed spatial and math assessments prior to and after participating in an origami and pop-up paper engineering-based program, called Think3d!. Think3d! uses embodied tasks, such as folding and cutting paper, to train two-dimensional to three-dimensional spatial thinking. Analyses explored spatial thinking gains, mathematics gains - specifically for problem types expected to show gains from spatial training - and factors predicting mathematics gains. Results showed spatial thinking gains in two assessments. Using a math categorization to target problems more and less likely to be impacted by spatial training, we found that all students improved on real-world math problems and older students improved on visual and spatial math problems. Further, the results are suggestive of developmental time points for implementing embodied spatial training related to applying spatial thinking to math. Finally, the spatial thinking assessment that was most highly related to training activities also predicted math performance gains. Future research should explore developmental issues related to how embodied spatial training might support STEM learning and outcomes.

The changing role of continuity and discontinuity in the history of philosophy and mathematics

Directory of Open Access Journals (Sweden)

Danie F.M. Strauss

2017-01-01

Full Text Available The aim of this article is to highlight the inevitability of employing discreteness and continuity as primitive (indefinable modes of explanation in the history of philosophy and mathematics. It embodies the general challenge to account for the coherence of what is unique. Gödel emphasises the coherence of ‘primitive concepts’. Greek philosophy already discovered the spatial whole and/or parts relation with its infinite divisibility. During and after the medieval era philosophers toggled between an atomistic appreciation of the continuum and its opposite, for example found in the thought of Leibniz who postulated his law of continuity (lex continui. The discovery of incommensurability (irrational numbers by the Greeks caused the first foundational crisis of mathematics, as well as its geometrisation. Leibniz and Newton did not resolve the problems surrounding the limit concept and soon it induced the third foundational crisis of mathematics. It caused Frege and the ‘continuum theoreticians’ to assign priority to the continuum – discreteness is a catastrophe. Recently Smooth Infinitesimal Analysis appreciated what is ‘continuous’ as constituting ‘an unbroken or uninterrupted whole’. Intuitionistic mathematics once more proceeded from an emphasis on the whole and/or parts relation. In spite of alternating attempts to understand continuity exclusively, either in arithmetical or in spatial terms, the history of philosophy and mathematics undeniably confirms that the co-conditioning role of these two modes of explanation remains a constant element in reflections on continuity and discontinuity. (The role of continuity and discontinuity within the disciplines of physics and biology will be discussed in a separate article.

Foundations of Total Functional Data-Flow Programming

Directory of Open Access Journals (Sweden)

Baltasar Trancón y Widemann

2014-06-01

Full Text Available The field of declarative stream programming (discrete time, clocked synchronous, modular, data-centric is divided between the data-flow graph paradigm favored by domain experts, and the functional reactive paradigm favored by academics. In this paper, we describe the foundations of a framework for unifying functional and data-flow styles that differs from FRP proper in significant ways: It is based on set theory to match the expectations of domain experts, and the two paradigms are reduced symmetrically to a low-level middle ground, with strongly compositional semantics. The design of the framework is derived from mathematical first principles, in particular coalgebraic coinduction and a standard relational model of stateful computation. The abstract syntax and semantics introduced here constitute the full core of a novel stream programming language.

Foreword to the Special Focus on Mathematics, Data and Knowledge

KAUST Repository

Chen, Xiaoyu

2013-12-01

There is a growing interest in applying mathematical theories and methods from topology, computational geometry, differential equations, fluid dynamics, quantum statistics, etc. to describe and to analyze scientific regularities of diverse, massive, complex, nonlinear, and fast changing data accumulated continuously around the world and in discovering and revealing valid, insightful, and valuable knowledge that data imply. With increasingly solid mathematical foundations, various methods and techniques have been studied and developed for data mining, modeling, and processing, and knowledge representation, organization, and verification; different systems and mechanisms have been designed to perform data-intensive tasks in many application fields for classification, predication, recommendation, ranking, filtering, etc. This special focus of Mathematics in Computer Science is organized to stimulate original research on the interaction of mathematics with data and knowledge, in particular the exploration of new mathematical theories and methodologies for data modeling and analysis and knowledge discovery and management, the study of mathematical models of big data and complex knowledge, and the development of novel solutions and strategies to enhance the performance of existing systems and mechanisms for data and knowledge processing. The present foreword provides a short review of some key ideas and techniques on how mathematics interacts with data and knowledge, together with a few selected research directions and problems and a brief introduction to the four papers published in the focus. © 2013 Springer Basel.

ABIM Foundation

Science.gov (United States)

... In conjunction with the… mailchi.mp View on Facebook ABIM Foundation shared Business Radio Powered by The Wharton School's post. 2 days ago View on Facebook ABIM Foundation 2 days ago The Android version ...

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...

Mathematical models of physics problems (physics research and technology)

CERN Document Server

Anchordoqui, Luis Alfredo

2013-01-01

This textbook is intended to provide a foundation for a one-semester introductory course on the advanced mathematical methods that form the cornerstones of the hard sciences and engineering. The work is suitable for first year graduate or advanced undergraduate students in the fields of Physics, Astronomy and Engineering. This text therefore employs a condensed narrative sufficient to prepare graduate and advanced undergraduate students for the level of mathematics expected in more advanced graduate physics courses, without too much exposition on related but non-essential material. In contrast to the two semesters traditionally devoted to mathematical methods for physicists, the material in this book has been quite distilled, making it a suitable guide for a one-semester course. The assumption is that the student, once versed in the fundamentals, can master more esoteric aspects of these topics on his or her own if and when the need arises during the course of conducting research. The book focuses on two cor...

The mathematics of medical imaging a beginner’s guide

CERN Document Server

Feeman, Timothy G

2015-01-01

The basic mathematics of computerized tomography, the CT scan, are aptly presented for an audience of undergraduates in mathematics and engineering. Assuming no prior background in advanced mathematical analysis, topics such as the Fourier transform, sampling, and discrete approximation algorithms are introduced from scratch and are developed within the context of medical imaging. A chapter on magnetic resonance imaging focuses on manipulation of the Bloch equation, the system of differential equations that is the foundation of this important technology. Extending the ideas of the acclaimed first edition, new material has been added to render an even more accessible textbook for course usage. This edition includes new discussions of the Radon transform, the Dirac delta function and its role in X-ray imaging, Kacmarz’s method and least squares approximation, spectral filtering,  and more.  Copious examples and exercises, several new computer-based exercises, and additional graphics have been added to fur...

6th International School of Mathematical Physics "Ettore Majorana"

CERN Document Server

Wightman, Arthur Strong

1986-01-01

The sixth Ettore Majorana International School of Mathematical Physics was held at the Centro della Cultura Scientifica Erice, Sicily, 1-14 July 1985. The present volume collects lecture notes on the ses­ sion which was devoted to Fundamental Problems of Gauge Field Theory. The School was a NATO Advanced Study Institute sponsored by the Italian Ministry of Public Education, the Italian Ministry of Scientific and Technological Research and the Regional Sicilian Government. As a result of the experimental and theoretical developments of the last two decades, gauge field theory, in one form or another, now pro­ vides the standard language for the description of Nature; QCD and the standard model of the electroweak interactions illustrate this point. It is a basic task of mathematical physics to provide a solid foundation for these developments by putting the theory in a physically transparent and mathematically rigorous form. The lectures and seminars of the school concentrated on the many unsolved pro...

The mathematical career of Pierre de Fermat 1601-1665

CERN Document Server

Mahoney, Michael Sean

1994-01-01

Hailed as one of the greatest mathematical results of the twentieth century, the recent proof of Fermat's Last Theorem by Andrew Wiles brought to public attention the enigmatic problem-solver Pierre de Fermat, who centuries ago stated his famous conjecture in a margin of a book, writing that he did not have enough room to show his "truly marvelous demonstration" Along with formulating this proposition-xn+yn=zn has no rational solution for n > 2-Fermat, an inventor of analytic geometry, also laid the foundations of differential and integral calculus, established, together with Pascal, the conceptual guidelines of the theory of probability, and created modern number theory. In one of the first full-length investigations of Fermat's life and work, Michael Sean Mahoney provides rare insight into the mathematical genius of a hobbyist who never sought to publish his work, yet who ranked with his contemporaries Pascal and Descartes in shaping the course of modern mathematics.

Understanding Calculus beyond Computations: A Descriptive Study of the Parallel Meanings and Expectations of Teachers and Users of Calculus

Science.gov (United States)

Ferguson, Leann J.

2012-01-01

Calculus is an important tool for building mathematical models of the world around us and is thus used in a variety of disciplines, such as physics and engineering. These disciplines rely on calculus courses to provide the mathematical foundation needed for success in their courses. Unfortunately, due to the basal conceptions of what it means to…

Examining Calculator Use among Students with and without Disabilities Educated with Different Mathematical Curricula

Science.gov (United States)

Bouck, Emily C.; Joshi, Gauri S.; Johnson, Linley

2013-01-01

This study assessed if students with and without disabilities used calculators (fourfunction, scientific, or graphing) to solve mathematics assessment problems and whether using calculators improved their performance. Participants were sixth and seventh-grade students educated with either National Science Foundation (NSF)-funded or traditional…

Oscillations of a Beam on a Non-Linear Elastic Foundation under Periodic Loads

Directory of Open Access Journals (Sweden)

Donald Mark Santee

2006-01-01

Full Text Available The complexity of the response of a beam resting on a nonlinear elastic foundation makes the design of this structural element rather challenging. Particularly because, apparently, there is no algebraic relation for its load bearing capacity as a function of the problem parameters. Such an algebraic relation would be desirable for design purposes. Our aim is to obtain this relation explicitly. Initially, a mathematical model of a flexible beam resting on a non-linear elastic foundation is presented, and its non-linear vibrations and instabilities are investigated using several numerical methods. At a second stage, a parametric study is carried out, using analytical and semi-analytical perturbation methods. So, the influence of the various physical and geometrical parameters of the mathematical model on the non-linear response of the beam is evaluated, in particular, the relation between the natural frequency and the vibration amplitude and the first period doubling and saddle-node bifurcations. These two instability phenomena are the two basic mechanisms associated with the loss of stability of the beam. Finally Melnikov's method is used to determine an algebraic expression for the boundary that separates a safe from an unsafe region in the force parameters space. It is shown that this can be used as a basis for a reliable engineering design criterion.

Mathematics textbooks and their use in English, French and German classrooms : a way to understand teaching and learning cultures

NARCIS (Netherlands)

Pepin, B.; Haggarty, L.

2001-01-01

After a through review of the relevant literature in terms of textbook analysis and mathematics teachers' user of textbooks in school contexts, this paper reports on selected and early findings from a study of mathematics textbooks and their use in English, French and German mathematics classrooms

The Implementation and Effects of the Mathematics Design Collaborative (MDC): Early Findings from Kentucky Ninth-Grade Algebra 1 Courses. CRESST Report 845

Science.gov (United States)

Herman, Joan L.; Matrundola, Deborah La Torre; Epstein, Scott; Leon, Seth; Dai, Yunyun; Reber, Sarah; Choi, Kilchan

2015-01-01

With support from the Bill and Melinda Gates Foundation, researchers and experts in mathematics education developed the Mathematics Design Collaborative (MDC) as a strategy to support the transition to Common Core State Standards in math. MDC provides short formative assessment lessons known as Classroom Challenges for use in middle and high…

IT Department User Survey Engineering Tools Usage Report

CERN Document Server

Jones, Pete

2017-01-01

Engineering tools are supports by the IT-CDA-AD section and these include Electronic, Mechanical, Mathematical and Field Solver tools. The survey carried out by IT-CDA during 2016 asked CERN users questions concerning their working environments, habits and preferences and also included several question pertaining to the use of engineering tools. This analysis will help IT-CDA to better understand who is using these tools, the user requirements and their problems and so help us to improve the service.

Contributions of executive function and spatial skills to preschool mathematics achievement.

Science.gov (United States)

Verdine, Brian N; Irwin, Casey M; Golinkoff, Roberta Michnick; Hirsh-Pasek, Kathryn

2014-10-01

Early mathematics achievement is highly predictive of later mathematics performance. Here we investigated the influence of executive function (EF) and spatial skills, two generalizable skills often overlooked in mathematics curricula, on mathematics performance in preschoolers. Children (N=44) of varying socioeconomic status (SES) levels were assessed at 3 years of age on a new assessment of spatial skill (Test of Spatial Assembly, TOSA) and a vocabulary measure (Peabody Picture Vocabulary Test, PPVT). The same children were tested at 4 years of age on the Beery Test of Visual-Motor Integration (VMI) as well as on measures of EF and mathematics. The TOSA was created specifically as an assessment for 3-year-olds, allowing the investigation of links among spatial, EF, and mathematical skills earlier than previously possible. Results of a hierarchical regression indicate that EF and spatial skills predict 70% of the variance in mathematics performance without an explicit math test, EF is an important predictor of math performance as prior research suggested, and spatial skills uniquely predict 27% of the variance in mathematics skills. Additional research is needed to understand whether EF is truly malleable and whether EF and spatial skills may be leveraged to support early mathematics skills, especially for lower SES children who are already falling behind in these skill areas by 3 and 4 years of age. These findings indicate that both skills are part of an important foundation for mathematics performance and may represent pathways for improving school readiness for mathematics. Copyright © 2014 Elsevier Inc. All rights reserved.

The foundations of chaos revisited from Poincaré to recent advancements

CERN Document Server

2016-01-01

With contributions from a number of pioneering researchers in the field, this collection is aimed not only at researchers and scientists in nonlinear dynamics but also at a broader audience interested in understanding and exploring how modern chaos theory has developed since the days of Poincaré. This book was motivated by and is an outcome of the CHAOS 2015 meeting held at the Henri Poincaré Institute in Paris, which provided a perfect opportunity to gain inspiration and discuss new perspectives on the history, development and modern aspects of chaos theory. Henri Poincaré is remembered as a great mind in mathematics, physics and astronomy. His works, well beyond their rigorous mathematical and analytical style, are known for their deep insights into science and research in general, and the philosophy of science in particular. The Poincaré conjecture (only proved in 2006) along with his work on the three-body problem are considered to be the foundation of modern chaos theory.

Renewing U.S. mathematics: A plan for the 1990s

Energy Technology Data Exchange (ETDEWEB)

NONE

1990-12-31

In 1981 a committee of the National Research Council was formed to investigate the health of the mathematical sciences in the US. Its 1984 report, Renewing US Mathematics: Critical Resource for the future found that although the field was thriving intellectually, government support had deteriorated to a dangerously low level. Moreover, the number of young people entering the mathematical sciences had decreased to a level inadequate to replenish the field. The 1984 Report recommended a plan for renewal, the National Plan for Graduate and Postdoctoral Education in the Mathematical Sciences. That plan`s essential feature was a call for funding to bring support for the mathematical sciences into balance with support for the physical sciences and engineering. The interdisciplinary committee that wrote the 1984 Report quickly realized that the low level of research support for US mathematical sciences was so severe that it threatened the vitality of the entire scientific enterprise. As requested by the National Science Foundation (NSF) and the Interagency Committee for Extramural Mathematics Programs (ICEMAP), this report updates the 1984 Report. Specifically, the charge directed the committee to (1) update that report, describing the infrastructure and support for US mathematical sciences research; (2) assess trends and progress over the intervening five years against the recommendations of the 1984 Report; (3) briefly assess the field scientifically and identify significant opportunities for research, including cross-disciplinary collaboration; and (4) make appropriate recommendations designed to ensure that US mathematical sciences research will meet national needs in coming years.

Foundation Structure

DEFF Research Database (Denmark)

2009-01-01

Method of installing a bucket foundation structure comprising one, two, three or more skirts, into soils in a controlled manner. The method comprises two stages: a first stage being a design phase and the second stage being an installation phase. In the first stage, design parameters are determined...... relating to the loads on the finished foundation structure; soil profile on the location; allowable installation tolerances, which parameters are used to estimate the minimum diameter and length of the skirts of the bucket. The bucket size is used to simulate load situations and penetration into foundation...

A Quantum Private Query Protocol for Enhancing both User and Database Privacy

Science.gov (United States)

Zhou, Yi-Hua; Bai, Xue-Wei; Li, Lei-Lei; Shi, Wei-Min; Yang, Yu-Guang

2018-01-01

In order to protect the privacy of query user and database, some QKD-based quantum private query (QPQ) protocols were proposed. Unfortunately some of them cannot resist internal attack from database perfectly; some others can ensure better user privacy but require a reduction of database privacy. In this paper, a novel two-way QPQ protocol is proposed to ensure the privacy of both sides of communication. In our protocol, user makes initial quantum states and derives the key bit by comparing initial quantum state and outcome state returned from database by ctrl or shift mode instead of announcing two non-orthogonal qubits as others which may leak part secret information. In this way, not only the privacy of database be ensured but also user privacy is strengthened. Furthermore, our protocol can also realize the security of loss-tolerance, cheat-sensitive, and resisting JM attack etc. Supported by National Natural Science Foundation of China under Grant Nos. U1636106, 61572053, 61472048, 61602019, 61502016; Beijing Natural Science Foundation under Grant Nos. 4152038, 4162005; Basic Research Fund of Beijing University of Technology (No. X4007999201501); The Scientific Research Common Program of Beijing Municipal Commission of Education under Grant No. KM201510005016

Mathematical aspects of quantum field theories

CERN Document Server

Strobl, Thomas

2015-01-01

Despite its long history and stunning experimental successes, the mathematical foundation of perturbative quantum field theory is still a subject of ongoing research. This book aims at presenting some of the most recent advances in the field, and at reflecting the diversity of approaches and tools invented and currently employed. Both leading experts and comparative newcomers to the field present their latest findings, helping readers to gain a better understanding of not only quantum but also classical field theories. Though the book offers a valuable resource for mathematicians and physicists alike, the focus is more on mathematical developments. This volume consists of four parts: The first Part covers local aspects of perturbative quantum field theory, with an emphasis on the axiomatization of the algebra behind the operator product expansion. The second Part highlights Chern-Simons gauge theories, while the third examines (semi-)classical field theories. In closing, Part 4 addresses factorization homolo...

Linear programming mathematics, theory and algorithms

CERN Document Server

1996-01-01

Linear Programming provides an in-depth look at simplex based as well as the more recent interior point techniques for solving linear programming problems. Starting with a review of the mathematical underpinnings of these approaches, the text provides details of the primal and dual simplex methods with the primal-dual, composite, and steepest edge simplex algorithms. This then is followed by a discussion of interior point techniques, including projective and affine potential reduction, primal and dual affine scaling, and path following algorithms. Also covered is the theory and solution of the linear complementarity problem using both the complementary pivot algorithm and interior point routines. A feature of the book is its early and extensive development and use of duality theory. Audience: The book is written for students in the areas of mathematics, economics, engineering and management science, and professionals who need a sound foundation in the important and dynamic discipline of linear programming.

User book of SPAD software

International Nuclear Information System (INIS)

Eschylle, R.

1987-01-01

Data-gathering and accumulation is swelling in any domain thanks to computer science. A data analysis is aimed at extraction of useful data easily readable for the user. Among the mathematical methods used three of them are developed in the Spad software: - principal component analysis, - factorial analysis of simple correspondence, - factorial analysis of multiple correspondence. Data tables are first defined in this paper together with terms used by statisticians. Then the user manual describes the six analysis steps (or modules) included in the program, the links of steps which give classical data analysis. At last, for each step an ''using notice'' is given which describes the step parameters after some comments on the step object [fr

The big-fish-little-pond effect on mathematics self-concept: Evidence from the United Arab Emirates.

Science.gov (United States)

Areepattamannil, Shaljan; Khine, Myint Swe; Al Nuaimi, Samira

2017-08-01

This study examined the big-fish-little-pond effect (BFLPE; Marsh, 1987) on mathematics self-concept of 7404 adolescents (female = 3767 [51%], male = 3637 [49%]; M age  = 15.85 years, SD = 0.28) from 456 schools in the United Arab Emirates, one of the Arab states of the Persian Gulf. The results of multilevel regression analyses indicated good support for the BFLPE's theoretical predictions: the effect of individual student mathematics achievement on individual student mathematics self-concept was positive and statistically significant, whereas the effect of school-average mathematics achievement on individual student mathematics self-concept was negative and statistically significant. Moreover, the interaction between school-average mathematics achievement and individual student mathematics achievement was small and non-significant. Implications of the findings for policy and practice are briefly discussed. Copyright © 2017 The Foundation for Professionals in Services for Adolescents. Published by Elsevier Ltd. All rights reserved.

Mathematical models in marketing a collection of abstracts

CERN Document Server

Funke, Ursula H

1976-01-01

Mathematical models can be classified in a number of ways, e.g., static and dynamic; deterministic and stochastic; linear and nonlinear; individual and aggregate; descriptive, predictive, and normative; according to the mathematical technique applied or according to the problem area in which they are used. In marketing, the level of sophistication of the mathe­ matical models varies considerably, so that a nurnber of models will be meaningful to a marketing specialist without an extensive mathematical background. To make it easier for the nontechnical user we have chosen to classify the models included in this collection according to the major marketing problem areas in which they are applied. Since the emphasis lies on mathematical models, we shall not as a rule present statistical models, flow chart models, computer models, or the empirical testing aspects of these theories. We have also excluded competitive bidding, inventory and transportation models since these areas do not form the core of ·the market...

Environmental Foundations in Germany

Directory of Open Access Journals (Sweden)

Thomas Krikser

2015-05-01

Full Text Available Foundations in Germany were examined in the context of environmental issues. Data from environmental foundations show that there is huge difference between private and public foundations concerning financial settings. Furthermore, environment is often not the only objective and sometimes not even processed. Our analysis shows that there are different types of foundations with regard to environmental scopes and activities. Although “attractive topics” such as biodiversity and landscape conservation seem to be more important to foundations, less visible topics such as pollution prevention remain merely a “blind spot.” Together, these findings suggest that there is only a limited potential of private foundations compared with public foundations. Nevertheless, there might be an impact on environmental awareness and local sustainability.

Computer Agent's Role in Modeling an Online Math Help User

OpenAIRE

Dragana Martinovic

2007-01-01

This paper investigates perspectives of deployments of open learner model on mathematics online help sites. It proposes enhancing a regular human-to-human interaction with an involvement of a computer agent suitable for tracking users, checking their input and making useful suggestions. Such a design would provide the most support for the interlocutors while keeping the nature of existing environment intact. Special considerations are given to peer-to-peer and expert-to-student mathematics on...

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.

A New Kind of Aesthetics —The Mathematical Structure of the Aesthetic

Directory of Open Access Journals (Sweden)

Akihiro Kubota

2017-06-01

Full Text Available This paper proposes a new approach to the investigation into aesthetics. Specifically, it~argues that it is possible to explain the aesthetic and its underlying dynamic relations with an~axiomatic structure (the octahedral axiom-derived category based on contemporary mathematics (namely category theory, and through this argument suggests the possibility for discussion about the mathematical structure of the aesthetic. If there were a way to describe the structure of the aesthetic with the language of mathematical structures and mathematical axioms---a~language completely devoid of arbitrariness---then we would make possible a universal argument about the essential human activity of ``the aesthetic'', and we would also gain a new method and viewpoint into the philosophy and meaning of the act of creating a work of art and artistic activities. This paper presents one mathematical structure as a foundation in constructing the science of dynamic aesthetics based on axiomatic functionalism, which is in turn based on a new interdisciplinary investigation into the generative structure of the aesthetic.

Mathematics and culture in Micronesia

Directory of Open Access Journals (Sweden)

A. J. (Sandy Dawson

2015-07-01

Full Text Available Wheatley and Frieze‟s book, Walk Out Walk On, provides the conceptual framework for an examination of Project MACIMISE, a National Science Foundation funded project that focused on the languages and cultural practices of nine Pacific islands and the state of Hawai„i. MACIMISE, pronounced as if spelled „maximize‟, is a 5-year Project. The Project‟s task is the development of elementary school mathematics curriculum units sensitive to local mathematical thought and experience. There were twenty-one participants (who call themselves the Macimisers in the Project. The participants were educated in ethnographic and anthropological research strategies to enable them to retrieve/uncover cultural practices extant in the communities where they lived. This academics work was accomplished partially via distance learning when the participants were registered in advanced degree programs at the University of Hawai„i—Mānoa. In this paper, the Project is analyzed in terms of the concepts (scaling across, start anywhere—follow it everywhere, intervention to friendship, the art of hosting and the use of circle advanced by Wheatley and Frieze.

Groups - Modular Mathematics Series

CERN Document Server

Jordan, David

1994-01-01

This text provides an introduction to group theory with an emphasis on clear examples. The authors present groups as naturally occurring structures arising from symmetry in geometrical figures and other mathematical objects. Written in a 'user-friendly' style, where new ideas are always motivated before being fully introduced, the text will help readers to gain confidence and skill in handling group theory notation before progressing on to applying it in complex situations. An ideal companion to any first or second year course on the topic.

Mathematical models of granular matter

CERN Document Server

Mariano, Paolo; Giovine, Pasquale

2008-01-01

Granular matter displays a variety of peculiarities that distinguish it from other appearances studied in condensed matter physics and renders its overall mathematical modelling somewhat arduous. Prominent directions in the modelling granular flows are analyzed from various points of view. Foundational issues, numerical schemes and experimental results are discussed. The volume furnishes a rather complete overview of the current research trends in the mechanics of granular matter. Various chapters introduce the reader to different points of view and related techniques. New models describing granular bodies as complex bodies are presented. Results on the analysis of the inelastic Boltzmann equations are collected in different chapters. Gallavotti-Cohen symmetry is also discussed.

Documentation and user's guide for DOSTOMAN: a pathways computer model of radionuclide movement

International Nuclear Information System (INIS)

Root, R.W. Jr.

1980-01-01

This report documents the mathematical development and the computer implementation of the Savannah River Laboratory computer code used to simulate radonuclide movement in the environment. The user's guide provides all the necessary information for the prospective user to input the required data, execute the computer program, and display the results

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...

HSC Foundation

Science.gov (United States)

... in disability information or services and that add value to our existing programs. The Foundation also works to bring additional support to initiatives by serving as funding partners on projects that have local impact and national relevance. Supporting a Continuum of Care The HSC Foundation ...

Mathematical gauge theory with applications to the standard model of particle physics

CERN Document Server

Hamilton, Mark J D

2017-01-01

The Standard Model is the foundation of modern particle and high energy physics. This book explains the mathematical background behind the Standard Model, translating ideas from physics into a mathematical language and vice versa. The first part of the book covers the mathematical theory of Lie groups and Lie algebras, fibre bundles, connections, curvature and spinors. The second part then gives a detailed exposition of how these concepts are applied in physics, concerning topics such as the Lagrangians of gauge and matter fields, spontaneous symmetry breaking, the Higgs boson and mass generation of gauge bosons and fermions. The book also contains a chapter on advanced and modern topics in particle physics, such as neutrino masses, CP violation and Grand Unification. This carefully written textbook is aimed at graduate students of mathematics and physics. It contains numerous examples and more than 150 exercises, making it suitable for self-study and use alongside lecture courses. Only a basic knowledge of d...

Interactive data visualization foundations, techniques, and applications

CERN Document Server

Ward, Matthew; Keim, Daniel

2010-01-01

Visualization is the process of representing data, information, and knowledge in a visual form to support the tasks of exploration, confirmation, presentation, and understanding. This book is designed as a textbook for students, researchers, analysts, professionals, and designers of visualization techniques, tools, and systems. It covers the full spectrum of the field, including mathematical and analytical aspects, ranging from its foundations to human visual perception; from coded algorithms for different types of data, information and tasks to the design and evaluation of new visualization techniques. Sample programs are provided as starting points for building one's own visualization tools. Numerous data sets have been made available that highlight different application areas and allow readers to evaluate the strengths and weaknesses of different visualization methods. Exercises, programming projects, and related readings are given for each chapter. The book concludes with an examination of several existin...

EQUIVOCATION IN THE FOUNDATIONS OF LEIBNIZ’S INFINITESIMAL FICTIONS

Directory of Open Access Journals (Sweden)

Tzuchien THO

2012-11-01

Full Text Available In this article, I address two different kinds of equivocations in reading Leibniz’s fictional infinite and infinitesimal. These equivocations form the background of a reductive reading of infinite and infinitesimal fictions either as ultimately finite or as something whose status can be taken together with any other mathematical object as such. The first equivocation is the association of a foundation of infinitesimals with their ontological status. I analyze this equivocation by criticizing the logicist influence on 20th century Anglophone reception of the syncategorematical infinite and infinitesimal. The second equivocation is the association of the rigor of mathematical demonstration with the problem of the admissibility of infinite or infinitesimal terms. I analyze this by looking at Leibniz’s constructive method and apagogic argument style in his quadrature method. In treating these equivocations, I critique some assumptions that underlie the reductive reading of Leibniz’s fictionalism concerning infinite and infinitesimals. In turn, I suggest that these infinitesimal “fictions” pointed to a problematic within Leibniz’s work that was conceived and reconsidered in Leibniz’s work from a range of different contexts and methods.Keywords: Leibniz, differential calculu

Applying mathematical finance tools to the competitive Nordic electricity market

OpenAIRE

Vehviläinen, Iivo

2004-01-01

This thesis models competitive electricity markets using the methods of mathematical finance. Fundamental problems of finance are market price modelling, derivative pricing, and optimal portfolio selection. The same questions arise in competitive electricity markets. The thesis presents an electricity spot price model based on the fundamental stochastic factors that affect electricity prices. The resulting price model has sound economic foundations, is able to explain spot market price mo...

A Handbook of Essential Mathematical Formulae

CERN Document Server

Davies, Alan

2005-01-01

Intended for students of mathematics as well as of engineering, physical science, economics, business studies, and computer science, this handbook contains vital information and formulas for algebra, geometry, calculus, numerical methods, and statistics. Comprehensive tables of standard derivatives and integrals, together with the tables of Laplace, Fourier, and Z transforms are included. A spiral binding that allows the handbook to lay flat for easy reference enhances the user-friendly design.

The Intention to Use GeoGebra in the Teaching of Mathematics among Malaysian Teachers

Science.gov (United States)

Belgheis, Soheila; Kamalludeen, Rosemaliza

2018-01-01

This quantitative study examined Malaysian teachers' perception towards using GeoGebra in mathematics teaching. The relationship between teachers' Perceived Current Competencies (PCC) of GeoGebra, and Intention to Use (IU) it as well as the difference between male and female teachers and between users and non-users of GeoGebra were investigated.…

Tensor Arithmetic, Geometric and Mathematic Principles of Fluid Mechanics in Implementation of Direct Computational Experiments

Directory of Open Access Journals (Sweden)

Bogdanov Alexander

2016-01-01

Full Text Available The architecture of a digital computing system determines the technical foundation of a unified mathematical language for exact arithmetic-logical description of phenomena and laws of continuum mechanics for applications in fluid mechanics and theoretical physics. The deep parallelization of the computing processes results in functional programming at a new technological level, providing traceability of the computing processes with automatic application of multiscale hybrid circuits and adaptive mathematical models for the true reproduction of the fundamental laws of physics and continuum mechanics.

Information literacy of the academic library users

Directory of Open Access Journals (Sweden)

Sanda Hasenay

2016-03-01

Full Text Available Information literacy should be a foundation of any educational system, which would enable students and library users a more efficient way to perform academically and in everyday life. The research goal was to determine the level of information literacy among the students, users of the Library of Faculty of Food and Technology Osijek (PTFOS. A special survey – quiz was used to determine students’ knowledge of library collection and services. The sample of 115 students was surveyed between 16th and 27th of February 2015. The library users are aware of the conditions of using the library collections as well as library services, but they don't read messages on the library's bulletin board, desks and web site. The research results will be used as guidelines for improving information literacy and future research.

Mathematical Formula Search using Natural Language Queries

Directory of Open Access Journals (Sweden)

YANG, S.

2014-11-01

Full Text Available This paper presents how to search mathematical formulae written in MathML when given plain words as a query. Since the proposed method allows natural language queries like the traditional Information Retrieval for the mathematical formula search, users do not need to enter any complicated math symbols and to use any formula input tool. For this, formula data is converted into plain texts, and features are extracted from the converted texts. In our experiments, we achieve an outstanding performance, a MRR of 0.659. In addition, we introduce how to utilize formula classification for formula search. By using class information, we finally achieve an improved performance, a MRR of 0.690.

Mathematics Education for Engineering Technology Students – A Bridge Too Far?

Directory of Open Access Journals (Sweden)

Noraishiyah Abdullah

2013-03-01

Full Text Available Trying to decide what is best suited for someone or something is an ever enduring task let alone trying to prepare students with the right engineering mind. So ‘how do you build an engineer?’ if that is the right word. What is the right ingredient? Mathematics has been said as the most important foundation in engineers’ life. Curriculum has been developed and reviewed over the years to meet this target. This work explores how much or lack of it has the curriculum prepares the future technologist to face the world of engineering technology as far as mathematics is concerned. Analysis of mathematics lectures, interviews of engineering technologist students and engineering technology subject lecturer is undertaken. Understand what each contributes help in understanding the picture that the current education is painting. Based on the theory of learning, APOS theory helps in explaining how students bridge their knowledge of mathematics when it comes to solving engineering technology problems. The question is, is it a bridge too far? 

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…

Communicating Mathematics on the Internet: Synchronous and Asynchronous Tools

Science.gov (United States)

Hodges, Charles B.; Hunger, Gail M.

2011-01-01

Communicating and collaborating online are becoming common requirements in education. The specialized notations and symbols necessary for some content areas where mathematical expressions are part of the conversation require that users select appropriate communication tools. The purpose of this article is to describe tools that can be used for…

Building a Community of Scholars: One University's Story of Students Engaged in Learning Science, Mathematics, and Engineering through a NSF S-STEM Grant--Part II

Science.gov (United States)

Kalevitch, Maria; Maurer, Cheryl; Badger, Paul; Holdan, Greg; Sirinterlikci, Arif

2015-01-01

The School of Engineering, Mathematics, and Science (SEMS) at Robert Morris University (RMU) was awarded a five-year grant from the National Science Foundation (NSF) to fund scholarships to 21 academically talented but financially challenged students majoring in the disciplines of science, technology, engineering, and mathematics (STEM). Each…

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

Role of cognitive theory in the study of learning disability in mathematics.

Science.gov (United States)

Geary, David C

2005-01-01

Gersten, Jordan, and Flojo (in this issue) provide the beginnings of an essential bridge between basic research on mathematical disabilities (MD) in young children and the application of this research for the early identification and remediation of these forms of learning disability. As they acknowledge, the field of MD is in the early stages of development, and thus recommendations regarding identification measures and remedial techniques must be considered preliminary. I discuss the importance of maintaining a tight link between theoretical and empirical research on children's developing numerical, arithmetical, and mathematical competencies and future research on learning disabilities in mathematics. This link will provide the foundation for transforming experimental procedures into assessment measures, understanding the cognitive strengths and weaknesses of children with these forms of learning disability, and developing remedial approaches based on the pattern of cognitive strengths and weaknesses for individual children.

Using mathematical software to design power electronic converters

Science.gov (United States)

Hinov, Nikolay; Hranov, Tsveti

2017-12-01

In the paper is presented mathematical software, which was used for design of power electronic devices. Examined to different example, which are applied to designing electronic converters. In this way, it is possible to play different combinations of the circuit elements by simple means, thus optimizing according to certain criteria and limitations. Free software with a simple and intuitive interface is selected. No special user training is required to work with it and no further training is required. The use of mathematical software greatly facilitates the design, assists and makes it attractive and accessible to a wider range of students and specialists in power electronics training.

HTGR Application Economic Model Users' Manual

International Nuclear Information System (INIS)

Gandrik, A.M.

2012-01-01

The High Temperature Gas-Cooled Reactor (HTGR) Application Economic Model was developed at the Idaho National Laboratory for the Next Generation Nuclear Plant Project. The HTGR Application Economic Model calculates either the required selling price of power and/or heat for a given internal rate of return (IRR) or the IRR for power and/or heat being sold at the market price. The user can generate these economic results for a range of reactor outlet temperatures; with and without power cycles, including either a Brayton or Rankine cycle; for the demonstration plant, first of a kind, or nth of a kind project phases; for up to 16 reactor modules; and for module ratings of 200, 350, or 600 MWt. This users manual contains the mathematical models and operating instructions for the HTGR Application Economic Model. Instructions, screenshots, and examples are provided to guide the user through the HTGR Application Economic Model. This model was designed for users who are familiar with the HTGR design and Excel and engineering economics. Modification of the HTGR Application Economic Model should only be performed by users familiar with the HTGR and its applications, Excel, and Visual Basic.

Mesothelioma Applied Research Foundation

Science.gov (United States)

... Foundation Experts Can Answer Your Questions! The Mesothelioma Applied Research Foundation's team of experts is available to answer ... a law firm. Read more about the Mesothelioma Applied Research Foundation . TO GET HELP CALL: (877) End-Meso ...

Final Technical Report: Mathematical Foundations for Uncertainty Quantification in Materials Design

Energy Technology Data Exchange (ETDEWEB)

Plechac, Petr [Univ. of Delaware, Newark, DE (United States); Vlachos, Dionisios G. [Univ. of Delaware, Newark, DE (United States)

2018-01-23

We developed path-wise information theory-based and goal-oriented sensitivity analysis and parameter identification methods for complex high-dimensional dynamics and in particular of non-equilibrium extended molecular systems. The combination of these novel methodologies provided the first methods in the literature which are capable to handle UQ questions for stochastic complex systems with some or all of the following features: (a) multi-scale stochastic models such as (bio)chemical reaction networks, with a very large number of parameters, (b) spatially distributed systems such as Kinetic Monte Carlo or Langevin Dynamics, (c) non-equilibrium processes typically associated with coupled physico-chemical mechanisms, driven boundary conditions, hybrid micro-macro systems, etc. A particular computational challenge arises in simulations of multi-scale reaction networks and molecular systems. Mathematical techniques were applied to in silico prediction of novel materials with emphasis on the effect of microstructure on model uncertainty quantification (UQ). We outline acceleration methods to make calculations of real chemistry feasible followed by two complementary tasks on structure optimization and microstructure-induced UQ.

Combining fuzzy mathematics with fuzzy logic to solve business management problems

Science.gov (United States)

Vrba, Joseph A.

1993-12-01

Fuzzy logic technology has been applied to control problems with great success. Because of this, many observers fell that fuzzy logic is applicable only in the control arena. However, business management problems almost never deal with crisp values. Fuzzy systems technology--a combination of fuzzy logic, fuzzy mathematics and a graphical user interface--is a natural fit for developing software to assist in typical business activities such as planning, modeling and estimating. This presentation discusses how fuzzy logic systems can be extended through the application of fuzzy mathematics and the use of a graphical user interface to make the information contained in fuzzy numbers accessible to business managers. As demonstrated through examples from actual deployed systems, this fuzzy systems technology has been employed successfully to provide solutions to the complex real-world problems found in the business environment.

Use of reinforced soil foundation (RSF) to support shallow foundation.

Science.gov (United States)

2008-11-01

The main objective of this research study is to investigate potential benefits of using the reinforced soil foundations to improve the bearing capacity and to reduce the settlement of shallow foundations on soils. This includes examining influences o...

A foundation for foundation phase teacher education: Making wise educational judgements

Directory of Open Access Journals (Sweden)

Karin Murris

2014-12-01

Full Text Available We start our paper with a critical exploration of the current ‘back to basics’ approach in South African foundation phase teacher education with its emphasis on strengthening the teaching of subject knowledge. We claim that such a proposal first demands an answer to the question ‘what is foundational in foundation phase teaching?’ We propose an answer in three stages. First we argue that teacher education should be concerned not only with schooling or qualification (knowledge, skills and dispositions and socialisation, but, drawing on Gert Biesta’s work, also with subjectification (educating the person towards the ability to make wise educational judgements. Secondly, these three aims of education lead to five core principles, and we finish by showing how these principles inform our storied, thinking and multimodal/semiotic curriculum. Our answer to our leading question is that pedagogical ‘know-how’ and views of ‘child’ and ‘childhood’ constitute the subject knowledge that is foundational in the foundation phase curriculum.

Dealing with Maths Anxiety: How "Do" You Teach Mathematics in a Geography Department?

Science.gov (United States)

Chapman, Lee

2010-01-01

Mathematics is often taught covertly as a "service" subject in geography departments, but can often be a cause of fear for students who may not have studied the subject post-GCSE. Negative attitudes are common and many students show signs of maths anxiety. This paper details how students' attitudes were changed by a new foundation mathematics…

A Short History of the Science and Mathematics Education Centre at Curtin University

Science.gov (United States)

Treagust, David F.

2011-01-01

This article is presented in four parts. In the first part, I describe the foundation of the Science and Mathematics Education Centre (SMEC) at Curtin University. In the second part, I explain the development of SMEC's teaching and research capacity under its three directors. In the third section, I describe how federal government support of SMEC…

Foundations for renewables

Energy Technology Data Exchange (ETDEWEB)

Neidlein, H.C. [German Agency Scherer Schnell Walser und Partner (Germany)

2007-07-01

In Germany, 77 foundations promote renewable energy technology with around Euro 25 million annually. The most important internationally active foundations, however, can be found in the Anglo-Saxon countries. (orig.)

User Participation and Participatory Design: Topics in Computing Education.

Science.gov (United States)

Kautz, Karlheinz

1996-01-01

Discusses user participation and participatory design in the context of formal education for computing professionals. Topics include the current curriculum debate; mathematical- and engineering-based education; traditional system-development training; and an example of a course program that includes computers and society, and prototyping. (53…

Approximate numerical abilities and mathematics: Insight from correlational and experimental training studies.

Science.gov (United States)

Hyde, D C; Berteletti, I; Mou, Y

2016-01-01

Humans have the ability to nonverbally represent the approximate numerosity of sets of objects. The cognitive system that supports this ability, often referred to as the approximate number system (ANS), is present in early infancy and continues to develop in precision over the life span. It has been proposed that the ANS forms a foundation for uniquely human symbolic number and mathematics learning. Recent work has brought two types of evidence to bear on the relationship between the ANS and human mathematics: correlational studies showing individual differences in approximate numerical abilities correlate with individual differences in mathematics achievement and experimental studies showing enhancing effects of nonsymbolic approximate numerical training on exact, symbolic mathematical abilities. From this work, at least two accounts can be derived from these empirical data. It may be the case that the ANS and mathematics are related because the cognitive and brain processes responsible for representing numerical quantity in each format overlap, the Representational Overlap Hypothesis, or because of commonalities in the cognitive operations involved in mentally manipulating the representations of each format, the Operational Overlap hypothesis. The two hypotheses make distinct predictions for future work to test. © 2016 Elsevier B.V. All rights reserved.

I and C functional test facility user guide

International Nuclear Information System (INIS)

Kwon, Ki Chun

1996-07-01

The objective of I and C functional test facility (FTF) is to validate newly developed digital control and protection algorithm, alarm reduction algorithm and the function of operator support system and so on. Test facility is divided into three major parts; software, hardware and graphic user interface. Software consists of mathematical modeling which simulates 3 loop pressurizer water reactor, 993 MWe Westinghouse plant and supervisory module which interpret user instructions and data interface program. FTF is implemented in HP747I workstation using FORTRAN77 and ''C'' language under UNIX operating system. This User Guide provides file structure, instructions and program modification method and provides initial data, malfunction list, process variables list and simulation diagram as an appendix to test developed prototype. 12 figs. (Author)

I and C functional test facility user guide

Energy Technology Data Exchange (ETDEWEB)

Kwon, Ki Chun [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)

1996-07-01

The objective of I and C functional test facility (FTF) is to validate newly developed digital control and protection algorithm, alarm reduction algorithm and the function of operator support system and so on. Test facility is divided into three major parts; software, hardware and graphic user interface. Software consists of mathematical modeling which simulates 3 loop pressurizer water reactor, 993 MWe Westinghouse plant and supervisory module which interpret user instructions and data interface program. FTF is implemented in HP747I workstation using FORTRAN77 and ``C`` language under UNIX operating system. This User Guide provides file structure, instructions and program modification method and provides initial data, malfunction list, process variables list and simulation diagram as an appendix to test developed prototype. 12 figs. (Author).

THE CASE STUDY TASKS AS A BASIS FOR THE FUND OF THE ASSESSMENT TOOLS AT THE MATHEMATICAL ANALYSIS FOR THE DIRECTION 01.03.02 APPLIED MATHEMATICS AND COMPUTER SCIENCE

Directory of Open Access Journals (Sweden)

Dina Aleksandrovna Kirillova

2015-12-01

Full Text Available The modern reform of the Russian higher education involves the implementation of competence-based approach, the main idea of which is the practical orientation of education. Mathematics is a universal language of description, modeling and studies of phenomena and processes of different nature. Therefore creating the fund of assessment tools for mathematical disciplines based on the applied problems is actual. The case method is the most appropriate mean of monitoring the learning outcomes, it is aimed at bridging the gap between theory and practice.The aim of the research is the development of methodical materials for the creating the fund of assessment tools that are based on the case-study for the mathematical analisis for direction «Applied Mathematics and Computer Science». The aim follows from the contradiction between the need for the introduction of case-method in the educational process in high school and the lack of study of the theoretical foundations of using of this method as applied to mathematical disciplines, insufficient theoretical basis and the description of the process of creating case-problems for use their in the monitoring of the learning outcomes.

Interactive data manipulation program. FAWTEK user guide

International Nuclear Information System (INIS)

Boyer, W.B.; Sauer, S.

1980-02-01

This report describes the interactive data acquisition and manipulation program FAWTEK.'The program allows users of the electron beam data acquisition facility to control the R7912 digitizers and to perform a variety of mathematical operations on data arrays. Commands are entered in a high level language via a Tektronix 4010 terminal console. Each command directive and associated parameters is described in detail

Static Behaviour of Bucket Foundations

DEFF Research Database (Denmark)

Larsen, Kim André

One new foundation concept in relation to offshore wind turbines is bucket foundations. The concept is known from the oil and gas industry, though the load conditions here are significantly different. The bucket foundation can be used as monopod or e.g. tripod foundations for offshore wind turbines....... The monopod concept is investigated in this thesis, regarding the static behaviour from loads relevant to offshore wind turbines. The main issue in this concept is the rotational stiffness of the foundation and the combined capacity dominated by moments. The vertical bearing capacity of bucket foundations...... theory is proposed. The proposed expression applies to plane strain as well as axis-symmetric stress conditions for foundations with smooth or rough bases. A thorough experimental investigation of the static behaviour of bucket foundations subjected to combined loading is carried out. Laboratory tests...

Modellus: Learning Physics with Mathematical Modelling

Science.gov (United States)

Teodoro, Vitor

Computers are now a major tool in research and development in almost all scientific and technological fields. Despite recent developments, this is far from true for learning environments in schools and most undergraduate studies. This thesis proposes a framework for designing curricula where computers, and computer modelling in particular, are a major tool for learning. The framework, based on research on learning science and mathematics and on computer user interface, assumes that: 1) learning is an active process of creating meaning from representations; 2) learning takes place in a community of practice where students learn both from their own effort and from external guidance; 3) learning is a process of becoming familiar with concepts, with links between concepts, and with representations; 4) direct manipulation user interfaces allow students to explore concrete-abstract objects such as those of physics and can be used by students with minimal computer knowledge. Physics is the science of constructing models and explanations about the physical world. And mathematical models are an important type of models that are difficult for many students. These difficulties can be rooted in the fact that most students do not have an environment where they can explore functions, differential equations and iterations as primary objects that model physical phenomena--as objects-to-think-with, reifying the formal objects of physics. The framework proposes that students should be introduced to modelling in a very early stage of learning physics and mathematics, two scientific areas that must be taught in very closely related way, as they were developed since Galileo and Newton until the beginning of our century, before the rise of overspecialisation in science. At an early stage, functions are the main type of objects used to model real phenomena, such as motions. At a later stage, rates of change and equations with rates of change play an important role. This type of equations

Toxicology Education Foundation

Science.gov (United States)

... bodies and our world. Welcome to the Toxicology Education Foundation! Our mission is to enhance public understanding ... In with us, follow our Tweets, choose Toxicology Education Foundation as your preferred charity through Smile.Amazon. ...

Skin Cancer Foundation

Science.gov (United States)

... Host a Fundraising Event | About Us | Store The Skin Cancer Foundation The Skin Cancer Foundation is the ... Handbook A "Sunscreen Gene"? Skin Cancer Facts & Statistics Skin Cancer Treatment Glossary Information on medications and procedures ...

Technology to Advance High School and Undergraduate Students with Disabilities in Science, Technology, Engineering, and Mathematics

Science.gov (United States)

Leddy, Mark H.

2010-01-01

Americans with disabilities are underemployed in science, technology, engineering and mathematics (STEM) at higher rates than their nondisabled peers. This article provides an overview of the National science Foundation's Research in Disabilities Education (RDE) program, of technology use by students with disabilities (SWD) in STEM, and of…

Interactions Between Mathematics and Physics

DEFF Research Database (Denmark)

Kjeldsen, Tinne Hoff; Lützen, Jesper

2015-01-01

In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined it as a var......In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined...... it as a variable that depends in an arbitrary manner on another variable. The change was required when mathematicians discovered that analytic expressions were not sufficient to represent physical phenomena such as the vibration of a string (Euler) and heat conduction (Fourier and Dirichlet). The introduction...... of generalized functions or distributions is shown to stem partly from the development of new theories of physics such as electrical engineering and quantum mechanics that led to the use of improper functions such as the delta function that demanded a proper foundation. We argue that the development of student...

Automated Generation of User Guidance by Combining Computation and Deduction

Directory of Open Access Journals (Sweden)

Walther Neuper

2012-02-01

Full Text Available Herewith, a fairly old concept is published for the first time and named "Lucas Interpretation". This has been implemented in a prototype, which has been proved useful in educational practice and has gained academic relevance with an emerging generation of educational mathematics assistants (EMA based on Computer Theorem Proving (CTP. Automated Theorem Proving (ATP, i.e. deduction, is the most reliable technology used to check user input. However ATP is inherently weak in automatically generating solutions for arbitrary problems in applied mathematics. This weakness is crucial for EMAs: when ATP checks user input as incorrect and the learner gets stuck then the system should be able to suggest possible next steps. The key idea of Lucas Interpretation is to compute the steps of a calculation following a program written in a novel CTP-based programming language, i.e. computation provides the next steps. User guidance is generated by combining deduction and computation: the latter is performed by a specific language interpreter, which works like a debugger and hands over control to the learner at breakpoints, i.e. tactics generating the steps of calculation. The interpreter also builds up logical contexts providing ATP with the data required for checking user input, thus combining computation and deduction. The paper describes the concepts underlying Lucas Interpretation so that open questions can adequately be addressed, and prerequisites for further work are provided.

Use of Intelligent Tutor in Post-Secondary Mathematics Education in the United Arab Emirates

Science.gov (United States)

Dani, Anita; Nasser, Ramzi

2016-01-01

The purpose of this paper is to determine potential identifiers of students' academic success in foundation mathematics course from the data logs of the intelligent tutor Assessment for Learning using Knowledge Spaces (ALEKS). A cross-sectional study design was used. A sample of 152 records, which accounts to approximately 60% of the population,…

FISPACT 97: user manual

International Nuclear Information System (INIS)

Forrest, R.A.; Sublet, J.-Ch.

1997-05-01

FISPACT is the inventory code included in the European Activation System (EASY). A new version of FISPACT: FISPACT-97 has been developed and this report is the User manual for the code. It explains the use of all the code words used in the input file to specify a FISPACT run and describes how all the data files are connected. A series of appendices cover the working of the code and the physical and mathematical details. Background information on the data files and extensive examples of input files suitable for various applications are included. (Author)

The Danish Industrial Foundations

DEFF Research Database (Denmark)

Thomsen, Steen

and governed, what role it plays in the Danish economy, and how industrial foundation-owned companies perform. The book is the result of a large collaborative research project, led by the author, on industrial foundations. Some global companies such as IKEA, Robert Bosch or the Tata Group are foundation...

Malicious Cognitive User Identification Algorithm in Centralized Spectrum Sensing System

Directory of Open Access Journals (Sweden)

Jingbo Zhang

2017-11-01

Full Text Available Collaborative spectral sensing can fuse the perceived results of multiple cognitive users, and thus will improve the accuracy of perceived results. However, the multi-source features of the perceived results result in security problems in the system. When there is a high probability of a malicious user attack, the traditional algorithm can correctly identify the malicious users. However, when the probability of attack by malicious users is reduced, it is almost impossible to use the traditional algorithm to correctly distinguish between honest users and malicious users, which greatly reduces the perceived performance. To address the problem above, based on the β function and the feedback iteration mathematical method, this paper proposes a malicious user identification algorithm under multi-channel cooperative conditions (β-MIAMC, which involves comprehensively assessing the cognitive user’s performance on multiple sub-channels to identify the malicious user. Simulation results show under the same attack probability, compared with the traditional algorithm, the β-MIAMC algorithm can more accurately identify the malicious users, reducing the false alarm probability of malicious users by more than 20%. When the attack probability is greater than 7%, the proposed algorithm can identify the malicious users with 100% certainty.

Grouting for Pile Foundation Improvement

NARCIS (Netherlands)

Van der Stoel, A.E.C.

2001-01-01

The aim of this research was to examine the use of grouting methods for pile foundation improvement, a generic term that is used here to define both foundation renovation (increasing the bearing capacity of a pile foundation that has insufficient bearing capacity) and foundation protection

A foundation for foundation phase teacher education: Making wise educational judgements

OpenAIRE

Karin Murris; Clare Verbeek

2014-01-01

We start our paper with a critical exploration of the current ‘back to basics’ approach in South African foundation phase teacher education with its emphasis on strengthening the teaching of subject knowledge. We claim that such a proposal first demands an answer to the question ‘what is foundational in foundation phase teaching?’ We propose an answer in three stages. First we argue that teacher education should be concerned not only with schooling or qualification (knowledge, skills and disp...

Mathematical and information-geometrical entropy for phenomenological Fourier and non-Fourier heat conduction

Science.gov (United States)

Li, Shu-Nan; Cao, Bing-Yang

2017-09-01

The second law of thermodynamics governs the direction of heat transport, which provides the foundational definition of thermodynamic Clausius entropy. The definitions of entropy are further generalized for the phenomenological heat transport models in the frameworks of classical irreversible thermodynamics and extended irreversible thermodynamics (EIT). In this work, entropic functions from mathematics are combined with phenomenological heat conduction models and connected to several information-geometrical conceptions. The long-time behaviors of these mathematical entropies exhibit a wide diversity and physical pictures in phenomenological heat conductions, including the tendency to thermal equilibrium, and exponential decay of nonequilibrium and asymptotics, which build a bridge between the macroscopic and microscopic modelings. In contrast with the EIT entropies, the mathematical entropies expressed in terms of the internal energy function can avoid singularity paired with nonpositive local absolute temperature caused by non-Fourier heat conduction models.

DEVELOPMENT OF ENTERPRISE RESOURCE PLANNING APPLICATIONS TO HELP RESOURCES MANAGEMENT OF FURNITURE COMPANY USING TECHNOLOGY WINDOWS COMMUNICATION FOUNDATION

Directory of Open Access Journals (Sweden)

Didiek S Wiyono

2013-09-01

Full Text Available Furniture companies need the latest information of its resources to maintain efficiency and productivity. ERP can be used as a tool to manage the existing resources on furniture company and can quickly display the suitable information. The study was conducted to design a simple ERP application that can help resource management on the furniture company. ERP application built with object-oriented methods. The implementation is using web technology as the user interface, Windows Communication Foundation (WCF as the application interface with other systems, and HTTP / HTTPS as the transport protocol to access the application. The results of study is a simple ERP application which consist of order management, production, inventory, purchasing, and reporting. ERP applications can be accessible to users through the web. For the purposes of integration, has built 72 services of WCF that can be accessed by other applications even though using different platforms. Keywords: erp, web, windows communication foundation, integration

NEWS: Solid foundations?

Science.gov (United States)

2000-07-01

Among the initiatives to be found at UK universities is a vocational award with the title `University Foundation Degree' at Nottingham Trent University. This qualification will be offered in 14 different subjects including four in the Faculty of Science and Mathematics, in the areas of applied biology, applied sciences, chemistry and physics. The courses will be available on a two-year full-time, three-year sandwich or a part-time basis. Set at a higher standard and specification than the Higher National Diplomas which it replaces, the UFD has been devised in consultation with industry and will cover the technical and specialist areas demanded by employers to combat skills shortages. The UFD in applied sciences concentrates on practical applications through laboratory, IT and project work, supported by lectures and seminars. At the end students can enter the employment market or transfer onto the second year of a degree course. Science-based careers including research and development would be the aim of those taking the UFD in physics. The first year develops the fundamentals of modern physics supported by studies in mathematics, IT and computer programming, whilst year 2 is vocational in nature with industrial problem solving and work experience as well as an academic theme associated with environmental aspects of the subject. Those who complete the UFD will be allowed automatic progression to a specified honours degree course and would normally be expected to study for a further two years for this award. However, those demonstrating an outstanding academic performance can transfer to the linked degree programme at the end of the first year via fast-track modules. Back in May the UK's Quality Assurance Agency (QAA) announced new standard benchmarks for degrees. These will be introduced into higher education institutions from 2002 to outline the knowledge, understanding and skills a student should gain from a particular higher education course. These benchmark

Norms for Participation in a Middle School Mathematics Classroom and Its Effect on Student Motivation

Science.gov (United States)

Megowan-Romanowicz, M. Colleen; Middleton, James A.; Ganesh, Tirupalavanam; Joanou, Jamie

2013-01-01

In this article we examine how students engage in learning mathematical concepts in the middle grades of an urban public school in the Southwestern United States. In the context of a 3-year National Science Foundation-funded longitudinal study of the development of students' rational number understanding, we encountered differing levels of…

Development and evaluation of nursing user interface screens using multiple methods.

Science.gov (United States)

Hyun, Sookyung; Johnson, Stephen B; Stetson, Peter D; Bakken, Suzanne

2009-12-01

Building upon the foundation of the Structured Narrative Electronic Health Record (EHR) model, we applied theory-based (combined Technology Acceptance Model and Task-Technology Fit Model) and user-centered methods to explore nurses' perceptions of functional requirements for an electronic nursing documentation system, design user interface screens reflective of the nurses' perspectives, and assess nurses' perceptions of the usability of the prototype user interface screens. The methods resulted in user interface screens that were perceived to be easy to use, potentially useful, and well-matched to nursing documentation tasks associated with Nursing Admission Assessment, Blood Administration, and Nursing Discharge Summary. The methods applied in this research may serve as a guide for others wishing to implement user-centered processes to develop or extend EHR systems. In addition, some of the insights obtained in this study may be informative to the development of safe and efficient user interface screens for nursing document templates in EHRs.

Improving the quality of numerical software through user-centered design

Energy Technology Data Exchange (ETDEWEB)

Pancake, C. M., Oregon State University

1998-06-01

The software interface - whether graphical, command-oriented, menu-driven, or in the form of subroutine calls - shapes the user`s perception of what software can do. It also establishes upper bounds on software usability. Numerical software interfaces typically are based on the designer`s understanding of how the software should be used. That is a poor foundation for usability, since the features that are ``instinctively right`` from the developer`s perspective are often the very ones that technical programmers find most objectionable or most difficult to learn. This paper discusses how numerical software interfaces can be improved by involving users more actively in design, a process known as user-centered design (UCD). While UCD requires extra organization and effort, it results in much higher levels of usability and can actually reduce software costs. This is true not just for graphical user interfaces, but for all software interfaces. Examples show how UCD improved the usability of a subroutine library, a command language, and an invocation interface.

Solar panel foundation device

Energy Technology Data Exchange (ETDEWEB)

Hawley, W.W.

1983-03-29

A transportable solar panel foundation device which has a bottom member, at least one upstanding side member, and an essentially open top. The side members are angled to permit nesting of a plurality of the foundation devices, and reinforcement pads are carried by the foundation device to support legs for one or more solar panels.

Interactive data manipulation program FAWTEK user guide

International Nuclear Information System (INIS)

Boyer, W.B.

1977-02-01

The interactive data acquisitio and manipulation program FAWTEK is described. The program allows users of the electron beam data acquisition facility to control the R7912 digitizers and to perform a variety of mathematical operations on data arrays. Commands are entered in a high-level language via a Tektronix 4010 terminal console. Each command directive, aling with its associated parameters, is described in detail

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...

Symposium on the Foundations of Newtonian Scholarship

CERN Document Server

Nauenberg, Michael; The foundations of Newtonian scholarship

2000-01-01

Newtonian scholarship has taken great steps forward in the last half-century.The recent completion of critical editions of Newton's mathematical papers and of his scientific correspondence, as well as the publication of the first volume of his optical papers and of variant readings of the Principia in the original Latin, have made most of Newton's scientific work generally available for study and analysis for the first time. This has provided a better understanding of Newton's Principia and Optics especially regarding their origin and interpretation, much of which has remained obscure for several centuries. Some of the new developments and insights are presented in this book by several of the scholars who have made these primary sources accessible, and by others who are using them to elucidate Newton's work. Most of the papers included were presented at the Symposium on the Foundations of Newtonian Scholarship, held at the Royal Society in London in March 1997.

A mathematical solution for the parameters of three interfering resonances

Science.gov (United States)

Han, X.; Shen, C. P.

2018-04-01

The multiple-solution problem in determining the parameters of three interfering resonances from a fit to an experimentally measured distribution is considered from a mathematical viewpoint. It is shown that there are four numerical solutions for a fit with three coherent Breit-Wigner functions. Although explicit analytical formulae cannot be derived in this case, we provide some constraint equations between the four solutions. For the cases of nonrelativistic and relativistic Breit-Wigner forms of amplitude functions, a numerical method is provided to derive the other solutions from that already obtained, based on the obtained constraint equations. In real experimental measurements with more complicated amplitude forms similar to Breit-Wigner functions, the same method can be deduced and performed to get numerical solutions. The good agreement between the solutions found using this mathematical method and those directly from the fit verifies the correctness of the constraint equations and mathematical methodology used. Supported by National Natural Science Foundation of China (NSFC) (11575017, 11761141009), the Ministry of Science and Technology of China (2015CB856701) and the CAS Center for Excellence in Particle Physics (CCEPP)

Forward the Foundation: Local Education Foundations Offer an Alternative Source for School Funding

Science.gov (United States)

Brooks-Young, Susan

2007-01-01

February's column "Going Corporate" discussed ideas for approaching private foundations for funding. Some districts take this idea several steps further by partnering with the community and local businesses to establish a not-for-profit foundation, or local education foundation (LEF). It probably comes as no surprise that the idea of forming a LEF…

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.

Can Innate, modular "foundations" explain morality? Challenges for Haidt's Moral Foundations Theory.

Science.gov (United States)

Suhler, Christopher L; Churchland, Patricia

2011-09-01

Jonathan Haidt's Moral Foundations Theory is an influential scientific account of morality incorporating psychological, developmental, and evolutionary perspectives. The theory proposes that morality is built upon five innate "foundations," each of which is believed to have been selected for during human evolution and, subsequently, tuned-up by learning during development. We argue here that although some general elements of Haidt's theory are plausible, many other important aspects of his account are seriously flawed. First, innateness and modularity figure centrally in Haidt's account, but terminological and conceptual problems foster confusion and ambiguities. Second, both the theory's proposed number of moral foundations and its taxonomy of the moral domain appear contrived, ignoring equally good candidate foundations and the possibility of substantial intergroup differences in the foundations' contents. Third, the mechanisms (viz., modules) and categorical distinctions (viz., between foundations) proposed by the theory are not consilient with discoveries in contemporary neuroscience concerning the organization, functioning, and development of the brain. In light of these difficulties, we suggest that Haidt's theory is inadequate as a scientific account of morality. Nevertheless, the theory's weaknesses are instructive, and hence, criticism may be useful to psychologists, neuroscientists, and philosophers attempting to advance theories of morality, as well as to researchers wishing to invoke concepts such as innateness and modularity more generally.

Finding Waldo: Learning about Users from their Interactions.

Science.gov (United States)

Brown, Eli T; Ottley, Alvitta; Zhao, Helen; Quan Lin; Souvenir, Richard; Endert, Alex; Chang, Remco

2014-12-01

Visual analytics is inherently a collaboration between human and computer. However, in current visual analytics systems, the computer has limited means of knowing about its users and their analysis processes. While existing research has shown that a user's interactions with a system reflect a large amount of the user's reasoning process, there has been limited advancement in developing automated, real-time techniques that mine interactions to learn about the user. In this paper, we demonstrate that we can accurately predict a user's task performance and infer some user personality traits by using machine learning techniques to analyze interaction data. Specifically, we conduct an experiment in which participants perform a visual search task, and apply well-known machine learning algorithms to three encodings of the users' interaction data. We achieve, depending on algorithm and encoding, between 62% and 83% accuracy at predicting whether each user will be fast or slow at completing the task. Beyond predicting performance, we demonstrate that using the same techniques, we can infer aspects of the user's personality factors, including locus of control, extraversion, and neuroticism. Further analyses show that strong results can be attained with limited observation time: in one case 95% of the final accuracy is gained after a quarter of the average task completion time. Overall, our findings show that interactions can provide information to the computer about its human collaborator, and establish a foundation for realizing mixed-initiative visual analytics systems.

HTGR Application Economic Model Users' Manual

Energy Technology Data Exchange (ETDEWEB)

A.M. Gandrik

2012-01-01

The High Temperature Gas-Cooled Reactor (HTGR) Application Economic Model was developed at the Idaho National Laboratory for the Next Generation Nuclear Plant Project. The HTGR Application Economic Model calculates either the required selling price of power and/or heat for a given internal rate of return (IRR) or the IRR for power and/or heat being sold at the market price. The user can generate these economic results for a range of reactor outlet temperatures; with and without power cycles, including either a Brayton or Rankine cycle; for the demonstration plant, first of a kind, or nth of a kind project phases; for up to 16 reactor modules; and for module ratings of 200, 350, or 600 MWt. This users manual contains the mathematical models and operating instructions for the HTGR Application Economic Model. Instructions, screenshots, and examples are provided to guide the user through the HTGR Application Economic Model. This model was designed for users who are familiar with the HTGR design and Excel and engineering economics. Modification of the HTGR Application Economic Model should only be performed by users familiar with the HTGR and its applications, Excel, and Visual Basic.

Spectrometer user interface to computer systems

International Nuclear Information System (INIS)

Salmon, L.; Davies, M.; Fry, F.A.; Venn, J.B.

1979-01-01

A computer system for use in radiation spectrometry should be designed around the needs and comprehension of the user and his operating environment. To this end, the functions of the system should be built in a modular and independent fashion such that they can be joined to the back end of an appropriate user interface. The point that this interface should be designed rather than just allowed to evolve is illustrated by reference to four related computer systems of differing complexity and function. The physical user interfaces in all cases are keyboard terminals, and the virtues and otherwise of these devices are discussed and compared with others. The language interface needs to satisfy a number of requirements, often conflicting. Among these, simplicity and speed of operation compete with flexibility and scope. Both experienced and novice users need to be considered, and any individual's needs may vary from naive to complex. To be efficient and resilient, the implementation must use an operating system, but the user needs to be protected from its complex and unfamiliar syntax. At the same time the interface must allow the user access to all services appropriate to his needs. The user must also receive an image of privacy in a multi-user system. The interface itself must be stable and exhibit continuity between implementations. Some of these conflicting needs have been overcome by the SABRE interface with languages operating at several levels. The foundation is a simple semimnemonic command language that activates indididual and independent functions. The commands can be used with positional parameters or in an interactive dialogue the precise nature of which depends upon the operating environment and the user's experience. A command procedure or macrolanguage allows combinations of commands with conditional branching and arithmetic features. Thus complex but repetitive operations are easily performed

A Graphical User Interface to Generalized Linear Models in MATLAB

Directory of Open Access Journals (Sweden)

Peter Dunn

1999-07-01

Full Text Available Generalized linear models unite a wide variety of statistical models in a common theoretical framework. This paper discusses GLMLAB-software that enables such models to be fitted in the popular mathematical package MATLAB. It provides a graphical user interface to the powerful MATLAB computational engine to produce a program that is easy to use but with many features, including offsets, prior weights and user-defined distributions and link functions. MATLAB's graphical capacities are also utilized in providing a number of simple residual diagnostic plots.

The Origin of Mathematics and Number Sense in the Cerebellum: with Implications for Finger Counting and Dyscalculia.

Science.gov (United States)

Vandervert, Larry

2017-01-01

Mathematicians and scientists have struggled to adequately describe the ultimate foundations of mathematics. Nobel laureates Albert Einstein and Eugene Wigner were perplexed by this issue, with Wigner concluding that the workability of mathematics in the real world is a mystery we cannot explain. In response to this classic enigma, the major purpose of this article is to provide a theoretical model of the ultimate origin of mathematics and "number sense" (as defined by S. Dehaene) that is proposed to involve the learning of inverse dynamics models through the collaboration of the cerebellum and the cerebral cortex (but prominently cerebellum-driven). This model is based upon (1) the modern definition of mathematics as the "science of patterns," (2) cerebellar sequence (pattern) detection, and (3) findings that the manipulation of numbers is automated in the cerebellum. This cerebro-cerebellar approach does not necessarily conflict with mathematics or number sense models that focus on brain functions associated with especially the intraparietal sulcus region of the cerebral cortex. A direct corollary purpose of this article is to offer a cerebellar inner speech explanation for difficulty in developing "number sense" in developmental dyscalculia. It is argued that during infancy the cerebellum learns (1) a first tier of internal models for a primitive physics that constitutes the foundations of visual-spatial working memory, and (2) a second (and more abstract) tier of internal models based on (1) that learns "number" and relationships among dimensions across the primitive physics of the first tier. Within this context it is further argued that difficulty in the early development of the second tier of abstraction (and "number sense") is based on the more demanding attentional requirements imposed on cerebellar inner speech executive control during the learning of cerebellar inverse dynamics models. Finally, it is argued that finger counting improves (does not

Enhancing Mathematical Communication for Virtual Math Teams

Directory of Open Access Journals (Sweden)

Gerry Stahl

2010-06-01

Full Text Available The Math Forum is an online resource center for pre-algebra, algebra, geometry and pre-calculus. Its Virtual Math Teams (VMT service provides an integrated web-based environment for small teams of people to discuss math and to work collaboratively on math problems or explore interesting mathematical micro-worlds together. The VMT Project studies the online math discourse that takes place during sessions of virtual math teams working on open-ended problem-solving tasks. In particular, it investigates methods of group cognition that are employed by teams in this setting. The VMT environment currently integrates social networking, synchronous text chat, a shared whiteboard for drawing, web browsers and an asynchronous wiki for exchanging findings within the larger community. A simple version of MathML is supported in the whiteboard, chat and wiki for displaying mathematical expressions. The VMT Project is currently integrating the dynamic mathematics application, GeoGebra, into its collaboration environment. This will create a multi-user version of GeoGebra, which can be used in concert with the chat, web browsers, curricular topics and wiki repository.

A mathematical approach to human pterygium shape

Directory of Open Access Journals (Sweden)

Pajic B

2016-07-01

Full Text Available Bojan Pajic,1–4 Iraklis Vastardis,1 Predrag Rajkovic,5 Brigitte Pajic-Eggspuehler,1 Daniel M Aebersold,6 Zeljka Cvejic2 1Eye Clinic ORASIS, Swiss Eye Research Foundation, Reinach AG, Switzerland; 2Department of Physics, Faculty of Sciences, University of Novi Sad, Novi Sad,3Faculty of Medicine of the Military Medical Academy, University of Defence, Belgrade, Serbia; 4Division of Ophthalmology, Department of Clinical Neurosciences, Geneva University Hospitals, Geneva, Switzerland; 5Department of Mathematics, Faculty of Mechanical Engineering, University of Niš, Niš, Serbia; 6Department of Radiation Oncology, Inselspital, Bern University Hospital, Bern, Switzerland Purpose: Pterygium is a common lesion affecting the population in countries with high levels of ultraviolet exposure. The final shape of a pterygium is the result of a growth pattern, which remains poorly understood. This manuscript provides a mathematical analysis as a tool to determine the shape of human pterygia.Materials and methods: Eighteen patients, all affected by nasal unilateral pterygia, were randomly selected from our patient database independently of sex, origin, or race. We included all primary or recurrent pterygia with signs of proliferation, dry eye, and induction of astigmatism. Pseudopterygia were excluded from this study. Pterygia were outlined and analyzed mathematically using a Cartesian coordinate system with two axes (X, Y and five accurate landmarks of the pterygium.Results: In 13 patients (72%, the shape of the pterygia was hyperbolic and in five patients (28%, the shape was rather elliptical.Conclusion: This analysis gives a highly accurate mathematical description of the shape of human pterygia. This might help to better assess the clinical results and outcome of the great variety of therapeutic approaches concerning these lesions. Keywords: etiology, pterygium, limbal stem cells, stem cells dysfunction, mathematical shape analysis

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...

Resource Review: Why So Few? Women in Science, Technology, Engineering, and Mathematics

OpenAIRE

Patricia A. Dawson

2014-01-01

“Why So Few? Women in Science, Technology, Engineering and Mathematics” (Hill, C., Corbett, C., Rose, A., 2010) reports on an extensive study of women’s underrepresentation in science, technology, engineering, and mathematics professions. Funded by the National Science Foundation, the project was conducted by American Association of University Women. The resource includes findings from eight research studies which examined social and environmental factors which contribute to women’s underrepr...

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.

Exploring links between foundation phase teachers’ content knowledge and their example spaces

Directory of Open Access Journals (Sweden)

Samantha Morrison

2013-12-01

Full Text Available This paper explores two foundation phase teachers’ example spaces (a space in the mind where examples exist when teaching number-related topics in relation to snapshots of their content knowledge (CK. Data was collected during a pilot primary maths for teaching course that included assessments of teacher content knowledge (CK. An analysis of a content-knowledge focused pre-test developed for the larger study indicated a relatively high score for one teacher and a low score for the other. Using Rowland’s (2008 framework, an analysis of classroom practice showed associations between a higher CK and the extent of a teacher’s example space and more coherent connections between different representational forms. Although no hard claims or generalisations of the link between teachers’ example spaces and their level of mathematics content knowledge can be made here, this study reinforces evidence of the need to increase teachers’ CK from a pedagogic perspective in order to raise the level of mathematics teaching and learning in the South African landscape.

The Radiological Safety Analysis Computer Program (RSAC-5) user's manual

International Nuclear Information System (INIS)

Wenzel, D.R.

1994-02-01

The Radiological Safety Analysis Computer Program (RSAC-5) calculates the consequences of the release of radionuclides to the atmosphere. Using a personal computer, a user can generate a fission product inventory from either reactor operating history or nuclear criticalities. RSAC-5 models the effects of high-efficiency particulate air filters or other cleanup systems and calculates decay and ingrowth during transport through processes, facilities, and the environment. Doses are calculated through the inhalation, immersion, ground surface, and ingestion pathways. RSAC+, a menu-driven companion program to RSAC-5, assists users in creating and running RSAC-5 input files. This user's manual contains the mathematical models and operating instructions for RSAC-5 and RSAC+. Instructions, screens, and examples are provided to guide the user through the functions provided by RSAC-5 and RSAC+. These programs are designed for users who are familiar with radiological dose assessment methods

Strategic Alliance to Advanced Technological Education through Enhanced Mathematics, Science, Technology, and English Education at the Secondary Level

Science.gov (United States)

Scarborough, Jule Dee

2004-01-01

This document (book) reports on the Strategic Alliance to Advance Technological Education through Enhanced Mathematics, Science, Technology, and English Education at the Secondary Level, funded by National Science Foundation. It was a collaborative partnership involving the Rockford Public Schools, Rock Valley College, and Northern Illinois…

Statistical Mechanics of Disordered Systems - Series: Cambridge Series in Statistical and Probabilistic Mathematics (No. 18)

Science.gov (United States)

Bovier, Anton

2006-06-01

Our mathematical understanding of the statistical mechanics of disordered systems is going through a period of stunning progress. This self-contained book is a graduate-level introduction for mathematicians and for physicists interested in the mathematical foundations of the field, and can be used as a textbook for a two-semester course on mathematical statistical mechanics. It assumes only basic knowledge of classical physics and, on the mathematics side, a good working knowledge of graduate-level probability theory. The book starts with a concise introduction to statistical mechanics, proceeds to disordered lattice spin systems, and concludes with a presentation of the latest developments in the mathematical understanding of mean-field spin glass models. In particular, recent progress towards a rigorous understanding of the replica symmetry-breaking solutions of the Sherrington-Kirkpatrick spin glass models, due to Guerra, Aizenman-Sims-Starr and Talagrand, is reviewed in some detail. Comprehensive introduction to an active and fascinating area of research Clear exposition that builds to the state of the art in the mathematics of spin glasses Written by a well-known and active researcher in the field

Using a Summer REU to Help Develop the Next Generation of Mathematical Ecologists.

Science.gov (United States)

Bennie, Barbara; Eager, Eric Alan; Peirce, James P; Sandland, Gregory J

2018-04-01

Understanding the complexities of environmental issues requires individuals to bring together ideas and data from different disciplines, including ecology and mathematics. With funding from the national science foundation (NSF), scientists from the University of Wisconsin-La Crosse and the US geological survey held a research experience for undergraduates (REU) program in the summer of 2016. The goals of the program were to expose students to open problems in the area of mathematical ecology, motivate students to pursue STEM-related positions, and to prepare students for research within interdisciplinary, collaborative settings. Based on backgrounds and interests, eight students were selected to participate in one of two research projects: wind energy and wildlife conservation or the establishment and spread of waterfowl diseases. Each research program was overseen by a mathematician and a biologist. Regardless of the research focus, the program first began with formal lectures to provide students with foundational knowledge followed by student-driven research projects. Throughout this period, student teams worked in close association with their mentors to create, parameterize and evaluate ecological models to better understand their systems of interest. Students then disseminated their results at local, regional, and international meetings and through publications (one in press and one in progress). Direct and indirect measures of student development revealed that our REU program fostered a deep appreciation for and understanding of mathematical ecology. Finally, the program allowed students to gain experiences working with individuals with different backgrounds and perspectives. Taken together, this REU program allowed us to successfully excite, motivate and prepare students for future positions in the area of mathematical biology, and because of this it can be used as a model for interdisciplinary programs at other institutions.

Enlightening symbols a short history of mathematical notation and its hidden powers

CERN Document Server

Mazur, Joseph

2014-01-01

While all of us regularly use basic math symbols such as those for plus, minus, and equals, few of us know that many of these symbols weren't available before the sixteenth century. What did mathematicians rely on for their work before then? And how did mathematical notations evolve into what we know today? In Enlightening Symbols, popular math writer Joseph Mazur explains the fascinating history behind the development of our mathematical notation system. He shows how symbols were used initially, how one symbol replaced another over time, and how written math was conveyed before and after symbols became widely adopted. Traversing mathematical history and the foundations of numerals in different cultures, Mazur looks at how historians have disagreed over the origins of the numerical system for the past two centuries. He follows the transfigurations of algebra from a rhetorical style to a symbolic one, demonstrating that most algebra before the sixteenth century was written in prose or in verse employing the wr...

An American Imperative: Transforming the Recruitment, Retention, and Renewal of Our Nation's Mathematics and Science Teaching Workforce

Science.gov (United States)

Business-Higher Education Forum (NJ1), 2007

2007-01-01

American students today have limited interest in studying mathematics and science, and academic achievement in these two foundational disciplines is demonstrably low. This reality poses an acute challenge to our ability to keep American society intellectually vibrant and to ensure that our economy is globally competitive. This Business-Higher…

Theorema 2.0: A Graphical User Interface for a Mathematical Assistant System

Directory of Open Access Journals (Sweden)

Wolfgang Windsteiger

2013-07-01

Full Text Available Theorema 2.0 stands for a re-design including a complete re-implementation of the Theorema system, which was originally designed, developed, and implemented by Bruno Buchberger and his Theorema group at RISC. In this paper, we present the first prototype of a graphical user interface (GUI for the new system. It heavily relies on powerful interactive capabilities introduced in recent releases of the underlying Mathematica system, most importantly the possibility of having dynamic objects connected to interface elements like sliders, menus, check-boxes, radio-buttons and the like. All these features are fully integrated into the Mathematica programming environment and allow the implementation of a modern user interface.

International note: Prediction of mathematics work ethic and performance from behavioral, normative, and control beliefs among Qatari adolescents.

Science.gov (United States)

Areepattamannil, Shaljan; Abdelfattah, Faisal; Mahasneh, Randa Ali; Khine, Myint Swe; Welch, Anita G; Melkonian, Michael; Al Nuaimi, Samira Ahmed

2016-01-01

Over half-a-million adolescents take part in each cycle of the Program for International Student Assessment (PISA). Yet often, researchers and policy makers across the globe tend to focus their attention primarily on the academic trajectories of adolescents hailing from highly successful education systems. Hence, a vast majority of the adolescent population who regionally and globally constitute the 'long tail of underachievement' often remain unnoticed and underrepresented in the growing literature on adolescents' academic trajectories. The present study, therefore, explored the relations of dispositions toward mathematics, subjective norms in mathematics, and perceived control of success in mathematics to mathematics work ethic as well as mathematics performance; and the mediational role of mathematics work ethic in the association between dispositional, normative, and control beliefs and mathematics performance among adolescents in one of the lowest performing education systems, Qatar. Structural equation modeling (SEM) analyses revealed that Qatari adolescents' dispositional, normative, and control beliefs about mathematics were significantly associated with their mathematics work ethic and mathematics performance, and mathematics work ethic significantly mediated the relationship between dispositional, normative, and control beliefs about mathematics and mathematics performance. However, multi-group SEM analyses indicated that these relationships were not invariant across the gender and the SES groups. Copyright © 2015 The Foundation for Professionals in Services for Adolescents. Published by Elsevier Ltd. All rights reserved.

An introduction to the mathematical theory of finite elements

CERN Document Server

Oden, J T

2011-01-01

This introduction to the theory of Sobolev spaces and Hilbert space methods in partial differential equations is geared toward readers of modest mathematical backgrounds. It offers coherent, accessible demonstrations of the use of these techniques in developing the foundations of the theory of finite element approximations.J. T. Oden is Director of the Institute for Computational Engineering & Sciences (ICES) at the University of Texas at Austin, and J. N. Reddy is a Professor of Engineering at Texas A&M University. They developed this essentially self-contained text from their seminars and co

Brain Functors: A Mathematical Model of Intentional Perception and Action

Directory of Open Access Journals (Sweden)

David Ellerman

2016-03-01

Full Text Available Category theory has foundational importance because it provides conceptual lenses to characterize what is important and universal in mathematics - with adjunctions being the primary lens. If adjunctions are so important in mathematics, then perhaps they will isolate concepts of some importance in the empirical sciences. But the applications of adjunctions have been hampered by an overly restrictive formulation that avoids heteromorphisms or hets. By reformulating an adjunction using hets, it is split into two parts, a left and a right semiadjunction. Semiadjunctions (essentially a formulation of universal mapping properties using hets can then be combined in a new way to define the notion of a brain functor that provides an abstract model of the intentionality of perception and action (as opposed to the passive reception of sense-data or the reflex generation of behavior.

Users' guide to CACECO containment analysis code. [LMFBR

Energy Technology Data Exchange (ETDEWEB)

Peak, R.D.

1979-06-01

The CACECO containment analysis code was developed to predict the thermodynamic responses of LMFBR containment facilities to a variety of accidents. The code is included in the National Energy Software Center Library at Argonne National Laboratory as Program No. 762. This users' guide describes the CACECO code and its data input requirements. The code description covers the many mathematical models used and the approximations used in their solution. The descriptions are detailed to the extent that the user can modify the code to suit his unique needs, and, indeed, the reader is urged to consider code modification acceptable.

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…

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.

Sudden Arrhythmia Death Syndromes (SADS) Foundation

Science.gov (United States)

... SADS Foundation UK SADS Foundation Netherlands SADS Foundation China SADS Foundation Hong Kong Search for: Log in ... research crucial for health of patients and the economy 7/18/2017 More funding for heart disease ...

Use of reinforced soil foundation (RSF) to support shallow foundation : summary report.

Science.gov (United States)

2008-05-01

This research study investigates the potential benefits of using reinforced soil foundations to improve the bearing capacity and reduce the settlement of shallow foundations on soils. To implement this objective, a total of 117 tests, including 38 la...

Foundations for Reasoning in Cognition-Based Computational Representations of Human Decision Making; TOPICAL

International Nuclear Information System (INIS)

SENGLAUB, MICHAEL E.; HARRIS, DAVID L.; RAYBOURN, ELAINE M.

2001-01-01

In exploring the question of how humans reason in ambiguous situations or in the absence of complete information, we stumbled onto a body of knowledge that addresses issues beyond the original scope of our effort. We have begun to understand the importance that philosophy, in particular the work of C. S. Peirce, plays in developing models of human cognition and of information theory in general. We have a foundation that can serve as a basis for further studies in cognition and decision making. Peircean philosophy provides a foundation for understanding human reasoning and capturing behavioral characteristics of decision makers due to cultural, physiological, and psychological effects. The present paper describes this philosophical approach to understanding the underpinnings of human reasoning. We present the work of C. S. Peirce, and define sets of fundamental reasoning behavior that would be captured in the mathematical constructs of these newer technologies and would be able to interact in an agent type framework. Further, we propose the adoption of a hybrid reasoning model based on his work for future computational representations or emulations of human cognition

Issues in Combining the Use of Various Tools in Solving Mathematical Problems--Why Is Copy-Paste Often Useless

Science.gov (United States)

Lokar, Matija; Libbrecht, Paul

2017-01-01

Mathematical formulae are information objects that can be entered in a computer, visualized, and evaluated. Thus, by the majority of (mostly occasional) users it is also expected that they are transferable through the simple copy-paste procedure. This transfer is particularly interesting when users are involved in tasks that span different…

RSAC 6.2 with WinRP 2.0 User Manual

Energy Technology Data Exchange (ETDEWEB)

Bradley Schrader

2005-09-01

The Radiological Safety Analysis Computer Program (RSAC-6.2) calculates the consequences of a release of radionuclides to the atmosphere. Using a personal computer, a user can generate a fission product inventory from either reactor operating history or a nuclear criticality accident. RSAC-6.2 models the effects of high-efficiency particulate air filters or other cleanup systems and calculates decay and ingrowth during transport through processes, facilities, and the environment. Doses are calculated for resuspension, inhalation, immersion, ground surface, and ingestion pathways. WinRP 2.0, a windows based overlay to RSAC-6.2, assists users in creating and running RSAC-6.2 input files. This users manual contains the mathematical models and operating instructions for RSAC-6.2 and WinRP 2.0. Instructions, screens, and examples are provided to guide the user through the functions provided by RSAC-6.2 and WinRP 2.0. These programs are designed for users who are familiar with radiological dose assessment methods.

The role of foundations: Rockefeller Foundation.

Science.gov (United States)

Rockefeller, David

The consequences of climate change and the impacts of human activity on the environment have made it clearer than ever before that we must evolve our current model of public health to better account for the inextricable link between human health and the natural systems on which it depends-creating a "public health 2.0" that builds on the innovations of the twentieth century to account for a world where humans have bypassed planetary boundaries to achieve well-being. First coined at the Rockefeller Foundation's Centennial gathering in Beijing in 2013, "Planetary Health" will factor in future health and environmental harms over present-day gains, particularly those that disproportionately affect the poor and those in developing nations. To build this new field, foundations must address the challenge of information, increasing support for research to bridge knowledge gaps on the links between economic development, natural systems, and human health.

Not the Norm: The Potential of Tree Analysis of Performance Data from Students in a Foundation Mathematics Module

Science.gov (United States)

Kirby, Nicola; Dempster, Edith

2015-01-01

Quantitative methods of data analysis usually involve inferential statistics, and are not well known for their ability to reflect the intricacies of a diverse student population. The South African tertiary education sector is characterised by extreme inequality and diversity. Foundation programmes address issues of inequality of access by…

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.

Compressor Foundation Analysis Tool(COFANTO)

NARCIS (Netherlands)

Eijk, A.; Lentzen, S.S.K; Zuada Coelho, B.E.; Galanti, F.M.B.

2012-01-01

Reciprocating compressors are generally supported on a heavy concrete foundation. In spite of the large inertia and stiffness of the foundation, problems can occur due to interaction between the mechanical installation and the foundation. Two types of problems may occur. In the first type, the

Vertical Dynamic Stiffness of Offshore Foundations

DEFF Research Database (Denmark)

Latini, Chiara; Cisternino, Michele; Zania, Varvara

2016-01-01

Nowadays, pile and suction caisson foundations are widely used to support offshore structures which are subjected to vertical dynamic loads. The dynamic soil-structure interaction of floating foundations (foundations embedded in a soil layer whose height is greater than the foundation length) is ...

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…

Simulation and Verification of Synchronous Set Relations in Rewriting Logic

Science.gov (United States)

Rocha, Camilo; Munoz, Cesar A.

2011-01-01

This paper presents a mathematical foundation and a rewriting logic infrastructure for the execution and property veri cation of synchronous set relations. The mathematical foundation is given in the language of abstract set relations. The infrastructure consists of an ordersorted rewrite theory in Maude, a rewriting logic system, that enables the synchronous execution of a set relation provided by the user. By using the infrastructure, existing algorithm veri cation techniques already available in Maude for traditional asynchronous rewriting, such as reachability analysis and model checking, are automatically available to synchronous set rewriting. The use of the infrastructure is illustrated with an executable operational semantics of a simple synchronous language and the veri cation of temporal properties of a synchronous system.

The 6th International Conference on Computer Science and Computational Mathematics (ICCSCM 2017)

Science.gov (United States)

2017-09-01

The ICCSCM 2017 (The 6th International Conference on Computer Science and Computational Mathematics) has aimed to provide a platform to discuss computer science and mathematics related issues including Algebraic Geometry, Algebraic Topology, Approximation Theory, Calculus of Variations, Category Theory; Homological Algebra, Coding Theory, Combinatorics, Control Theory, Cryptology, Geometry, Difference and Functional Equations, Discrete Mathematics, Dynamical Systems and Ergodic Theory, Field Theory and Polynomials, Fluid Mechanics and Solid Mechanics, Fourier Analysis, Functional Analysis, Functions of a Complex Variable, Fuzzy Mathematics, Game Theory, General Algebraic Systems, Graph Theory, Group Theory and Generalizations, Image Processing, Signal Processing and Tomography, Information Fusion, Integral Equations, Lattices, Algebraic Structures, Linear and Multilinear Algebra; Matrix Theory, Mathematical Biology and Other Natural Sciences, Mathematical Economics and Financial Mathematics, Mathematical Physics, Measure Theory and Integration, Neutrosophic Mathematics, Number Theory, Numerical Analysis, Operations Research, Optimization, Operator Theory, Ordinary and Partial Differential Equations, Potential Theory, Real Functions, Rings and Algebras, Statistical Mechanics, Structure Of Matter, Topological Groups, Wavelets and Wavelet Transforms, 3G/4G Network Evolutions, Ad-Hoc, Mobile, Wireless Networks and Mobile Computing, Agent Computing & Multi-Agents Systems, All topics related Image/Signal Processing, Any topics related Computer Networks, Any topics related ISO SC-27 and SC- 17 standards, Any topics related PKI(Public Key Intrastructures), Artifial Intelligences(A.I.) & Pattern/Image Recognitions, Authentication/Authorization Issues, Biometric authentication and algorithms, CDMA/GSM Communication Protocols, Combinatorics, Graph Theory, and Analysis of Algorithms, Cryptography and Foundation of Computer Security, Data Base(D.B.) Management & Information

Information Quality as a Foundation for User Trustworthiness of Earth Science Data.

Science.gov (United States)

Wei, Y.; Moroni, D. F.; Ramapriyan, H.; Peng, G.

2017-12-01

Information quality is multidimensional. Four different aspects of information quality can be defined based on the lifecycle stages of Earth Science data products: science, product, stewardship and services. With increasing requirements on ensuring and improving information quality coming from multiple government agencies and throughout industry, there have been considerable efforts toward improving information quality during the last decade, much of which has not been well vetted in a collective sense until recently. Given this rich background of prior work, the Information Quality Cluster (IQC), established within the Federation of Earth Science Information Partners (ESIP) in 2011, and reactivated in the summer of 2014, has been active with membership from multiple organizations. The IQC's objectives and activities, aimed at ensuring and improving information quality for Earth science data and products, are also considered vital toward improving the trustworthiness of Earth science data to a vast and interdisciplinary community of data users. During 2016, several members of the IQC have led the development and assessment of four use cases. This was followed up in 2017 with multiple panel sessions at the 2017 Winter and Summer ESIP Meetings to survey the challenges posed in the various aspects of information quality. What was discovered to be most lacking is the transparency of data lineage (i.e., provenance and maturity), uniform methods for uncertainty characterization, and uniform quality assurance data and metadata. While solutions to these types of issues exist, most data producers have little time to investigate and collaborate to arrive at and conform to a consensus approach. The IQC has positioned itself as a community platform to bring together all relevant stakeholders from data producers, repositories, program managers, and the end users. A combination of both well-vetted and "trailblazing" solutions are presented to address how data trustworthiness can

Mathematical correlation of modal-parameter-identification methods via system-realization theory

Science.gov (United States)

Juang, Jer-Nan

1987-01-01

A unified approach is introduced using system-realization theory to derive and correlate modal-parameter-identification methods for flexible structures. Several different time-domain methods are analyzed and treated. A basic mathematical foundation is presented which provides insight into the field of modal-parameter identification for comparison and evaluation. The relation among various existing methods is established and discussed. This report serves as a starting point to stimulate additional research toward the unification of the many possible approaches for modal-parameter identification.

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…

CEASAW: A User-Friendly Computer Environment Analysis for the Sawmill Owner

Science.gov (United States)

Guillermo Mendoza; William Sprouse; Philip A. Araman; William G. Luppold

1991-01-01

Improved spreadsheet software capabilities have brought optimization to users with little or no background in mathematical programming. Better interface capabilities of spreadsheet models now make it possible to combine optimization models with a spreadsheet system. Sawmill production and inventory systems possess many features that make them suitable application...

Robert Wood Johnson Foundation