Some unsolved problems in discrete mathematics and mathematical cybernetics

Science.gov (United States)

Korshunov, Aleksei D.

2009-10-01

There are many unsolved problems in discrete mathematics and mathematical cybernetics. Writing a comprehensive survey of such problems involves great difficulties. First, such problems are rather numerous and varied. Second, they greatly differ from each other in degree of completeness of their solution. Therefore, even a comprehensive survey should not attempt to cover the whole variety of such problems; only the most important and significant problems should be reviewed. An impersonal choice of problems to include is quite hard. This paper includes 13 unsolved problems related to combinatorial mathematics and computational complexity theory. The problems selected give an indication of the author's studies for 50 years; for this reason, the choice of the problems reviewed here is, to some extent, subjective. At the same time, these problems are very difficult and quite important for discrete mathematics and mathematical cybernetics. Bibliography: 74 items.

Some unsolved problems in discrete mathematics and mathematical cybernetics

International Nuclear Information System (INIS)

Korshunov, Aleksei D

2009-01-01

There are many unsolved problems in discrete mathematics and mathematical cybernetics. Writing a comprehensive survey of such problems involves great difficulties. First, such problems are rather numerous and varied. Second, they greatly differ from each other in degree of completeness of their solution. Therefore, even a comprehensive survey should not attempt to cover the whole variety of such problems; only the most important and significant problems should be reviewed. An impersonal choice of problems to include is quite hard. This paper includes 13 unsolved problems related to combinatorial mathematics and computational complexity theory. The problems selected give an indication of the author's studies for 50 years; for this reason, the choice of the problems reviewed here is, to some extent, subjective. At the same time, these problems are very difficult and quite important for discrete mathematics and mathematical cybernetics. Bibliography: 74 items.

Mathematical models for the definition of cell manufacturing layout. Literature review

Directory of Open Access Journals (Sweden)

Gustavo Andrés Romero Duque

2015-11-01

Full Text Available This review article discusses the approach to the layout problem of cell manufacturing (LCM in a descriptive form; considering at first the problem and its variations, then the elements of the mathematical models, subsequently presenting solution methods used; and finally some future perspectives about this topic are considered.

A REVIEW AND CONTENT ANALYSIS OF MATHEMATICS TEXTBOOKS IN EDUCATIONAL RESEARCH

Directory of Open Access Journals (Sweden)

Cheng Chieh Chang

2017-06-01

Full Text Available Research collected and reviewed a number of empirical studies in the field of educational research regarding the analysis of mathematics textbooks to provide summary and overview the information there in. The questions were identified via Google Scholar and collected from different data sources. A total of 44 papers published from 1953 to 2015 were selected based specific criteria, with 24 articles include in the SSCI database. Descriptive statistics were used to evaluate and interpret the results. A perspective on the learning analysis methods was used to collect studies and showed the mathematics textbooks analyzed were investigated under four themes: The analysis of standards, distributive property, language in mathematics, and others. School’s level which is investigated textbooks: Kindergarten, elementary, junior school, and senior school. Subjects covered in the mathematics textbooks included algebra and arithmetic, geometry, measurement, data analysis and probability, number and operations, among others. Research found the most frequently discussed in perspective on learning was the analysis of the standards and the distributive property (15 studies, the most common subject was number and operations (16 studies, and the highest number in school’s level was elementary school (18 studies. Nevertheless, fewer studies have been found to analyzing mathematics textbooks. Future research can pay attention for the relevant theoretical issues and collaborate studies in more perspective learning analysis.

Cognitive and Neural Correlates of Mathematical Giftedness in Adults and Children: A Review

Directory of Open Access Journals (Sweden)

Timothy Myers

2017-10-01

Full Text Available Most mathematical cognition research has focused on understanding normal adult function and child development as well as mildly and moderately impaired mathematical skill, often labeled developmental dyscalculia and/or mathematical learning disability. In contrast, much less research is available on cognitive and neural correlates of gifted/excellent mathematical knowledge in adults and children. In order to facilitate further inquiry into this area, here we review 40 available studies, which examine the cognitive and neural basis of gifted mathematics. Studies associated a large number of cognitive factors with gifted mathematics, with spatial processing and working memory being the most frequently identified contributors. However, the current literature suffers from low statistical power, which most probably contributes to variability across findings. Other major shortcomings include failing to establish domain and stimulus specificity of findings, suggesting causation without sufficient evidence and the frequent use of invalid backward inference in neuro-imaging studies. Future studies must increase statistical power and neuro-imaging studies must rely on supporting behavioral data when interpreting findings. Studies should investigate the factors shown to correlate with math giftedness in a more specific manner and determine exactly how individual factors may contribute to gifted math ability.

Some unsolved problems in discrete mathematics and mathematical cybernetics

Energy Technology Data Exchange (ETDEWEB)

Korshunov, Aleksei D [S.L. Sobolev Institute for Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk (Russian Federation)

2009-10-31

There are many unsolved problems in discrete mathematics and mathematical cybernetics. Writing a comprehensive survey of such problems involves great difficulties. First, such problems are rather numerous and varied. Second, they greatly differ from each other in degree of completeness of their solution. Therefore, even a comprehensive survey should not attempt to cover the whole variety of such problems; only the most important and significant problems should be reviewed. An impersonal choice of problems to include is quite hard. This paper includes 13 unsolved problems related to combinatorial mathematics and computational complexity theory. The problems selected give an indication of the author's studies for 50 years; for this reason, the choice of the problems reviewed here is, to some extent, subjective. At the same time, these problems are very difficult and quite important for discrete mathematics and mathematical cybernetics. Bibliography: 74 items.

Optimizing radiology peer review: a mathematical model for selecting future cases based on prior errors.

Science.gov (United States)

Sheu, Yun Robert; Feder, Elie; Balsim, Igor; Levin, Victor F; Bleicher, Andrew G; Branstetter, Barton F

2010-06-01

Peer review is an essential process for physicians because it facilitates improved quality of patient care and continuing physician learning and improvement. However, peer review often is not well received by radiologists who note that it is time intensive, is subjective, and lacks a demonstrable impact on patient care. Current advances in peer review include the RADPEER() system, with its standardization of discrepancies and incorporation of the peer-review process into the PACS itself. The purpose of this study was to build on RADPEER and similar systems by using a mathematical model to optimally select the types of cases to be reviewed, for each radiologist undergoing review, on the basis of the past frequency of interpretive error, the likelihood of morbidity from an error, the financial cost of an error, and the time required for the reviewing radiologist to interpret the study. The investigators compiled 612,890 preliminary radiology reports authored by residents and attending radiologists at a large tertiary care medical center from 1999 to 2004. Discrepancies between preliminary and final interpretations were classified by severity and validated by repeat review of major discrepancies. A mathematical model was then used to calculate, for each author of a preliminary report, the combined morbidity and financial costs of expected errors across 3 modalities (MRI, CT, and conventional radiography) and 4 departmental divisions (neuroradiology, abdominal imaging, musculoskeletal imaging, and thoracic imaging). A customized report was generated for each on-call radiologist that determined the category (modality and body part) with the highest total cost function. A universal total cost based on probability data from all radiologists was also compiled. The use of mathematical models to guide case selection could optimize the efficiency and effectiveness of physician time spent on peer review and produce more concrete and meaningful feedback to radiologists

A Systematic Review of the Literature on Mathematics Manipulatives to Support Students with Disabilities

Science.gov (United States)

Bouck, Emily C.; Park, Jiyoon

2018-01-01

Manipulatives are considered a common tool for mathematics teaching and learning, for both students with and without disabilities. Yet, a systematic review of the current state of research regarding manipulatives for students with disabilities did not exist prior to this article. This manuscript presents a systematic review of the literature…

Mathematics without boundaries surveys in pure mathematics

CERN Document Server

Pardalos, Panos

2014-01-01

The contributions in this volume have been written by eminent scientists from the international mathematical community and present significant advances in several theories, methods and problems of Mathematical Analysis, Discrete Mathematics, Geometry and their Applications. The chapters focus on both old and recent developments in Functional Analysis, Harmonic Analysis, Complex Analysis, Operator Theory, Combinatorics, Functional Equations, Differential Equations as well as a variety of Applications. The book also contains some review works, which could prove particularly useful for a broader audience of readers in Mathematical Sciences, and especially to graduate students looking for the  latest information.

A review of mathematical models in economic environmental problems

DEFF Research Database (Denmark)

Nahorski, Z.; Ravn, H.F.

2000-01-01

The paper presents a review of mathematical models used,in economic analysis of environmental problems. This area of research combines macroeconomic models of growth, as dependent on capital, labour, resources, etc., with environmental models describing such phenomena like natural resources...... exhaustion or pollution accumulation and degradation. In simpler cases the models can be treated analytically and the utility function can be optimized using, e.g., such tools as the maximum principle. In more complicated cases calculation of the optimal environmental policies requires a computer solution....

Mathematics

CERN Document Server

Eringen, A Cemal

2013-01-01

Continuum Physics: Volume 1 - Mathematics is a collection of papers that discusses certain selected mathematical methods used in the study of continuum physics. Papers in this collection deal with developments in mathematics in continuum physics and its applications such as, group theory functional analysis, theory of invariants, and stochastic processes. Part I explains tensor analysis, including the geometry of subspaces and the geometry of Finsler. Part II discusses group theory, which also covers lattices, morphisms, and crystallographic groups. Part III reviews the theory of invariants th

Mathematics, anxiety, and the brain.

Science.gov (United States)

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

2017-05-24

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

Learning mathematics in two dimensions: a review and look ahead at teaching and learning early childhood mathematics with children's literature.

Science.gov (United States)

Flevares, Lucia M; Schiff, Jamie R

2014-01-01

In the past 25 years an identifiable interest in using children's literature in mathematics learning emerged (Clyne and Griffiths, 1991; Welchman-Tischler, 1992; Hong, 1996; Hellwig etal., 2000; Haury, 2001). We critically review the rationales given for the use of picture books in mathematics learning, with a special focus on geometry due to its underrepresentation in this body of literature and the need for greater focus on this topic. The benefits and effectiveness of using picture books for children's mathematics learning and interest have been documented (Hong, 1996; O'Neill etal., 2004; Young-Loveridge, 2004). For geometry, although much learning of shape ideas should be hands-on, two-dimensional figures are essential to develop children's understanding of plane geometry. Books may effectively engage pre-literate children with plane shapes (van den Heuvel-Panhuizen and van den Boogaard, 2008; Skoumpourdi and Mpakopoulou, 2011) and shapes as gestalt wholes or prototypes (van Hiele, 1986; Clements etal., 1999; Hannibal, 1999). We review several guidelines and evaluative criteria for book selection, including Cianciolo (2000), Schiro (1997), Hunsader (2004), and van den Heuvel-Panhuizen and Elia (2012). Geometry concepts have proven challenging for young students, but their difficulties may stem, in part, from inadequate teacher training and professional development (Clements and Sarama, 2000; Chard etal., 2008) which lead to misconceptions (Oberdorf and Taylor-Cox, 1999; Inan and Dogan-Temur, 2010). Using picture books in teacher training may be an inviting way for early childhood teachers to enhance their own knowledge. We will examine the literature for guidance on incorporating children's literature into teacher training. In closing we will outline a comprehensive, multi-pronged agenda for best instructional practices for selection and use of children's books in mathematics activities and for teacher training.

A Review of Mathematical Learning Disabilities in Children with Fragile X Syndrome

Science.gov (United States)

Murphy, Melissa M.

2009-01-01

The prevalence rate of mathematical learning disabilities (MLD) among children with fragile X syndrome who do not meet criteria for intellectual and developmental disabilities ([approximately equal to] 50% of female children) exceeds the rate reported in the general population. The purpose of this article is two-fold: (1) to review the findings on…

Women of Color in Mathematics, Science & Engineering: A Review of the Literature.

Science.gov (United States)

Clewell, Beatriz Chu; Anderson, Bernice

This review of the literature on women of color in mathematics, science, and engineering helps define the need for a national agenda for equity in these fields sponsored by the Educational Equity Policy Studies Program of the Center for Women Policy Studies, and for a comprehensive research program that examines barriers to the participation of…

Clinical implications of in silico mathematical modeling for glioblastoma: a critical review.

Science.gov (United States)

Protopapa, Maria; Zygogianni, Anna; Stamatakos, Georgios S; Antypas, Christos; Armpilia, Christina; Uzunoglu, Nikolaos K; Kouloulias, Vassilis

2018-01-01

Glioblastoma remains a clinical challenge in spite of years of extensive research. Novel approaches are needed in order to integrate the existing knowledge. This is the potential role of mathematical oncology. This paper reviews mathematical models on glioblastoma from the clinical doctor's point of view, with focus on 3D modeling approaches of radiation response of in vivo glioblastomas based on contemporary imaging techniques. As these models aim to provide a clinically useful tool in the era of personalized medicine, the integration of the latest advances in molecular and imaging science and in clinical practice by the in silico models is crucial for their clinical relevance. Our aim is to indicate areas of GBM research that have not yet been addressed by in silico models and to point out evidence that has come up from in silico experiments, which may be worth considering in the clinic. This review examines how close these models have come in predicting the outcome of treatment protocols and in shaping the future of radiotherapy treatments.

Learning mathematics in two dimensions: a review and look ahead at teaching and learning early childhood mathematics with children’s literature

Science.gov (United States)

Flevares, Lucia M.; Schiff, Jamie R.

2014-01-01

In the past 25 years an identifiable interest in using children’s literature in mathematics learning emerged (Clyne and Griffiths, 1991; Welchman-Tischler, 1992; Hong, 1996; Hellwig etal., 2000; Haury, 2001). We critically review the rationales given for the use of picture books in mathematics learning, with a special focus on geometry due to its underrepresentation in this body of literature and the need for greater focus on this topic. The benefits and effectiveness of using picture books for children’s mathematics learning and interest have been documented (Hong, 1996; O’Neill etal., 2004; Young-Loveridge, 2004). For geometry, although much learning of shape ideas should be hands-on, two-dimensional figures are essential to develop children’s understanding of plane geometry. Books may effectively engage pre-literate children with plane shapes (van den Heuvel-Panhuizen and van den Boogaard, 2008; Skoumpourdi and Mpakopoulou, 2011) and shapes as gestalt wholes or prototypes (van Hiele, 1986; Clements etal., 1999; Hannibal, 1999). We review several guidelines and evaluative criteria for book selection, including Cianciolo (2000), Schiro (1997), Hunsader (2004), and van den Heuvel-Panhuizen and Elia (2012). Geometry concepts have proven challenging for young students, but their difficulties may stem, in part, from inadequate teacher training and professional development (Clements and Sarama, 2000; Chard etal., 2008) which lead to misconceptions (Oberdorf and Taylor-Cox, 1999; Inan and Dogan-Temur, 2010). Using picture books in teacher training may be an inviting way for early childhood teachers to enhance their own knowledge. We will examine the literature for guidance on incorporating children’s literature into teacher training. In closing we will outline a comprehensive, multi-pronged agenda for best instructional practices for selection and use of children’s books in mathematics activities and for teacher training. PMID:24904475

Learning Mathematics in Two Dimensions: A Review and Look Ahead at Teaching and Learning Early Childhood Mathematics with Children’s Literature

Directory of Open Access Journals (Sweden)

Lucia M. Flevares

2014-05-01

Full Text Available In the past 25 years an identifiable interest in using children’s literature in mathematics learning emerged (Clyne & Griffiths, 1991; Haury, 2001; Hellwig, Monroe, & Jacobs, 2000; Hong, 1996; Welchman-Tischler, 1992. We critically review the rationales given for the use of picture books in mathematics learning, with a special focus on geometry due to its underrepresentation in this body of literature and the need for greater focus on this topic. The benefits and effectiveness of using picture books for children’s mathematics learning and interest have been documented (Hong, 1996; O’Neill, Pearce & Pick, 2004; Young-Loveridge, 2004. For geometry, although much learning of shape ideas should be hands-on, two-dimensional figures are essential to develop children’s understanding of plane geometry. Books may effectively engage pre-literate children with plane shapes (Skoumpourdi & Mpakopoulou, 2011; van den Heuvel-Panhuizen & Van den Boogaard, 2008 and shapes as gestalt wholes or prototypes (Clements et al., 1999; Hannibal, 1999; van Hiele, 1986. We review several guidelines and evaluative criteria for book selection, including Cianciolo (2000, Schiro (1997, Hunsader (2004 and Van den Heuvel-Panhuizen and Elia (2012. Geometry concepts have proven challenging for young students, but their difficulties may stem, in part, from inadequate teacher training and professional development (Chard, Baker & Clarke, 2008; Clements & Sarama, 2000 which lead to misconceptions (Inan & Dogan-Temur, 2010; Oberdorf & Taylor-Cox, 1999. Using picture books in teacher training may be an inviting way for early childhood teachers to enhance their own knowledge. We will examine the literature for guidance on incorporating children’s literature into teacher training. In closing we will outline a comprehensive, multi-pronged agenda for best instructional practices for selection and use of children’s books in mathematics activities and for teacher training.

A review of mathematical modeling and simulation of controlled-release fertilizers.

Science.gov (United States)

Irfan, Sayed Ameenuddin; Razali, Radzuan; KuShaari, KuZilati; Mansor, Nurlidia; Azeem, Babar; Ford Versypt, Ashlee N

2018-02-10

Nutrients released into soils from uncoated fertilizer granules are lost continuously due to volatilization, leaching, denitrification, and surface run-off. These issues have caused economic loss due to low nutrient absorption efficiency and environmental pollution due to hazardous emissions and water eutrophication. Controlled-release fertilizers (CRFs) can change the release kinetics of the fertilizer nutrients through an abatement strategy to offset these issues by providing the fertilizer content in synchrony with the metabolic needs of the plants. Parametric analysis of release characteristics of CRFs is of paramount importance for the design and development of new CRFs. However, the experimental approaches are not only time consuming, but they are also cumbersome and expensive. Scientists have introduced mathematical modeling techniques to predict the release of nutrients from the CRFs to elucidate fundamental understanding of the dynamics of the release processes and to design new CRFs in a shorter time and with relatively lower cost. This paper reviews and critically analyzes the latest developments in the mathematical modeling and simulation techniques that have been reported for the characteristics and mechanisms of nutrient release from CRFs. The scope of this review includes the modeling and simulations techniques used for coated, controlled-release fertilizers. Copyright © 2017 Elsevier B.V. All rights reserved.

Journal of applied mathematics

National Research Council Canada - National Science Library

2001-01-01

"[The] Journal of Applied Mathematics is a refereed journal devoted to the publication of original research papers and review articles in all areas of applied, computational, and industrial mathematics...

Applied mathematics

CERN Document Server

Logan, J David

2013-01-01

Praise for the Third Edition"Future mathematicians, scientists, and engineers should find the book to be an excellent introductory text for coursework or self-study as well as worth its shelf space for reference." -MAA Reviews Applied Mathematics, Fourth Edition is a thoroughly updated and revised edition on the applications of modeling and analyzing natural, social, and technological processes. The book covers a wide range of key topics in mathematical methods and modeling and highlights the connections between mathematics and the applied and nat

Problem-Based Learning in K-8 Mathematics and Science Education: A Literature Review

Science.gov (United States)

Merritt, Joi; Lee, Mi Yeon; Rillero, Peter; Kinach, Barbara M.

2017-01-01

This systematic literature review was conducted to explore the effectiveness of problem-based and project-based learning (PBL) implemented with students in early elementary to grade 8 (ages 3-14) in mathematics and science classrooms. Nine studies met the following inclusion criteria: (a) focus on PBL, (b) experimental study, (c) kindergarten to…

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.

Computational physics and applied mathematics capability review June 8-10, 2010

Energy Technology Data Exchange (ETDEWEB)

Lee, Stephen R [Los Alamos National Laboratory

2010-01-01

Los Alamos National Laboratory will review its Computational Physics and Applied Mathematics (CPAM) capabilities in 2010. The goals of capability reviews are to assess the quality of science, technology, and engineering (STE) performed by the capability, evaluate the integration of this capability across the Laboratory and within the scientific community, examine the relevance of this capability to the Laboratory's programs, and provide advice on the current and future directions of this capability. This is the first such review for CPAM, which has a long and unique history at the Laboratory, starting from the inception of the Laboratory in 1943. The CPAM capability covers an extremely broad technical area at Los Alamos, encompassing a wide array of disciplines, research topics, and organizations. A vast array of technical disciplines and activities are included in this capability, from general numerical modeling, to coupled multi-physics simulations, to detailed domain science activities in mathematics, methods, and algorithms. The CPAM capability involves over 12 different technical divisions and a majority of our programmatic and scientific activities. To make this large scope tractable, the CPAM capability is broken into the following six technical 'themes.' These themes represent technical slices through the CPAM capability and collect critical core competencies of the Laboratory, each of which contributes to the capability (and each of which is divided into multiple additional elements in the detailed descriptions of the themes in subsequent sections), as follows. Theme 1: Computational Fluid Dynamics - This theme speaks to the vast array of scientific capabilities for the simulation of fluids under shocks, low-speed flow, and turbulent conditions - which are key, historical, and fundamental strengths of the Laboratory. Theme 2: Partial Differential Equations - The technical scope of this theme is the applied mathematics and numerical solution

Secondary Students' Perceptions of an Interactive Mathematics Review Program: An Action Research Study

Science.gov (United States)

Wingard, Crystal Burroughs

2017-01-01

The present action research study describes an Interactive Mathematics Review Program (IMRP) developed by the participant-researcher to enable remedial algebra students to learn in a cooperative classroom with pedagogy that promoted collaboration and hands-on, active learning. Data are comprised of surveys, field notes, semi-structured interviews,…

A Review of New Mathematics Curriculum Materials.

Science.gov (United States)

Vanderlin, Carl J., Jr.

This manual outlines the nature of some of the major curriculum projects in mathematics and lists materials which are available from these projects. An introductory statement concerning the history and philosophy of each program is indicated. The curriculum projects reported on are: (1) Boston College Mathematics Institute, (2) Cambridge…

Complex manifolds

CERN Document Server

Morrow, James

2006-01-01

This book, a revision and organization of lectures given by Kodaira at Stanford University in 1965-66, is an excellent, well-written introduction to the study of abstract complex (analytic) manifolds-a subject that began in the late 1940's and early 1950's. It is largely self-contained, except for some standard results about elliptic partial differential equations, for which complete references are given. -D. C. Spencer, MathSciNet The book under review is the faithful reprint of the original edition of one of the most influential textbooks in modern complex analysis and geometry. The classic

Peak Vertical Ground Reaction Force during Two-Leg Landing: A Systematic Review and Mathematical Modeling

Directory of Open Access Journals (Sweden)

Wenxin Niu

2014-01-01

Full Text Available Objectives. (1 To systematically review peak vertical ground reaction force (PvGRF during two-leg drop landing from specific drop height (DH, (2 to construct a mathematical model describing correlations between PvGRF and DH, and (3 to analyze the effects of some factors on the pooled PvGRF regardless of DH. Methods. A computerized bibliographical search was conducted to extract PvGRF data on a single foot when participants landed with both feet from various DHs. An innovative mathematical model was constructed to analyze effects of gender, landing type, shoes, ankle stabilizers, surface stiffness and sample frequency on PvGRF based on the pooled data. Results. Pooled PvGRF and DH data of 26 articles showed that the square root function fits their relationship well. An experimental validation was also done on the regression equation for the medicum frequency. The PvGRF was not significantly affected by surface stiffness, but was significantly higher in men than women, the platform than suspended landing, the barefoot than shod condition, and ankle stabilizer than control condition, and higher than lower frequencies. Conclusions. The PvGRF and root DH showed a linear relationship. The mathematical modeling method with systematic review is helpful to analyze the influence factors during landing movement without considering DH.

Mathematical Learning Disabilities in Children with 22q11.2 Deletion Syndrome: A Review

Science.gov (United States)

De Smedt, Bert; Swillen, Ann; Verschaffel, Lieven; Ghesquiere, Pol

2009-01-01

Mathematical learning disabilities (MLD) occur frequently in children with specific genetic disorders, like Turner syndrome, fragile X syndrome and neurofibromatosis. This review focuses on MLD in children with chromosome 22q11.2 deletion syndrome (22q11DS). This syndrome is the most common known microdeletion syndrome with a prevalence of at…

Nuclear medicine and mathematics

Energy Technology Data Exchange (ETDEWEB)

Pedroso de Lima, J.J. [Dept. de Biofisica e Proc. de Imagem, IBILI - Faculdade de Medicina, Coimbra (Portugal)

1996-06-01

The purpose of this review is not to present a comprehensive description of all the mathematical tools used in nuclear medicine, but to emphasize the importance of the mathematical method in nuclear medicine and to elucidate some of the mathematical concepts currently used. We can distinguish three different areas in which mathematical support has been offered to nuclear medicine: Physiology, methodology and data processing. Nevertheless, the boundaries between these areas can be indistinct. It is impossible in a single article to give even an idea of the extent and complexity of the procedures currently usede in nuclear medicine, such as image processing, reconstruction from projections and artificial intelligence. These disciplines do not belong to nuclear medicine: They are already branches of engineering, and my interest will reside simply in revealing a little of the elegance and the fantastic potential of these new `allies` of nuclear medicine. In this review the mathematics of physiological interpretation and methodology are considered together in the same section. General aspects of data-processing methods, including image processing and artificial intelligence, are briefly analysed. The mathematical tools that are most often used to assist the interpretation of biological phenomena in nuclear medicine are considered; these include convolution and deconvolution methods, Fourier analysis, factorial analysis and neural networking. (orig.)

Nuclear medicine and mathematics

International Nuclear Information System (INIS)

Pedroso de Lima, J.J.

1996-01-01

The purpose of this review is not to present a comprehensive description of all the mathematical tools used in nuclear medicine, but to emphasize the importance of the mathematical method in nuclear medicine and to elucidate some of the mathematical concepts currently used. We can distinguish three different areas in which mathematical support has been offered to nuclear medicine: Physiology, methodology and data processing. Nevertheless, the boundaries between these areas can be indistinct. It is impossible in a single article to give even an idea of the extent and complexity of the procedures currently usede in nuclear medicine, such as image processing, reconstruction from projections and artificial intelligence. These disciplines do not belong to nuclear medicine: They are already branches of engineering, and my interest will reside simply in revealing a little of the elegance and the fantastic potential of these new 'allies' of nuclear medicine. In this review the mathematics of physiological interpretation and methodology are considered together in the same section. General aspects of data-processing methods, including image processing and artificial intelligence, are briefly analysed. The mathematical tools that are most often used to assist the interpretation of biological phenomena in nuclear medicine are considered; these include convolution and deconvolution methods, Fourier analysis, factorial analysis and neural networking. (orig.)

Mathematical and Metaheuristic Applications in Design Optimization of Steel Frame Structures: An Extensive Review

Directory of Open Access Journals (Sweden)

Mehmet Polat Saka

2013-01-01

Full Text Available The type of mathematical modeling selected for the optimum design problems of steel skeletal frames affects the size and mathematical complexity of the programming problem obtained. Survey on the structural optimization literature reveals that there are basically two types of design optimization formulation. In the first type only cross sectional properties of frame members are taken as design variables. In such formulation when the values of design variables change during design cycles, it becomes necessary to analyze the structure and update the response of steel frame to the external loading. Structural analysis in this type is a complementary part of the design process. In the second type joint coordinates are also treated as design variables in addition to the cross sectional properties of members. Such formulation eliminates the necessity of carrying out structural analysis in every design cycle. The values of the joint displacements are determined by the optimization techniques in addition to cross sectional properties. The structural optimization literature contains structural design algorithms that make use of both type of formulation. In this study a review is carried out on mathematical and metaheuristic algorithms where the effect of the mathematical modeling on the efficiency of these algorithms is discussed.

pp ii Brain, behaviour and mathematics: Are we using the right approaches? [review article

Science.gov (United States)

Perez Velazquez, Jose Luis

2005-12-01

Mathematics are used in biological sciences mostly as a quantifying tool, for it is the science of numbers after all. There is a long-standing interest in the application of mathematical methods and concepts to neuroscience in attempts to decipher brain activity. While there has been a very wide use of mathematical/physical methodologies, less effort has been made to formulate a comprehensive and integrative theory of brain function. This review concentrates on recent developments, uses and abuses of mathematical formalisms and techniques that are being applied in brain research, particularly the current trend of using dynamical system theory to unravel the global, collective dynamics of brain activity. It is worth emphasising that the theoretician-neuroscientist, eager to apply mathematical analysis to neuronal recordings, has to consider carefully some crucial anatomo-physiological assumptions, that may not be as accurate as the specific methods require. On the other hand, the experimentalist neuro-physicist, with an inclination to implement mathematical thoughts in brain science, has to make an effort to comprehend the bases of the theoretical concepts that can be used as frameworks or as analysis methods of brain electrophysiological recordings, and to critically inspect the accuracy of the interpretations of the results based on the neurophysiological ground. It is hoped that this brief overview of anatomical and physiological presumptions and their relation to theoretical paradigms will help clarify some particular points of interest in current trends in brain science, and may provoke further reflections on how certain or uncertain it is to conceptualise brain function based on these theoretical frameworks, if the physiological and experimental constraints are not as accurate as the models prescribe.

Episodes in the mathematics of medieval Islam

CERN Document Server

Berggren, J L

1986-01-01

From the reviews: The book is, in spite of the author's more modest claims, an introductory survey of main developments in those disciplines which were particularly important in Medieval Islamic mathematics...No knowledge of mathematics (or of the history of mathematics) beyond normal high-school level is presupposed, and everything required beyond that (be it Apollonian theory of conics or the definitions of celestial circles) is explained carefully and clearly. Scattered throughout the work are a number of lucid remarks on the character of Islamic mathematics or of mathematical work in general. The book will hence not only be an excellent textbook for the teaching of the history of mathematics but also for the liberal art aspect of mathematics teaching in general. - Jens Høyrup, Mathematical Reviews ...as a textbook, this work is highly commendable...It is definitely the product of a skillful mathematician who has collected over the years a reasonably large number of interesting problems from medieval Arab...

Review on mathematical basis for thermal conduction equation

Energy Technology Data Exchange (ETDEWEB)

Park, D. G.; Kim, H. M

2007-10-15

In the view point of thermal conductivity measurement technology, It is very useful to understand mathematical theory of thermal conduction equation in order to evaluation of measurement data and to solve diverse technical problem in measurement. To approach this mathematical theory, thermal conduction equation is derived by Fourier thermal conduction law. Since thermal conduction equation depends on the Lapacian operator basically, mathematical meaning of Lapalacian and various diffusion equation including Laplacian have been studied. Stum-Liouville problem and Bessel function were studied in this report to understand analytical solution of various diffusion equation.

Review on mathematical basis for thermal conduction equation

International Nuclear Information System (INIS)

Park, D. G.; Kim, H. M.

2007-10-01

In the view point of thermal conductivity measurement technology, It is very useful to understand mathematical theory of thermal conduction equation in order to evaluation of measurement data and to solve diverse technical problem in measurement. To approach this mathematical theory, thermal conduction equation is derived by Fourier thermal conduction law. Since thermal conduction equation depends on the Lapacian operator basically, mathematical meaning of Lapalacian and various diffusion equation including Laplacian have been studied. Stum-Liouville problem and Bessel function were studied in this report to understand analytical solution of various diffusion equation

Mathematical Modeling: A Bridge to STEM Education

Science.gov (United States)

Kertil, Mahmut; Gurel, Cem

2016-01-01

The purpose of this study is making a theoretical discussion on the relationship between mathematical modeling and integrated STEM education. First of all, STEM education perspective and the construct of mathematical modeling in mathematics education is introduced. A review of literature is provided on how mathematical modeling literature may…

Bingo! Select Games for Mathematical Thinking

Science.gov (United States)

Jackson, Christa; Taylor, Cynthia; Buchheister, Kelley

2013-01-01

Games can both generate excitement among students and motivate them to participate in mathematics. Although games have been used primarily to "review" mathematical concepts at the middle school level, games should, and often do, have other instructional purposes. When teachers use mathematical games as an instructional strategy, they are…

Chinese Number Words, Culture, and Mathematics Learning

Science.gov (United States)

Ng, Sharon Sui Ngan; Rao, Nirmala

2010-01-01

This review evaluates the role of language--specifically, the Chinese-based system of number words and the simplicity of Chinese mathematical terms--in explaining the relatively superior performance of Chinese and other East Asian students in cross-national studies of mathematics achievement. Relevant research is critically reviewed focusing on…

The graphics calculator in mathematics education: A critical review of recent research

Science.gov (United States)

Penglase, Marina; Arnold, Stephen

1996-04-01

The graphics calculator, sometimes referred to as the "super calculator," has sparked great interest among mathematics educators. Considered by many to be a tool which has the potential to revolutionise mathematics education, a significant amount of research has been conducted into its effectiveness as a tool for instruction and learning within precalculus and calculus courses, specifically in the study of functions, graphing and modelling. Some results suggest that these devices (a) can facilitate the learning of functions and graphing concepts and the development of spatial visualisation skills; (b) promote mathematical investigation and exploration; and (c) encourage a shift in emphasis from algebraic manipulation and proof to graphical investigation and examination of the relationship between graphical, algebraic and geometric representations. Other studies, however, indicate that there is still a need for manipulative techniques in the learning of function and graphing concepts, that the use of graphics calculators may not facilitate the learning of particular precalculus topics, and that some "de-skilling" may occur, especially among males. It is the contention of this paper, however, that much of the research in this new and important field fails to provide clear guidance or even to inform debate in adequate ways regarding the role of graphics calculators in mathematics teaching and learning. By failing to distinguish the role of the tool from that of the instructional process, many studies reviewed could be more appropriately classified as "program evaluations" rather than as research on the graphics calculator per se. Further, claims regarding the effectiveness of the graphics calculator as a tool for learning frequently fail to recognise that judgments of effectiveness result directly from existing assumptions regarding both assessment practice and student "achievement."

Mathematical methods for physical and analytical chemistry

CERN Document Server

Goodson, David Z

2011-01-01

Mathematical Methods for Physical and Analytical Chemistry presents mathematical and statistical methods to students of chemistry at the intermediate, post-calculus level. The content includes a review of general calculus; a review of numerical techniques often omitted from calculus courses, such as cubic splines and Newton's method; a detailed treatment of statistical methods for experimental data analysis; complex numbers; extrapolation; linear algebra; and differential equations. With numerous example problems and helpful anecdotes, this text gives chemistry students the mathematical

An Investigation of the Relative Effectiveness of the Basic Mathematics Review Program at Essex Community College.

Science.gov (United States)

Bloomberg, Jerome

Basic Mathematics Review (BMR) is a remedial non-credit course at Essex Community College (Maryland) being taught on an individualized basis. Following diagnostic testing and placement, instruction utilizes programmed materials, tutors, and self-tests. Evaluation of the new individualized BMR and comparison with the traditional remedial course…

Mathematical tools for physicists

International Nuclear Information System (INIS)

Trigg, G.L.

2005-01-01

Mathematical Tools for Physisists is a unique collection of 18 review articles, each one written by a renowned expert of its field. Their professional style will be beneficial for advanced students as well as for the scientist at work. The first may find a comprehensive introduction while the latter use it as a quick reference. Great attention was paid to ensuring fast access to the information, and each carefully reviewed article includes a glossary of terms and a guide to further reading. The contributions range from fundamental methods right up to the latest applications, including: - Algebraic Methods - Analytic Methods - Fourier and Other Mathematical Transforms - Fractal Geometry - Geometrical Methods - Green's Functions - Group Theory - Mathematical Modeling - Monte Carlo Methods - Numerical Methods - Perturbation Methods - Quantum Computation - Quantum Logic - Special Functions - Stochastic Processes - Symmetries and Conservation Laws - Topology - Variational Methods. (orig.)

A Review of Multi-Sensory Technologies in a Science, Technology, Engineering, Arts and Mathematics (STEAM) Classroom

Science.gov (United States)

Taljaard, Johann

2016-01-01

This article reviews the literature on multi-sensory technology and, in particular, looks at answering the question: "What multi-sensory technologies are available to use in a science, technology, engineering, arts and mathematics (STEAM) classroom, and do they affect student engagement and learning outcomes?" Here engagement is defined…

Mathematical analysis of complex cellular activity

CERN Document Server

Bertram, Richard; Teka, Wondimu; Vo, Theodore; Wechselberger, Martin; Kirk, Vivien; Sneyd, James

2015-01-01

This book contains two review articles on mathematical physiology that deal with closely related topics but were written and can be read independently. The first article reviews the basic theory of calcium oscillations (common to almost all cell types), including spatio-temporal behaviors such as waves. The second article uses, and expands on, much of this basic theory to show how the interaction of cytosolic calcium oscillators with membrane ion channels can result in highly complex patterns of electrical spiking. Through these examples one can see clearly how multiple oscillatory processes interact within a cell, and how mathematical methods can be used to understand such interactions better. The two reviews provide excellent examples of how mathematics and physiology can learn from each other, and work jointly towards a better understanding of complex cellular processes. Review 1: Richard Bertram, Joel Tabak, Wondimu Teka, Theodore Vo, Martin Wechselberger: Geometric Singular Perturbation Analysis of Burst...

Mathematics for the liberal arts

CERN Document Server

Brown, Jason I

2014-01-01

The Math in Your Life Health, Safety, and Mathematics Found in Translation The Essentials of Conversion Making Sense of Your World with Statistics Summarizing Data with a Few Good Numbers Estimating Unknowns Leading You Down the Garden Path with Statistics Visualizing with Mathematics Seeing Data A Graph Is Worth a Thousand Words Money and Risk Money - Now or Later Risk Taking and Probability The Life in Your Math! Deciding to Make the Best Decisions Making the Right Choices for You Game Theory - Coming Out on Top Making Joint Decisions Art Imitating Math The Math that Makes the Art Believing What You See (or Not) The Mathematics of Sound (and the Sound of Mathematics) The Mathematics of Listening The Mathematics of Composing Solving Musical Mysteries with MSI (Math Scene Investigations) Late Night Mathematics - Humor and Philosophy Laughing with Mathematics The Limits of Mathematics Bibliography Index Review questions appear at the end of each chapter.

The Ability of Students’ Mathematical Proof in Determining the Validity of Argument Reviewed from Gender Differences

Science.gov (United States)

Feriyanto

2018-01-01

This research aims to describe the ability of students’ mathematical proof in determining the validity of argument reviewed from gender differences. The subjects of this research were one male and one female student of the fifth semester of Mathematic Education study program. The subjects were selected based on the highest mathematics ability which was assesed from their previous assignments and tests. In addition, the communication ability of the subjects was also considered in order to facilitate the researcher in conducting interviews. Based on the result of the test with direct and indirect proof, it could be concluded that the subjects were able to: 1) mention all facts/premises and write about what should be shown (conclusion) in direct proof and write additional premise in indirect proof; 2) connect facts/premises to concepts which must be mastered; 3) use equivalent concept to manipulate and organize the proof; 4) use the concept of syllogism and tollens mode to obtain the desired conclusion; 5) construct mathematical evidence systematically, and logically; 6) complement the reason for each step appropriately. The difference was that the male subject wrote the final conclusion, while the female subject did not write the final conclusion on the proof.

Mathematical aspects of field quantization. Quantum electrodynamics

International Nuclear Information System (INIS)

Bongaarts, P.J.M.

1983-01-01

Fundamental mathematical aspects of quantum field theory are discussed. A brief review of various approaches to mathematical problems of quantum electrodynamics is given, preceded by a more extensive account of the development of ideas on the mathematical nature of quantum fields in general, providing an appropriate historical context. (author)

Gender and participation in mathematics and further mathematics A-levels: a literature review for the Further Mathematics Support Programme

OpenAIRE

Smith, Cathy

2014-01-01

In preparing this report I have considered evidence from over 60 documents that relate to raising girls’ participation in mathematics. These include published research papers and reports compiled by expert bodies that present an evidence base. Although research specifically addressing Further Mathematics A-level is rare, the last ten years have seen considerable efforts to synthesise and update knowledge from different research perspectives about the relationship between gender...

Mathematical models used to inform study design or surveillance systems in infectious diseases: a systematic review.

Science.gov (United States)

Herzog, Sereina A; Blaizot, Stéphanie; Hens, Niel

2017-12-18

Mathematical models offer the possibility to investigate the infectious disease dynamics over time and may help in informing design of studies. A systematic review was performed in order to determine to what extent mathematical models have been incorporated into the process of planning studies and hence inform study design for infectious diseases transmitted between humans and/or animals. We searched Ovid Medline and two trial registry platforms (Cochrane, WHO) using search terms related to infection, mathematical model, and study design from the earliest dates to October 2016. Eligible publications and registered trials included mathematical models (compartmental, individual-based, or Markov) which were described and used to inform the design of infectious disease studies. We extracted information about the investigated infection, population, model characteristics, and study design. We identified 28 unique publications but no registered trials. Focusing on compartmental and individual-based models we found 12 observational/surveillance studies and 11 clinical trials. Infections studied were equally animal and human infectious diseases for the observational/surveillance studies, while all but one between humans for clinical trials. The mathematical models were used to inform, amongst other things, the required sample size (n = 16), the statistical power (n = 9), the frequency at which samples should be taken (n = 6), and from whom (n = 6). Despite the fact that mathematical models have been advocated to be used at the planning stage of studies or surveillance systems, they are used scarcely. With only one exception, the publications described theoretical studies, hence, not being utilised in real studies.

The Chicken or the Egg? The Direction of the Relationship Between Mathematics Anxiety and Mathematics Performance.

Science.gov (United States)

Carey, Emma; Hill, Francesca; Devine, Amy; Szücs, Dénes

2015-01-01

This review considers the two possible causal directions between mathematics anxiety (MA) and poor mathematics performance. Either poor maths performance may elicit MA (referred to as the Deficit Theory), or MA may reduce future maths performance (referred to as the Debilitating Anxiety Model). The evidence is in conflict: the Deficit Theory is supported by longitudinal studies and studies of children with mathematical learning disabilities, but the Debilitating Anxiety Model is supported by research which manipulates anxiety levels and observes a change in mathematics performance. It is suggested that this mixture of evidence might indicate a bidirectional relationship between MA and mathematics performance (the Reciprocal Theory), in which MA and mathematics performance can influence one another in a vicious cycle.

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

Parameters for the mathematical modelling of Clostridium difficile acquisition and transmission: a systematic review.

Directory of Open Access Journals (Sweden)

Eroboghene H Otete

Full Text Available INTRODUCTION: Mathematical modelling of Clostridium difficile infection dynamics could contribute to the optimisation of strategies for its prevention and control. The objective of this systematic review was to summarise the available literature specifically identifying the quantitative parameters required for a compartmental mathematical model of Clostridium difficile transmission. METHODS: Six electronic healthcare databases were searched and all screening, data extraction and study quality assessments were undertaken in duplicate. Results were synthesised using a narrative approach. RESULTS: Fifty-four studies met the inclusion criteria. Reproduction numbers for hospital based epidemics were described in two studies with a range from 0.55 to 7. Two studies provided consistent data on incubation periods. For 62% of cases, symptoms occurred in less than 4 weeks (3-28 days after infection. Evidence on contact patterns was identified in four studies but with limited data reported for populating a mathematical model. Two studies, including one without clinically apparent donor-recipient pairs, provided information on serial intervals for household or ward contacts, showing transmission intervals of <1 week in ward based contacts compared to up to 2 months for household contacts. Eight studies reported recovery rates of between 75%-100% for patients who had been treated with either metronidazole or vancomycin. Forty-nine studies gave recurrence rates of between 3% and 49% but were limited by varying definitions of recurrence. No study was found which specifically reported force of infection or net reproduction numbers. CONCLUSIONS: There is currently scant literature overtly citing estimates of the parameters required to inform the quantitative modelling of Clostridium difficile transmission. Further high quality studies to investigate transmission parameters are required, including through review of published epidemiological studies where these

The chicken or the egg? The direction of the relationship between mathematics anxiety and mathematics performance

Directory of Open Access Journals (Sweden)

Emma eCarey

2016-01-01

Full Text Available This review considers the two possible causal directions between mathematics anxiety (MA and poor mathematics performance. Either poor maths performance may elicit MA (referred to as the Deficit Theory, or MA may reduce future maths performance (referred to as the Debilitating Anxiety Model. The evidence is in conflict: the Deficit Theory is supported by longitudinal studies and studies of children with mathematical learning disabilities, but the Debilitating Anxiety Model is supported by research which manipulates anxiety levels and observes a change in mathematics performance. It is suggested that this mixture of evidence might indicate a bidirectional relationship between MA and mathematics performance (the Reciprocal Theory, in which MA and mathematics performance can influence one another in a vicious cycle.

Discrete algorithmic mathematics

CERN Document Server

Maurer, Stephen B

2005-01-01

The exposition is self-contained, complemented by diverse exercises and also accompanied by an introduction to mathematical reasoning … this book is an excellent textbook for a one-semester undergraduate course and it includes a lot of additional material to choose from.-EMS, March 2006In a textbook, it is necessary to select carefully the statements and difficulty of the problems … in this textbook, this is fully achieved … This review considers this book an excellent one.-The Mathematical Gazette, March 2006

The Mathematics of Medical Imaging in the Classroom.

Science.gov (United States)

Funkhouser, Charles P.; Jafari, Farhad; Eubank, William B.

2002-01-01

Presents an integrated exposition of aspects of secondary school mathematics and a medical science specialty. Reviews clinical medical practice and theoretical and empirical literature in mathematics education and radiology to develop and pilot model integrative classroom topics and activities. Suggests mathematical applications in numeration and…

The Chicken or the Egg? The Direction of the Relationship Between Mathematics Anxiety and Mathematics Performance

OpenAIRE

Carey, Emma; Hill, Francesca; Devine, Amy; Sz?cs, D?nes

2016-01-01

This review considers the two possible causal directions between mathematics anxiety (MA) and poor mathematics performance. Either poor maths performance may elicit MA (referred to as the Deficit Theory), or MA may reduce future maths performance (referred to as the Debilitating Anxiety Model). The evidence is in conflict: the Deficit Theory is supported by longitudinal studies and studies of children with mathematical learning disabilities, but the Debilitating Anxiety Model is supported by ...

Research in collegiate mathematics education V

CERN Document Server

Selden, Annie; Harel, Guershon; Hitt, Fernando

2003-01-01

This fifth volume of Research in Collegiate Mathematics Education presents state-of-the-art research on understanding, teaching, and learning mathematics at the post-secondary level. The articles in RCME are peer-reviewed for two major features: (1) advancing our understanding of collegiate mathematics education, and (2) readability by a wide audience of practicing mathematicians interested in issues affecting their own students. This is not a collection of scholarly arcana, but a compilation of useful and informative research regarding the ways our students think about and learn mathematics.

Making Meaning of Creativity and Mathematics Teaching

DEFF Research Database (Denmark)

Misfeldt, Morten

2014-01-01

. One reason is that it is not clear what relation such creative and innovative skills have to mathematics, and how we should teach them. In this paper, I review different conceptions of creativity in mathematics education and investigate what mathematical innovation and creativity “are......Creativity and innovation are important 21st-century skills, and mathematics education contributes to the development of these skills. However, it is far from clear how we as mathematics educators should respond to the need to contribute to our students’ development of creativity and innovation......” in the mathematical classroom. I show how different conceptions of mathematical innovation and creativity dominate different parts of the mathematics education literature, and explain how these differences can be viewed as framing mathematical creativity toward different domains....

Progress in Industrial Mathematics at ECMI 96

DEFF Research Database (Denmark)

mathematicians get inspiration from industrial demands. The European Consortium for Mathematics in Industry aims to create contact between industry and academia, and to promote research in industrial mathematics. This book contains a broad spectrum of mathematics applied to industrial problems. Applied...... mathematics, case studies, and review papers in the following fields are included: Environmental modelling, railway systems, industrial processes, electronics, ships, oil industry, optimization, machine dynamics, fluids in industry. Applied mathematicians and other professionals working in academia...

A review of heat transfer in human tooth--experimental characterization and mathematical modeling.

Science.gov (United States)

Lin, Min; Xu, Feng; Lu, Tian Jian; Bai, Bo Feng

2010-06-01

With rapid advances in modern dentistry, high-energy output instruments (e.g., dental lasers and light polymerizing units) are increasingly employed in dental surgery for applications such as laser assisted tooth ablation, bleaching, hypersensitivity treatment and polymerization of dental restorative materials. Extreme high temperature occurs within the tooth during these treatments, which may induce tooth thermal pain (TTP) sensation. Despite the wide application of these dental treatments, the underlying mechanisms are far from clear. Therefore, there is an urgent need to better understand heat transfer (HT) process in tooth, thermally induced damage of tooth, and the corresponding TTP. This will enhance the design and optimization of clinical treatment strategies. This paper presents the state-of-the-art of the current understanding on HT in tooth, with both experimental study and mathematical modeling reviewed. Limitations of the current experimental and mathematical methodologies are discussed and potential solutions are suggested. Interpretation of TTP in terms of thermally stimulated dentinal fluid flow is also discussed. Copyright (c) 2010 Academy of Dental Materials. All rights reserved.

Challenging Transitions and Crossing Borders: Preparing Novice Mathematics Teacher Educators to Support Novice K-12 Mathematics Teachers

Science.gov (United States)

Yow, Jan A.; Eli, Jennifer A.; Beisiegel, Mary; McCloskey, Andrea; Welder, Rachael M.

2016-01-01

Sixty-nine recently graduated doctoral students in mathematics education completed a survey to determine their perceptions of transitioning from a doctoral program into an academic position at an institution of higher education. Research literature for novice mathematics school teachers was also reviewed to document their experiences transitioning…

Using Two Languages when Learning Mathematics

Science.gov (United States)

Moschkovich, Judit

2007-01-01

This article reviews two sets of research studies from outside of mathematics education to consider how they may be relevant to the study of bilingual mathematics learners using two languages. The first set of studies is psycholinguistics experiments comparing monolinguals and bilinguals using two languages during arithmetic computation (language…

Fundamentals of modern mathematics a practical review

CERN Document Server

MacNeil, David B

2013-01-01

Students and others wishing to know more about the practical side of mathematics will find this volume a highly informative resource. Accessible explanations of important concepts feature worked examples and diagrams. 1963 edition.

Mathematical writing

CERN Document Server

Vivaldi, Franco

2014-01-01

This book teaches the art of writing mathematics, an essential -and difficult- skill for any mathematics student.   The book begins with an informal introduction on basic writing principles and a review of the essential dictionary for mathematics. Writing techniques are developed gradually, from the small to the large: words, phrases, sentences, paragraphs, to end with short compositions. These may represent the introduction of a concept, the abstract of a presentation or the proof of a theorem. Along the way the student will learn how to establish a coherent notation, mix words and symbols effectively, write neat formulae, and structure a definition.   Some elements of logic and all common methods of proofs are featured, including various versions of induction and existence proofs. The book concludes with advice on specific aspects of thesis writing (choosing of a title, composing an abstract, compiling a bibliography) illustrated by large number of real-life examples. Many exercises are included; over 150...

Linking geometry and algebra in the school mathematics curriculum

OpenAIRE

Jones, Keith

2010-01-01

This chapter focuses on the linking of geometry and algebra in the teaching and learning of mathematics - and how, through such linking, the mathematics curriculum might be strengthened. Through reviewing the case of the school mathematics curriculum in England, together with examples of how the power of geometry can bring contemporary mathematics to life in the classroom, the chapter argues for greater concinnity in the mathematics curriculum, especially in terms of the harmonious/purposeful...

Mathematical transforms and image compression: A review

Directory of Open Access Journals (Sweden)

Satish K. Singh

2010-07-01

Full Text Available It is well known that images, often used in a variety of computer and other scientific and engineering applications, are difficult to store and transmit due to their sizes. One possible solution to overcome this problem is to use an efficient digital image compression technique where an image is viewed as a matrix and then the operations are performed on the matrix. All the contemporary digital image compression systems use various mathematical transforms for compression. The compression performance is closely related to the performance by these mathematical transforms in terms of energy compaction and spatial frequency isolation by exploiting inter-pixel redundancies present in the image data. Through this paper, a comprehensive literature survey has been carried out and the pros and cons of various transform-based image compression models have also been discussed.

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

Science.gov (United States)

Eikenberry, Steffen E; Gumel, Abba B

2018-04-24

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

Topics in mathematical analysis and applications

CERN Document Server

Tóth, László

2014-01-01

This volume presents significant advances in a number of theories and problems of Mathematical Analysis and its applications in disciplines such as Analytic Inequalities, Operator Theory, Functional Analysis, Approximation Theory, Functional Equations, Differential Equations, Wavelets, Discrete Mathematics and Mechanics. The contributions focus on recent developments and are written by eminent scientists from the international mathematical community. Special emphasis is given to new results that have been obtained in the above mentioned disciplines in which Nonlinear Analysis plays a central role. Some review papers published in this volume will be particularly useful for a broader readership in Mathematical Analysis, as well as for graduate students. An attempt is given to present all subjects in this volume in a unified and self-contained manner, to be particularly useful to the mathematical community.

Coursework in Cognition by Mathematics Undergraduates: A Seven Year Review.

Science.gov (United States)

Nelson, David

2000-01-01

It has become increasingly possible for mathematics students to include a limited number of approved optional, non-traditional modules in their programs. Surveys coursework in four non-specialist modules over a seven-year period, and examines work in the area of mathematical cognition. (Contains 16 references.) (Author/ASK)

AMS Mathematical Review of the book "Géométrie discrète et images numériques" (French)

DEFF Research Database (Denmark)

Anton, François

2010-01-01

(through implict surfaces with skeletons, chapter 18), applications of discrete geometry to medical imaging (chapter 19) and generalization of discrete geometry objects and operators to multiresolution grids (chapter 20). This book presents very interesting mathematical methodological tools from discrete......This is the AMS Mathematical Review for the book: Géométrie discrète et images numériques [Discrete geometry and numerical images] Edited by David Coeurjolly, Annick Montanvert and Jean-Marc Chassery. Traité IC2. Série Signal et Image. [IC2 Treatise. Series Signal and Image] Hermes Science......”. The book is structured in five parts. The first part (chapters 2 through 4) presents the general mathematical foundations of discrete geometry and topology: arithmetic (chapter 2, which is later referred to in chapters 6, 7 and 11), topology (chapter 3, which is referred to in chapter 8) and combinatorics...

Persian architecture and mathematics

CERN Document Server

2012-01-01

This volulme features eight original papers dedicated to the theme “Persian Architecture and Mathematics,” guest edited by Reza Sarhangi. All papers were approved through a rigorous process of blind peer review and edited by an interdisciplinary scientific editorial committee. Topics range from symmetry in ancient Persian architecture to the elaborate geometric patterns and complex three-dimensional structures of standing monuments of historical periods, from the expression of mathematical ideas to architectonic structures, and from decorative ornament to the representation of modern group theory and quasi-crystalline patterns. The articles discuss unique monuments Persia, including domed structures and two-dimensional patterns, which have received significant scholarly attention in recent years. This book is a unique contribution to studies of Persian architecture in relation to mathematics.

Computational physics and applied mathematics capability review June 8-10, 2010 (Advance materials to committee members)

Energy Technology Data Exchange (ETDEWEB)

Lee, Stephen R [Los Alamos National Laboratory

2010-01-01

Los Alamos National Laboratory will review its Computational Physics and Applied Mathematics (CPAM) capabilities in 2010. The goals of capability reviews are to assess the quality of science, technology, and engineering (STE) performed by the capability, evaluate the integration of this capability across the Laboratory and within the scientific community, examine the relevance of this capability to the Laboratory's programs, and provide advice on the current and future directions of this capability. This is the first such review for CPAM, which has a long and unique history at the laboratory, starting from the inception of the Laboratory in 1943. The CPAM capability covers an extremely broad technical area at Los Alamos, encompassing a wide array of disciplines, research topics, and organizations. A vast array of technical disciplines and activities are included in this capability, from general numerical modeling, to coupled mUlti-physics simulations, to detailed domain science activities in mathematics, methods, and algorithms. The CPAM capability involves over 12 different technical divisions and a majority of our programmatic and scientific activities. To make this large scope tractable, the CPAM capability is broken into the following six technical 'themes.' These themes represent technical slices through the CP AM capability and collect critical core competencies of the Laboratory, each of which contributes to the capability (and each of which is divided into multiple additional elements in the detailed descriptions of the themes in subsequent sections): (1) Computational Fluid Dynamics - This theme speaks to the vast array of scientific capabilities for the simulation of fluids under shocks, low-speed flow, and turbulent conditions - which are key, historical, and fundamental strengths of the laboratory; (2) Partial Differential Equations - The technical scope of this theme is the applied mathematics and numerical solution of partial

Analytical calculations by computer in physics and mathematics

International Nuclear Information System (INIS)

Gerdt, V.P.; Tarasov, O.V.; Shirokov, D.V.

1978-01-01

The review of present status of analytical calculations by computer is given. Some programming systems for analytical computations are considered. Such systems as SCHOONSCHIP, CLAM, REDUCE-2, SYMBAL, CAMAL, AVTO-ANALITIK which are implemented or will be implemented in JINR, and MACSYMA - one of the most developed systems - are discussed. It is shown on the basis of mathematical operations, realized in these systems, that they are appropriated for different problems of theoretical physics and mathematics, for example, for problems of quantum field theory, celestial mechanics, general relativity and so on. Some problems solved in JINR by programming systems for analytical computations are described. The review is intended for specialists in different fields of theoretical physics and mathematics

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...

Praxis II mathematics content knowledge test (0061)

CERN Document Server

McCune, Ennis Donice

2007-01-01

Your guide to a higher score on the Praxis II?: Mathematics Content Knowledge Test (0061) Why CliffsTestPrep Guides? Go with the name you know and trust Get the information you need--fast! Written by test-prep specialists About the contents: Introduction * Overview of the exam * How to use this book * Proven study strategies and test-taking tips Part I: Subject Review * Focused review of all exam topics: arithmetic and basic algebra, geometry, trigonometry, analytic geometry, functions and their graphs, calculus, probability and statistics, discrete mathematics, linear algebra, compute

Mathematical finance theory review and exercises from binomial model to risk measures

CERN Document Server

Gianin, Emanuela Rosazza

2013-01-01

The book collects over 120 exercises on different subjects of Mathematical Finance, including Option Pricing, Risk Theory, and Interest Rate Models. Many of the exercises are solved, while others are only proposed. Every chapter contains an introductory section illustrating the main theoretical results necessary to solve the exercises. The book is intended as an exercise textbook to accompany graduate courses in mathematical finance offered at many universities as part of degree programs in Applied and Industrial Mathematics, Mathematical Engineering, and Quantitative Finance.

Tracking Developmental Students into Their First College Level Mathematics Course

Science.gov (United States)

Waycaster, Pansy

2011-01-01

A recent SACS review at the author's institution prompted an assessment of the school's developmental mathematics program. The author needed to examine the effectiveness of the developmental mathematics courses in preparing students for their first college level mathematics course. Rather than just examine success rates in developmental…

A review of mathematical models for the formation of vascular networks

KAUST Repository

Scianna, M.

2013-09-01

Two major mechanisms are involved in the formation of blood vasculature: vasculogenesis and angiogenesis. The former term describes the formation of a capillary-like network from either a dispersed or a monolayered population of endothelial cells, reproducible also in vitro by specific experimental assays. The latter term describes the sprouting of new vessels from an existing capillary or post-capillary venule. Similar mechanisms are also involved in the formation of the lymphatic system through a process generally called lymphangiogenesis. A number of mathematical approaches have been used to analyze these phenomena. In this paper, we review the different types of models, with special emphasis on their ability to reproduce different biological systems and to predict measurable quantities which describe the overall processes. Finally, we highlight the advantages specific to each of the different modelling approaches. © 2013 Elsevier Ltd.

A course in mathematical methods for physicists

CERN Document Server

Herman, Russell L

2014-01-01

Based on the author’s junior-level undergraduate course, this introductory textbook is designed for a course in mathematical physics. Focusing on the physics of oscillations and waves, A Course in Mathematical Methods for Physicists helps students understand the mathematical techniques needed for their future studies in physics. It takes a bottom-up approach that emphasizes physical applications of the mathematics. The book offers: •A quick review of mathematical prerequisites, proceeding to applications of differential equations and linear algebra •Classroom-tested explanations of complex and Fourier analysis for trigonometric and special functions •Coverage of vector analysis and curvilinear coordinates for solving higher dimensional problems •Sections on nonlinear dynamics, variational calculus, numerical solutions of differential equations, and Green's functions

Innovative and collaborative industrial mathematics in Europe

DEFF Research Database (Denmark)

Hjorth, Poul G.

2017-01-01

This paper presents a brief review of how industrial mathematics, inspired by the Oxford Study Group activity, organized itself in Europe, gave rise to the European Consortium for Mathematics in Industry, the series of European Study Groups with Industry, and to new modes of productive contacts b...... between industry and applied mathematicians in academia....

Research on Mathematical Literacy in Schools--Aim, Approach and Attention

Science.gov (United States)

Haara, Frode Olav; Bolstad, Oda Heidi; Jenssen, Eirik S.

2017-01-01

The development of mathematical literacy in schools is of significant concern at the policy level, and research is an important source of information in this process. This review article focuses on areas of research interest identified in empirical projects on mathematical literacy, and how mathematical literacy in schools is approached by…

Mathematics education and comparative historical studies

Directory of Open Access Journals (Sweden)

Wagner RODRIGUES VALENTE

2013-11-01

Full Text Available This paper has as its aims: to characterize the area of research «history of mathematics education» and to defend the idea that mathematics education has constituted a privileged research theme within the field of comparative historical studies. To achieve these aims, the text includes references to a review of the literature concerning comparative studies, the analysis of two fundamental moments focused on attempts to internationalize the mathematics curriculum, both of which occurred during the 20th century, and, to end, a case study emanating from an international cooperation between researchers in Brazil and Portugal.

Cognitive Psychology and Mathematical Thinking.

Science.gov (United States)

Greer, Brian

1981-01-01

This review illustrates aspects of cognitive psychology relevant to the understanding of how people think mathematically. Developments in memory research, artificial intelligence, visually mediated processes, and problem-solving research are discussed. (MP)

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…

Collegiate Mathematics Teaching: An Unexamined Practice

Science.gov (United States)

Speer, Natasha M.; Smith, John P., III; Horvath, Aladar

2010-01-01

Though written accounts of collegiate mathematics teaching exist (e.g., mathematicians' reflections and analyses of learning and teaching in innovative courses), research on collegiate teachers' actual classroom teaching practice is virtually non-existent. We advance this claim based on a thorough review of peer-reviewed journals where scholarship…

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

International seminar series on mathematics and applied mathematics and a series of three focused international research workshops on engineering mathematics organised by the Research Environment in Mathematics and Applied Mathematics at Mälardalen University from autumn 2014 to autumn 2015: the International Workshop on Engineering Mathematics for Electromagnetics and Health Technology; the International Workshop on Engineering Mathematics, Algebra, Analysis and Electromagnetics; and the 1st Swedish-Estonian International Workshop on Engineering Mathematics, Algebra, Analysis and Applications

CERN Document Server

Rancic, Milica

2016-01-01

This book highlights the latest advances in engineering mathematics with a main focus on the mathematical models, structures, concepts, problems and computational methods and algorithms most relevant for applications in modern technologies and engineering. It addresses mathematical methods of algebra, applied matrix analysis, operator analysis, probability theory and stochastic processes, geometry and computational methods in network analysis, data classification, ranking and optimisation. The individual chapters cover both theory and applications, and include a wealth of figures, schemes, algorithms, tables and results of data analysis and simulation. Presenting new methods and results, reviews of cutting-edge research, and open problems for future research, they equip readers to develop new mathematical methods and concepts of their own, and to further compare and analyse the methods and results discussed. The book consists of contributed chapters covering research developed as a result of a focused interna...

Unity and disunity and other mathematical essays

CERN Document Server

Davis, Philip J

2015-01-01

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

The mathematics of banking and finance

CERN Document Server

Cox, Dennis

2006-01-01

Throughout banking, mathematical techniques are used. Some of these are within software products or models; mathematicians use others to analyse data. The current literature on the subject is either very basic or very advanced. The Mathematics of Banking offers an intermediate guide to the various techniques used in the industry, and a consideration of how each one should be approached. Written in a practical style, it will enable readers to quickly appreciate the purpose of the techniques and, through illustrations, see how they can be applied in practice. Coverage is extensive and includes techniques such as VaR analysis, Monte Carlo simulation, extreme value theory, variance and many others.A practical review of mathematical techniques needed in banking which does not expect a high level of mathematical competence from the reader

Developing mathematics edutainment media for Android based on students’ understanding and interest: a teachers’ review

Science.gov (United States)

Setyaningrum, W.; Waryanto, N. H.

2018-03-01

This paper aimed to describe the development of interactive edutainment mathematics media using Construct 2 software for grade 7 Junior High School, and to determine the quality of the interactive edutainment media developed in regards to improve students’ understanding and interest. This research employs Research and Development design, which media was developed using ADDIE model consisting of analysing, designing, developing, implementing and evaluating. This paper focuses on the steps of development and validity of the interactive media from teachers’ point of view. The teachers review focuses on three aspects – instructional, audio-visual and operational design. The review suggested that the media was very good in regard to the three aspects, with the average score was 144.55 from the maximum score of 175. Several contexts used in the game, however, need to be adjusted to students age.

A review on mathematical methods of conventional and Islamic derivatives

Science.gov (United States)

Hisham, Azie Farhani Badrol; Jaffar, Maheran Mohd

2014-12-01

Despite the impressive growth of risk management tools in financial institutions, Islamic finance remains miles away behind the conventional institutions. Islamic finance products need to comply with the syariah law and prohibitions, therefore they can use fewer of the available risk management tools compared to conventional. Derivatives have proven to be the effective hedging technique and instrument that broadly being used in the conventional institutions to manage their risks. However, derivatives are not generally accepted as the legitimate products in Islamic finance and they remain controversial issues among the Islamic scholars. This paper reviews the evolution of derivatives such as forwards, futures and options and then explores the mathematical models that being used to solve derivatives such as random walk model, asset pricing model that follows Brownian motion and Black-Scholes model. Other than that, this paper also critically discuss the perspective of derivatives from Islamic point of view. In conclusion, this paper delivers the traditional Islamic products such as salam, urbun and istijrar that can be used to create building blocks of Islamic derivatives.

Modelling Of Flotation Processes By Classical Mathematical Methods - A Review

Science.gov (United States)

Jovanović, Ivana; Miljanović, Igor

2015-12-01

Flotation process modelling is not a simple task, mostly because of the process complexity, i.e. the presence of a large number of variables that (to a lesser or a greater extent) affect the final outcome of the mineral particles separation based on the differences in their surface properties. The attempts toward the development of the quantitative predictive model that would fully describe the operation of an industrial flotation plant started in the middle of past century and it lasts to this day. This paper gives a review of published research activities directed toward the development of flotation models based on the classical mathematical rules. The description and systematization of classical flotation models were performed according to the available references, with emphasize exclusively given to the flotation process modelling, regardless of the model application in a certain control system. In accordance with the contemporary considerations, models were classified as the empirical, probabilistic, kinetic and population balance types. Each model type is presented through the aspects of flotation modelling at the macro and micro process levels.

Mathematical programming and game theory for decision making

CERN Document Server

Bapat, R B; Das, A K; Parthasarathy, T

2008-01-01

This edited book presents recent developments and state-of-the-art review in various areas of mathematical programming and game theory. It is a peer-reviewed research monograph under the ISI Platinum Jubilee Series on Statistical Science and Interdisciplinary Research. This volume provides a panoramic view of theory and the applications of the methods of mathematical programming to problems in statistics, finance, games and electrical networks. It also provides an important as well as timely overview of research trends and focuses on the exciting areas like support vector machines, bilevel pro

Physics and Mathematics as Interwoven Disciplines in Science Education

Science.gov (United States)

Galili, Igal

2018-03-01

The relationship between physics and mathematics is reviewed upgrading the common in physics classes' perspective of mathematics as a toolkit for physics. The nature of the physics-mathematics relationship is considered along a certain historical path. The triadic hierarchical structure of discipline-culture helps to identify different ways in which mathematics is used in physics and to appreciate its contribution, to recognize the difference between mathematics and physics as disciplines in approaches, values, methods, and forms. We mentioned certain forms of mathematical knowledge important for physics but often missing in school curricula. The geometrical mode of codification of mathematical knowledge is compared with the analytical one in context of teaching school physics and mathematics; their complementarity is exemplified. Teaching may adopt the examples facilitating the claims of the study to reach science literacy and meaningful learning.

German Undergraduate Mathematics Enrolment Numbers: Background and Change

Science.gov (United States)

Ammann, Claudia; Frauendiener, Jorg; Holton, Derek

2010-01-01

Before we consider the German tertiary system, we review the education system and consider other relevant background details. We then concentrate on the tertiary system and observe that the mathematical enrolments are keeping up with the overall student enrolments. At the same time, the first year mathematics enrolments for women are greater than…

Critical issues in mathematics education major contributions of Alan Bishop

CERN Document Server

Presmeg, Norma C; Presmeg, Norma C

2008-01-01

Here are presented the contributions of Professor Alan Bishop within the mathematics education research community. Six critical issues in the development of mathematics education research are reviewed and the current developments in each area are discussed.

Videogames as an incipient research object inMathematics Education

OpenAIRE

Albarracín, Lluís; Hernández-Sabaté, Aura; Gorgorió, Núria

2017-01-01

[EN] This article presents a review of research made in the eld of mathematics education onthe use of video games in the classroom. These investigations have focused on four areas:impact in academic performance focused on mathematical contents, speci c mathematicalcontents learning, videogame design elements for mathematical learning and relation bet-ween videogames and problem solving. Finally, we propose two research new approachesthat have not been explored so far, like ...

Enabling collaboration on semiformal mathematical knowledge by semantic web integration

CERN Document Server

Lange, C

2011-01-01

Mathematics is becoming increasingly collaborative, but software does not sufficiently support that: Social Web applications do not currently make mathematical knowledge accessible to automated agents that have a deeper understanding of mathematical structures. Such agents exist but focus on individual research tasks, such as authoring, publishing, peer-review, or verification, instead of complex collaboration workflows. This work effectively enables their integration by bridging the document-oriented perspective of mathematical authoring and publishing, and the network perspective of threaded

Mathematical Model of (R,Q Inventory Policy under Limited Storage Space for Continuous and Periodic Review Policies with Backlog and Lost Sales

Directory of Open Access Journals (Sweden)

Kanokwan Singha

2017-01-01

Full Text Available This paper involves developing new mathematical expressions to find reorder point and order quantity for inventory management policies that explicitly consider storage space capacity. Both continuous and periodic reviews, as well as backlogged and lost demand during stockout, are considered. With storage space capacity, when on-hand inventory exceeds the capacity, the over-ordering cost of storage at an external warehouse is charged on a per-unit-period basis. The objective is to minimize the total cost, consisting of ordering, shortage, holding, and over-ordering costs. Demand and lead time are stochastic and discrete in nature. Demand during varying lead time is modeled using an empirical distribution so that the findings are not subject to assumptions of demand and lead time probability distributions. Due to the complexity of the developed mathematical expressions, the problems are solved using an iterative method. The method is tested with problem instances that use real data from industry. Optimal solutions of the problem instance are determined by performing exhaustive search. The proposed method can effectively find optimal solutions for continuous review policies and near optimal solutions for periodic review policies. Fundamental insights about the inventory policies are reported from a comparison between continuous review and periodic review solutions, as well as a comparison between backlog and lost sales cases.

Videogames as an incipient research object inMathematics Education

Directory of Open Access Journals (Sweden)

Lluís Albarracín

2017-01-01

Full Text Available This article presents a review of research made in the field of mathematics education on the use of video games in the classroom. These investigations have focused on four areas: impact in academic performance focused on mathematical contents, specific mathematical contents learning, videogame design elements for mathematical learning and relation bet-ween videogames and problem solving.  Finally,  we  propose  two  research  new  approaches that  have  not  been  explored  so  far,  like  the  use  of  commercial  videogames  for  mathematical  activities  or  the  use  of  simulation  games  as  environment  to  promote  mathematical modeling.

The impact of Game-based learning on the achievement of learning goals and motivation for learning mathematics - literature review

Directory of Open Access Journals (Sweden)

Blaženka Divjak

2011-06-01

Full Text Available Normal 0 21 false false false SH X-NONE X-NONE Information technologies are an integral part of a contemporary society which bases its progress on knowledge being one goal of education. Beside acquiring knowledge, skills and routines, the goal of education is to create a complete individual who can rationally and timely make decisions, purposefully react in new situations and be trained for life-long learning. In order to accomplish all this, it is necessary to make educational process more creative, contemporary and adjusted to new generations of computer literate pupils who demand quicker and more frequent interactions, a lot of information at the same time, generations who quickly acquire rules of computer games. Computer games meeting pedagogical criteria should become an integral part of learning. Teaching with mathematical computer games, which fulfil pedagogical criteria, influences pupils’ motivation, learning, retention and forgetting. This paper provides a review of literature in this field and determines whether the use of mathematical computer games contributes to more efficient realisation of educational goals at all level of education. Furthermore, considering prior research we have attempted to establish whether the use of mathematical games for teaching has an impact on the formation of a positive attitude of pupils of different ages toward the subject of mathematics, their motivation and knowledge acquisition when compared to learning without computer games. Finally, we have analysed different research methods concerning this issue and assessed the impact of pedagogically designed mathematical computer games on the realisation of educational goals and quality improvement of teaching and learning.

Teaching Elementary Mathematics through Problem Solving and Its Relationship to Mathematics Achievement

Science.gov (United States)

Bullock, Audrey N.

2017-01-01

Problem solving in mathematics has been a goal for students for decades. In the reviewed literature, problem solving was most often treated as the dependent variable and was defined very broadly; however, few studies were found that included problem solving as a treatment or independent variable. The purpose of this study was to investigate the…

Mathematics Difficulties: Does One Approach Fit All?

Science.gov (United States)

Gifford, Sue; Rockliffe, Freda

2012-01-01

This article reviews the nature of learning difficulties in mathematics and, in particular, the nature and prevalence of dyscalculia, a condition that affects the acquisition of arithmetical skills. The evidence reviewed suggests that younger children (under the age of 10) often display a combination of problems, including minor physical…

15th International Congress on Mathematical Physics

CERN Document Server

New Trends in Mathematical Physics

2009-01-01

This book collects selected papers written by invited and plenary speakers of the 15th International Congress on Mathematical Physics (ICMP) in the aftermath of the conference. In extensive review articles and expository texts as well as advanced research articles the world leading experts present the state of the art in modern mathematical physics. New mathematical concepts and ideas are introduced by prominent mathematicalphysicists and mathematicians, covering among others the fields of Dynamical Systems, Operator Algebras, Partial Differential Equations, Probability Theory, Random Matrices, Condensed Matter Physics, Statistical Mechanics, General Relativity, Quantum Mechanics, Quantum Field Theory, Quantum Information and String Theory. All together the contributions in this book give a panoramic view of the latest developments in mathematical physics. They will help readers with a general interest in mathematical physics to get an update on the most recent developments in their field, and give a broad ov...

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...

Gender, culture, and mathematics performance.

Science.gov (United States)

Hyde, Janet S; Mertz, Janet E

2009-06-02

Using contemporary data from the U.S. and other nations, we address 3 questions: Do gender differences in mathematics performance exist in the general population? Do gender differences exist among the mathematically talented? Do females exist who possess profound mathematical talent? In regard to the first question, contemporary data indicate that girls in the U.S. have reached parity with boys in mathematics performance, a pattern that is found in some other nations as well. Focusing on the second question, studies find more males than females scoring above the 95th or 99th percentile, but this gender gap has significantly narrowed over time in the U.S. and is not found among some ethnic groups and in some nations. Furthermore, data from several studies indicate that greater male variability with respect to mathematics is not ubiquitous. Rather, its presence correlates with several measures of gender inequality. Thus, it is largely an artifact of changeable sociocultural factors, not immutable, innate biological differences between the sexes. Responding to the third question, we document the existence of females who possess profound mathematical talent. Finally, we review mounting evidence that both the magnitude of mean math gender differences and the frequency of identification of gifted and profoundly gifted females significantly correlate with sociocultural factors, including measures of gender equality across nations.

Wronski's Foundations of Mathematics.

Science.gov (United States)

Wagner, Roi

2016-09-01

Argument This paper reconstructs Wronski's philosophical foundations of mathematics. It uses his critique of Lagrange's algebraic analysis as a vignette to introduce the problems that he raised, and argues that these problems have not been properly appreciated by his contemporaries and subsequent commentators. The paper goes on to reconstruct Wronski's mathematical law of creation and his notions of theory and techne, in order to put his objections to Lagrange in their philosophical context. Finally, Wronski's proof of his universal law (the expansion of a given function by any series of functions) is reviewed in terms of the above reconstruction. I argue that Wronski's philosophical approach poses an alternative to the views of his contemporary mainstream mathematicians, which brings up the contingency of their choices, and bridges the foundational concerns of early modernity with those of the twentieth-century foundations crisis. I also argue that Wronski's views may be useful to contemporary philosophy of mathematical practice, if they are read against their metaphysical grain.

New directions for situated cognition in mathematics education

CERN Document Server

Winbourne, Peter; Winbourne, Peter

2008-01-01

This book draws together a range of papers by experienced writers in mathematics education who have used the concept of situated cognition in their research within recent years. Thus it provides an up-to-date overview of developments and applications to which other researchers can refer and which will inspire future research. It is appropriate to review the field now and collect a range of papers which all relate to situated cognition and show how its application to mathematics education has matured and become usefully embedded in our approach to central issues about learning mathematics.

Refractive Thinking Profile In Solving Mathematical Problem Reviewed from Students Math Capability

Science.gov (United States)

Maslukha, M.; Lukito, A.; Ekawati, R.

2018-01-01

Refraction is a mental activity experienced by a person to make a decision through reflective thinking and critical thinking. Differences in mathematical capability have an influence on the difference of student’s refractive thinking processes in solving math problems. This descriptive research aims to generate a picture of refractive thinking of students in solving mathematical problems in terms of students’ math skill. Subjects in this study consisted of three students, namely students with high, medium, and low math skills based on mathematics capability test. Data collection methods used are test-based methods and interviews. After collected data is analyzed through three stages that are, condensing and displaying data, data display, and drawing and verifying conclusion. Results showed refractive thinking profiles of three subjects is different. This difference occurs at the planning and execution stage of the problem. This difference is influenced by mathematical capability and experience of each subject.

Pre-college Mathematics *Optional subject

OpenAIRE

ISHIDA, Yukio

2015-01-01

This course is a companion course to Calculus I. It aims to help students with little or no precalculus knowledge to master the basic calculus material in preparation for the more advanced course of Calculus I. This is done by reviewing high school mathematics.

LIMES Large Infrastructure in Mathematics - Enhanced Services

CERN Document Server

Fachinformationszentrum Energie, Physik, Mathematik. Karlsruhe

The Large Infrastructure in Mathematics - Enhanced Services (LIMES) Project is a RTD project within the Fifth (EC) Framework Programme - Horizontal Programme "Improving human research potential and the socio-economic knowledge base", Access to Resear The objective of this project is to upgrade the existing database Zentralblatt-MATH into a European based world class database for mathematics (pure and applied) by a process of technical improvement and wide Europeanisation, improving the present distribuited system. The goal is to make Zentralblatt MATH a world reference database, offering full coverage of the mathematics literature worldwide ncluding bibliographic data, peer reviews and/or abstracts, indexing, classification and search,

REVIEW OF MATHEMATICAL METHODS AND ALGORITHMS OF MEDICAL IMAGE PROCESSING ON THE EXAMPLE OF TECHNOLOGY OF MEDICAL IMAGE PROCESSING FROM WOLFRAM MATHEMATICS

Directory of Open Access Journals (Sweden)

O. Ye. Prokopchenko

2015-10-01

Full Text Available The article analyzes the basic methods and algorithms of mathematical processing of medical images as objects of computer mathematics. The presented methods and computer algorithms of mathematics relevant and may find application in the field of medical imaging - automated processing of images; as a tool for measurement and determination the optical parameters; identification and formation of medical images database. Methods and computer algorithms presented in the article and based on Wolfram Mathematica are also relevant to the problem of modern medical education. As an example of Wolfram Mathematics may be considered appropriate demonstration, such as recognition of special radiographs and morphological imaging. These methods are used to improve  the diagnostic significance and value of medical (clinical research and can serve as an educational interactive demonstration. Implementation submitted individual methods and algorithms of computer Wolfram Mathematics contributes, in general, the optimization process of practical processing and presentation of medical images.

Discrete thoughts essays on mathematics, science, and philosophy

CERN Document Server

Kac, Mark; Schwartz, Jacob T

1992-01-01

This is a volume of essays and reviews that delightfully explore mathematics in all its moods — from the light and the witty, and humorous to serious, rational, and cerebral. Topics include: logic, combinatorics, statistics, economics, artificial intelligence, computer science, and applications of mathematics broadly. You will also find history and philosophy covered, including discussion of the work of Ulam, Kant, Heidegger among others. "...these papers reflect on mathematics and its influence on human society. They can help the specialist to notice what is going on around him, and they may lead educated people from other domains to a better understanding of mathematics. Many of these papers can advise educators how to form a modern mathematics education, which develops approved ideas and institutions...I admire the stimulating perspectives of the authors."---American Mathematical Society "‘Mathematicians, like Proust and everyone else, are at their best when writing about their first love’ … They a...

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…

Research Collaboration Workshop for Women in Mathematical Biology

CERN Document Server

Miller, Laura

2017-01-01

Inspired by the Research Collaboration Workshop for Women in Mathematical Biology, this volume contains research and review articles that cover topics ranging from models of animal movement to the flow of blood cells in the embryonic heart. Hosted by the National Institute for Mathematics and Biological Synthesis (NIMBioS), the workshop brought together women working in biology and mathematics to form four research groups that encouraged multidisciplinary collaboration and lifetime connections in the STEM field. This volume introduces many of the topics from the workshop, including the aerodynamics of spider ballooning; sleep, circadian rhythms, and pain; blood flow regulation in the kidney; and the effects of antimicrobial therapy on gut microbiota and microbiota and Clostridium difficile. Perfect for students and researchers in mathematics and biology, the papers included in this volume offer an introductory glimpse at recent research in mathematical biology. .

Application of computer mathematical modeling in nuclear well-logging industry

International Nuclear Information System (INIS)

Cai Shaohui

1994-01-01

Nuclear well logging techniques have made rapid progress since the first well log calibration facility (the API pits) was dedicated in 1959. Then came the first computer mathematical model in the late 70's. Mathematical modeling can now minimize design and experiment time, as well as provide new information and idea on tool design, environmental effects and result interpretation. The author gives a brief review on the achievements of mathematical modeling on nuclear logging problems

Unpacking the Male Superiority Myth and Masculinization of Mathematics at the Intersections: A Review of Research on Gender in Mathematics Education

Science.gov (United States)

Leyva, Luis A.

2017-01-01

Gender research in mathematics education has experienced methodological and theoretical shifts over the past 45 years. Although achievement studies have used assessment tools to explore and subsequently challenge the assumption of male superiority on mathematics assessments, research on participation has unpacked these studies' sex-based…

Mathematical model in economic environmental problems

Energy Technology Data Exchange (ETDEWEB)

Nahorski, Z. [Polish Academy of Sciences, Systems Research Inst. (Poland); Ravn, H.F. [Risoe National Lab. (Denmark)

1996-12-31

The report contains a review of basic models and mathematical tools used in economic regulation problems. It starts with presentation of basic models of capital accumulation, resource depletion, pollution accumulation, and population growth, as well as construction of utility functions. Then the one-state variable model is discussed in details. The basic mathematical methods used consist of application of the maximum principle and phase plane analysis of the differential equations obtained as the necessary conditions of optimality. A summary of basic results connected with these methods is given in appendices. (au) 13 ills.; 17 refs.

Applied mathematics for engineers and physicists

CERN Document Server

Pipes, Louis A

2014-01-01

One of the most widely used reference books on applied mathematics for a generation, distributed in multiple languages throughout the world, this text is geared toward use with a one-year advanced course in applied mathematics for engineering students. The treatment assumes a solid background in the theory of complex variables and a familiarity with complex numbers, but it includes a brief review. Chapters are as self-contained as possible, offering instructors flexibility in designing their own courses. The first eight chapters explore the analysis of lumped parameter systems. Succeeding topi

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.

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…

A critique on the role of social justice perspectives in mathematics education

DEFF Research Database (Denmark)

Dahl, Bettina

2008-01-01

This review of the monograph, International Perspectives on Social Justice in Mathematics Education, is not a chapter-by-chapter summary of each of the 14 chapters per se, but rather, revolves around three overarching themes.......This review of the monograph, International Perspectives on Social Justice in Mathematics Education, is not a chapter-by-chapter summary of each of the 14 chapters per se, but rather, revolves around three overarching themes....

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

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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…

Stress, Time Pressure, Strategy Selection and Math Anxiety in Mathematics: A Review of the Literature.

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Caviola, Sara; Carey, Emma; Mammarella, Irene C; Szucs, Denes

2017-01-01

We review how stress induction, time pressure manipulations and math anxiety can interfere with or modulate selection of problem-solving strategies (henceforth "strategy selection") in arithmetical tasks. Nineteen relevant articles were identified, which contain references to strategy selection and time limit (or time manipulations), with some also discussing emotional aspects in mathematical outcomes. Few of these take cognitive processes such as working memory or executive functions into consideration. We conclude that due to the sparsity of available literature our questions can only be partially answered and currently there is not much evidence of clear associations. We identify major gaps in knowledge and raise a series of open questions to guide further research.

Stress, Time Pressure, Strategy Selection and Math Anxiety in Mathematics: A Review of the Literature

Directory of Open Access Journals (Sweden)

Sara Caviola

2017-09-01

Full Text Available We review how stress induction, time pressure manipulations and math anxiety can interfere with or modulate selection of problem-solving strategies (henceforth “strategy selection” in arithmetical tasks. Nineteen relevant articles were identified, which contain references to strategy selection and time limit (or time manipulations, with some also discussing emotional aspects in mathematical outcomes. Few of these take cognitive processes such as working memory or executive functions into consideration. We conclude that due to the sparsity of available literature our questions can only be partially answered and currently there is not much evidence of clear associations. We identify major gaps in knowledge and raise a series of open questions to guide further research.

Teaching Mathematical Modeling in Mathematics Education

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Saxena, Ritu; Shrivastava, Keerty; Bhardwaj, Ramakant

2016-01-01

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

Mathematical Models for Immunology: Current State of the Art and Future Research Directions.

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Eftimie, Raluca; Gillard, Joseph J; Cantrell, Doreen A

2016-10-01

The advances in genetics and biochemistry that have taken place over the last 10 years led to significant advances in experimental and clinical immunology. In turn, this has led to the development of new mathematical models to investigate qualitatively and quantitatively various open questions in immunology. In this study we present a review of some research areas in mathematical immunology that evolved over the last 10 years. To this end, we take a step-by-step approach in discussing a range of models derived to study the dynamics of both the innate and immune responses at the molecular, cellular and tissue scales. To emphasise the use of mathematics in modelling in this area, we also review some of the mathematical tools used to investigate these models. Finally, we discuss some future trends in both experimental immunology and mathematical immunology for the upcoming years.

Blended Learning, E-Learning and Mobile Learning in Mathematics Education

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Borba, Marcelo C.; Askar, Petek; Engelbrecht, Johann; Gadanidis, George; Llinares, Salvador; Aguilar, Mario Sánchez

2016-01-01

In this literature survey we focus on identifying recent advances in research on digital technology in the field of mathematics education. To conduct the survey we have used internet search engines with keywords related to mathematics education and digital technology and have reviewed some of the main international journals, including the ones in…

Mathematical methods in medicine: neuroscience, cardiology and pathology

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Amigó, José M.

2017-01-01

The application of mathematics, natural sciences and engineering to medicine is gaining momentum as the mutual benefits of this collaboration become increasingly obvious. This theme issue is intended to highlight the trend in the case of mathematics. Specifically, the scope of this theme issue is to give a general view of the current research in the application of mathematical methods to medicine, as well as to show how mathematics can help in such important aspects as understanding, prediction, treatment and data processing. To this end, three representative specialties have been selected: neuroscience, cardiology and pathology. Concerning the topics, the 12 research papers and one review included in this issue cover biofluids, cardiac and virus dynamics, computational neuroscience, functional magnetic resonance imaging data processing, neural networks, optimization of treatment strategies, time-series analysis and tumour growth. In conclusion, this theme issue contains a collection of fine contributions at the intersection of mathematics and medicine, not as an exercise in applied mathematics but as a multidisciplinary research effort that interests both communities and our society in general. This article is part of the themed issue ‘Mathematical methods in medicine: neuroscience, cardiology and pathology’. PMID:28507240

Mathematical methods in medicine: neuroscience, cardiology and pathology.

Science.gov (United States)

Amigó, José M; Small, Michael

2017-06-28

The application of mathematics, natural sciences and engineering to medicine is gaining momentum as the mutual benefits of this collaboration become increasingly obvious. This theme issue is intended to highlight the trend in the case of mathematics. Specifically, the scope of this theme issue is to give a general view of the current research in the application of mathematical methods to medicine, as well as to show how mathematics can help in such important aspects as understanding, prediction, treatment and data processing. To this end, three representative specialties have been selected: neuroscience, cardiology and pathology. Concerning the topics, the 12 research papers and one review included in this issue cover biofluids, cardiac and virus dynamics, computational neuroscience, functional magnetic resonance imaging data processing, neural networks, optimization of treatment strategies, time-series analysis and tumour growth. In conclusion, this theme issue contains a collection of fine contributions at the intersection of mathematics and medicine, not as an exercise in applied mathematics but as a multidisciplinary research effort that interests both communities and our society in general.This article is part of the themed issue 'Mathematical methods in medicine: neuroscience, cardiology and pathology'. © 2017 The Author(s).

Mathematical Modeling and Pure Mathematics

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Usiskin, Zalman

2015-01-01

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

BOOK REVIEW: Symmetry and the Monster: One of the Greatest Quests of Mathematics

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Szabo, R. J.

2007-04-01

The book Symmetry and the Monster: One of the Greatest Quests of Mathematics describes historical events leading up to the discovery of the Monster sporadic group, the largest simple sporadic group. It also expounds the significance and deep relationships between this group and other areas of mathematics and theoretical physics. It begins, in the prologue, with a nice overview of some of the mathematical drama surrounding the discovery of the Monster and its subsequent relationship to number theory (the so-called Moonshine conjectures). From a historical perspective, the book traces back to the roots of group theory, Galois theory, and steadily runs through time through the many famous mathematicians who contributed to group theory, including Lie, Killing and Cartan. Throughout, the author has provided a very nice and deep insight into the sociological and scientific problems at the time, and gives the reader a very prominent inside view of the real people behind the mathematics. The book should be an enjoyable read to anyone with an interest in the history of mathematics. For the non-mathematician the book makes a good, and mostly successful, attempt at being non-technical. Technical mathematical jargon is replaced with more heuristic, intuitive terminology, making the mathematical descriptions in the book fairly easy going. A glossary\\hspace{0.25pc} of\\hspace{0.25pc} terminology for noindent the more scientifically inclined is included in various footnotes throughout the book and in a comprehensive listing at the end of the book. Some more technical material is also included in the form of appendices at the end of the book. Some aspects of physics are also explained in a simple, intuitive way. The author further attempts at various places to give the non-specialist a glimpse into what mathematical proof is all about, and explains the difficulties and technicalities involved in this very nicely (for instance, he mentions the various 100+ page articles that

Book Review: Invitation to Topological Robotics by Michael Farber

DEFF Research Database (Denmark)

Raussen, Martin

2009-01-01

Book Review: Invitaton to Topological Robotics by Michael Farber. Zurich Lectures in Advanced Mathematics, European Mathematical Society (2008), ISBN 978-3-03719-054-8......Book Review: Invitaton to Topological Robotics by Michael Farber. Zurich Lectures in Advanced Mathematics, European Mathematical Society (2008), ISBN 978-3-03719-054-8...

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

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

2011-01-01

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

Mathematic anxiety, help seeking behavior and cooperative learning

OpenAIRE

Masoud Gholamali Lavasani; Farah Khandan

2011-01-01

Present project assess the effectiveness of cooperative learning over the mathematic anxiety and review the behavior of help seeking in first grade high school girl students. The experimental research procedure was in the form of pre-post tests after a period of 8 sessions of teaching. To measure the variables, the questionnaire of mathematic anxiety (Shokrani, 2002) and the questionnaire of help seeking technique (Ghadampour, 1998) were practiced (accepting or avoiding help seeking).To perfo...

Understanding engineering mathematics

CERN Document Server

Cox, Bill

2001-01-01

* Unique interactive style enables students to diagnose their strengths and weaknesses and focus their efforts where needed* Ideal for self-study and tutorial work, building from an initially supportive approach to the development of independent learning skills * Free website includes solutions to all exercises, additional topics and applications, guide to learning mathematics, and practice materialStudents today enter engineering courses with a wide range of mathematical skills, due to the many different pre-university qualifications studied. Bill Cox''s aim is for students to gain a thorough understanding of the maths they are studying, by first strengthening their background in the essentials of each topic. His approach allows a unique self-paced study style, in which students Review their strengths and weaknesses through self-administered diagnostic tests, then focus on Revision where they need it, to finally Reinforce the skills required.The book is structured around a highly successful ''transition'' ma...

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

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Darlington, Ellie

2014-01-01

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

Educational Borrowing and Mathematics Curriculum: Realistic Mathematics Education in the Dutch and Indonesian Primary Curriculum

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Shintia Revina

2018-02-01

Full Text Available Since the late 1990s, Indonesian mathematics educators have considered Realistic Mathematics Education (RME, the Dutch approach to mathematics instruction, to be the basis for educational reform. In the National curriculum development, RME has, therefore, been reviewed as among the theoretical references to the curriculum goals and content. In the present study, an analysis of the consistency between RME and the curriculum descriptors and contents in Indonesia is presented. This is supplemented with some comparisons to that in the Netherlands. Findings in this study revealed that while most of RME principles are reflected in the Indonesian curriculum, the descriptions were often very general and less explicit compared to the Dutch curriculum. They were also limited by the content-based approach as well as by the centralized decision making process of the contents to be taught which have been pre-determined at the national level. This study suggests future research to see how the curriculum may influence teachers’ enactment of RME at classroom level.

The image of mathematics held by Irish post-primary students

Science.gov (United States)

Lane, Ciara; Stynes, Martin; O'Donoghue, John

2014-08-01

The image of mathematics held by Irish post-primary students was examined and a model for the image found was constructed. Initially, a definition for 'image of mathematics' was adopted with image of mathematics hypothesized as comprising attitudes, beliefs, self-concept, motivation, emotions and past experiences of mathematics. Research focused on students studying ordinary level mathematics for the Irish Leaving Certificate examination - the final examination for students in second-level or post-primary education. Students were aged between 15 and 18 years. A questionnaire was constructed with both quantitative and qualitative aspects. The questionnaire survey was completed by 356 post-primary students. Responses were analysed quantitatively using Statistical Package for the Social Sciences (SPSS) and qualitatively using the constant comparative method of analysis and by reviewing individual responses. Findings provide an insight into Irish post-primary students' images of mathematics and offer a means for constructing a theoretical model of image of mathematics which could be beneficial for future research.

Mathematical modeling of physiological systems: an essential tool for discovery.

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Glynn, Patric; Unudurthi, Sathya D; Hund, Thomas J

2014-08-28

Mathematical models are invaluable tools for understanding the relationships between components of a complex system. In the biological context, mathematical models help us understand the complex web of interrelations between various components (DNA, proteins, enzymes, signaling molecules etc.) in a biological system, gain better understanding of the system as a whole, and in turn predict its behavior in an altered state (e.g. disease). Mathematical modeling has enhanced our understanding of multiple complex biological processes like enzyme kinetics, metabolic networks, signal transduction pathways, gene regulatory networks, and electrophysiology. With recent advances in high throughput data generation methods, computational techniques and mathematical modeling have become even more central to the study of biological systems. In this review, we provide a brief history and highlight some of the important applications of modeling in biological systems with an emphasis on the study of excitable cells. We conclude with a discussion about opportunities and challenges for mathematical modeling going forward. In a larger sense, the review is designed to help answer a simple but important question that theoreticians frequently face from interested but skeptical colleagues on the experimental side: "What is the value of a model?" Copyright © 2014 Elsevier Inc. All rights reserved.

The epidemiological impact of antiretroviral use predicted by mathematical models: a review

Directory of Open Access Journals (Sweden)

Ferguson Neil M

2005-09-01

Full Text Available Abstract This review summarises theoretical studies attempting to assess the population impact of antiretroviral therapy (ART use on mortality and HIV incidence. We describe the key parameters that determine the impact of therapy, and argue that mathematical models of disease transmission are the natural framework within which to explore the interaction between antiviral use and the dynamics of an HIV epidemic. Our review focuses on the potential effects of ART in resource-poor settings. We discuss choice of model type and structure, the potential for risk behaviour change following widespread introduction of ART, the importance of the stage of HIV infection at which treatment is initiated, and the potential for spread of drug resistance. These issues are illustrated with results from models of HIV transmission. We demonstrate that HIV transmission models predicting the impact of ART use should incorporate a realistic progression through stages of HIV infection in order to capture the effect of the timing of treatment initiation on disease spread. The realism of existing models falls short of properly reproducing patterns of diagnosis timing, incorporating heterogeneity in sexual behaviour, and describing the evolution and transmission of drug resistance. The uncertainty surrounding certain effects of ART, such as changes in sexual behaviour and transmission of ART-resistant HIV strains, demands exploration of best and worst case scenarios in modelling, but this must be complemented by surveillance and behavioural surveys to quantify such effects in settings where ART is implemented.

Assessment of contemporary mathematical methods for magnetic fusion research

International Nuclear Information System (INIS)

Treve, Y.M.

1978-03-01

The mathematical techniques reviewed have been selected on the basis of their relevance to at least four outstanding theoretical problems of magnetic fusion research, namely: (a) ion heating; (b) particle-wave interactions; (c) stability of magnetic surfaces in real tokamaks; and (d) strong plasma turbulence. These problems have a common feature: they all involve chaotic motions in spite of the perfectly deterministic nature of the mathematical models used for their description. In the first section devoted to Hamiltonian systems we briefly review the essentials of the Hamilton-Jacobi theory and discuss the Kolmogorov-Arnold-Moser theorem and its implications. In section 2 we review the difficulties of the problem of turbulence and present the Ruelle-Takens picture. An example of a dynamical system with a strange attractor is constructed and the Hopf bifurcation theory is discussed. Finally we review the properties of the Lorenz model for the convective instability of an atmospheric layer which is known to have a strange attractor for sufficiently high Rayleigh numbers

Using Mathematics Literature with Prospective Secondary Mathematics Teachers

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Jett, Christopher C.

2014-01-01

Literature in mathematics has been found to foster positive improvements in mathematics learning. This manuscript reports on a mathematics teacher educator's use of literature via literature circles with 11 prospective secondary mathematics teachers in a mathematics content course. Using survey and reflection data, the author found that…

9th Annual UNCG Regional Mathematics and Statistics Conference

CERN Document Server

Chhetri, Maya; Gupta, Sat; Shivaji, Ratnasingham

2015-01-01

This volume contains rigorously reviewed papers on the topics presented by students at The 9th Annual University of North Carolina at Greensboro Regional Mathematics and Statistics Conference (UNCG RMSC) that took place on November 2, 2013.  All papers are coauthored by student researchers and their faculty mentors. This conference series was inaugurated in 2005, and it now attracts over 150 participants from over 30 universities from North Carolina and surrounding states. The conference is specifically tailored for students to present their research projects that encompass a broad spectrum of topics in mathematics, mathematical biology, statistics, and computer science.

Contributions of Islamic Civilization to The Mathematics Development

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Liya Khaulah Asy-Syaimaa' Hussain

2017-12-01

Full Text Available The development of Islamic civilization goes hand in hand with physical and spiritual development. This development can be highlighted since the beginning of the golden age of Islam that witnessed the development of knowledge by Muslims scholars in various disciplines, including mathematics. The discourse in mathematical science only involves numbers, letters, and formulas. Muslims scholars took them as instruments to manifest the greatest of God. This paper investigates the contributions of Muslim scholars in Mathematics. The method of this study is qualitative through literature review. The resulting study found that the Quran became a source of inspiration to Muslim scholars in mathematics that form the branch of knowledge such as number theory, arithmetic, algebra, and geometry. This paper also promotes Islamization of Knowledge and its necessity to solve current Muslim world’s educational problems.

Scott Foresman-Addison Wesley Elementary Mathematics. What Works Clearinghouse Intervention Report

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What Works Clearinghouse, 2010

2010-01-01

"Scott Foresman-Addison Wesley Elementary Mathematics" is a core curriculum for students at all ability levels in prekindergarten through grade 6. The program supports students' understanding of key math concepts and skills and covers a range of mathematical content across grades. The What Works Clearinghouse (WWC) reviewed 12 studies on…

Doing Mathematics with Purpose: Mathematical Text Types

Science.gov (United States)

Dostal, Hannah M.; Robinson, Richard

2018-01-01

Mathematical literacy includes learning to read and write different types of mathematical texts as part of purposeful mathematical meaning making. Thus in this article, we describe how learning to read and write mathematical texts (proof text, algorithmic text, algebraic/symbolic text, and visual text) supports the development of students'…

Annual Perspectives in Mathematics Education 2016: Mathematical Modeling and Modeling Mathematics

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Hirsch, Christian R., Ed.; McDuffie, Amy Roth, Ed.

2016-01-01

Mathematical modeling plays an increasingly important role both in real-life applications--in engineering, business, the social sciences, climate study, advanced design, and more--and within mathematics education itself. This 2016 volume of "Annual Perspectives in Mathematics Education" ("APME") focuses on this key topic from a…

Mathematical sciences with multidisciplinary applications in honor of professor Christiane Rousseau and in recognition of the Mathematics for Planet Earth initiative

CERN Document Server

2016-01-01

This book is the fourth in a multidisciplinary series which brings together leading researchers in the STEAM-H disciplines (Science, Technology, Engineering, Agriculture, Mathematics and Health) to present their perspective on advances in their own specific fields, and to generate a genuinely interdisciplinary collaboration that transcends parochial subject-matter boundaries. All contributions are carefully edited, peer-reviewed, reasonably self-contained, and pedagogically crafted for a multidisciplinary readership. Contributions are drawn from a variety of fields including mathematics, statistics, game theory and behavioral sciences, biomathematics and physical chemistry, computer science and human-centered computing. This volume is dedicated to Professor Christiane Rousseau, whose work inspires the STEAM-H series, in recognition of her passion for the mathematical sciences and her on-going initiative, the Mathematics of Planet Earth paradigm of interdisciplinarity. The volume's primary goal is to enhance i...

Numerical methods of mathematical optimization with Algol and Fortran programs

CERN Document Server

Künzi, Hans P; Zehnder, C A; Rheinboldt, Werner

1971-01-01

Numerical Methods of Mathematical Optimization: With ALGOL and FORTRAN Programs reviews the theory and the practical application of the numerical methods of mathematical optimization. An ALGOL and a FORTRAN program was developed for each one of the algorithms described in the theoretical section. This should result in easy access to the application of the different optimization methods.Comprised of four chapters, this volume begins with a discussion on the theory of linear and nonlinear optimization, with the main stress on an easily understood, mathematically precise presentation. In addition

A mathematical primer on quantum mechanics

CERN Document Server

Teta, Alessandro

2018-01-01

This book offers a rigorous yet elementary approach to quantum mechanics that will meet the needs of Master’s-level Mathematics students and is equally suitable for Physics students who are interested in gaining a deeper understanding of the mathematical structure of the theory. Throughout the coverage, which is limited to single-particle quantum mechanics, the focus is on formulating theory and developing applications in a mathematically precise manner. Following a review of selected key concepts in classical physics and the historical background, the basic elements of the theory of operators in Hilbert spaces are presented and used to formulate the rules of quantum mechanics. The discussion then turns to free particles, harmonic oscillators, delta potential, and hydrogen atoms, providing rigorous proofs of the corresponding dynamical properties. Starting from an analysis of these applications, readers are subsequently introduced to more advanced topics such as the classical limit, scattering theory, and s...

Mathematical methods for diffusion MRI processing

International Nuclear Information System (INIS)

Lenglet, C.; Lenglet, C.; Sapiro, G.; Campbell, J.S.W.; Pike, G.B.; Campbell, J.S.W.; Siddiqi, K.; Descoteaux, M.; Haro, G.; Wassermann, D.; Deriche, R.; Wassermann, D.; Anwander, A.; Thompson, P.M.

2009-01-01

In this article, we review recent mathematical models and computational methods for the processing of diffusion Magnetic Resonance Images, including state-of-the-art reconstruction of diffusion models, cerebral white matter connectivity analysis, and segmentation techniques. We focus on Diffusion Tensor Images (DTI) and Q-Ball Images (QBI). (authors)

A mathematical medley fifty easy pieces on mathematics

CERN Document Server

Szpiro, George G

2010-01-01

Szpiro's book provides a delightful, well-written, eclectic selection of mathematical tidbits that makes excellent airplane reading for anyone with an interest in mathematics, regardless of their mathematical background. Excellent gift material. -Keith Devlin, Stanford University, author of The Unfinished Game and The Language of Mathematics It is great to have collected in one volume the many varied, insightful and often surprising mathematical stories that George Szpiro has written in his mathematical columns for the newspapers through the years. -Marcus du Sautoy, Oxford University, author

Mathematics of students’ culture: A goal of localized ethnomathematics

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Lawrence Shirley

2015-07-01

Full Text Available Ethnomathematics is the mathematics of cultural groups, but often those cultural groups are “others” and “elsewhere”. However, it is also valuable to look inward to see the interaction of mathematics and one’s own culture. An assignment in a graduate course offers this opportunity to students. The assignment is to find an area of the student’s personal “culture” (sometimes defined rather broadly and find its use of mathematics. Students are asked to write about (a the cultural area; (b how they are personally tied to it; and (c how and where it uses mathematics. In addition to the paper, students make an oral presentation. Thus, all students learn (often surprising aspects of their classmates’ non-professional life, and the presenter digs into areas of family and heritage that may not have been reviewed before. Since all students are classroom mathematics teachers, finding their own cultural mathematics is not only enlightening for themselves, but also offers opportunities to include new mathematics applications in their teaching. This paper includes much personal background that led to this assignment and is a report on more than a decade of using it, including brief student examples.

The Relationship among Elementary Teachers’ Mathematics Anxiety, Mathematics Instructional Practices, and Student Mathematics Achievement

OpenAIRE

Hadley, Kristin M.; Dorward, Jim

2011-01-01

Many elementary teachers have been found to have high levels of mathematics anxiety but the impact on student achievement was unknown. Elementary teachers (N = 692) completed the modified Mathematics Anxiety Rating Scale-Revised (Hopko, 2003) along with a questionnaire probing anxiety about teaching mathematics and current mathematics instructional practices. Student mathematics achievement data were collected for the classrooms taught by the teachers. A positive relationship was found betwee...

The Use of Computers in Mathematics Education: A Paradigm Shift from "Computer Assisted Instruction" towards "Student Programming"

Science.gov (United States)

Aydin, Emin

2005-01-01

The purpose of this study is to review the changes that computers have on mathematics itself and on mathematics curriculum. The study aims at investigating different applications of computers in education in general, and mathematics education in particular and their applications on mathematics curriculum and on teaching and learning of…

The language of mathematics telling mathematical tales

CERN Document Server

Barton, Bill

2008-01-01

Everyday mathematical ideas are expressed differently in different languages. This book probes those differences and explores their implications for mathematics education, arguing for alternatives to how we teach and learn mathematics.

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.

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 ...

Mathematical modelling of fracture hydrology

International Nuclear Information System (INIS)

Herbert, A.W.; Hodgkindon, D.P.; Lever, D.A.; Robinson, P.C.; Rae, J.

1985-01-01

This report reviews work carried out between January 1983 and December 1984 for the CEC/DOE contract 'Mathematical Modelling of Fracture Hydrology' which forms part of the CEC Mirage project (CEC 1984. Come 1985. Bourke et. al. 1983). It describes the development and use of a variety of mathematical models for the flow of water and transport of radionuclides in flowing groundwater. These models have an important role to play in assessing the long-term safety of radioactive waste burial, and in the planning and interpretation of associated experiments. The work is reported under five headings, namely 1) Statistical fracture network modelling, 2) Continuum models of flow and transport, 3) Simplified models, 4) Analysis of laboratory experiments, 5) Analysis of field experiments

Ocular hemodynamics and glaucoma: the role of mathematical modeling.

Science.gov (United States)

Harris, Alon; Guidoboni, Giovanna; Arciero, Julia C; Amireskandari, Annahita; Tobe, Leslie A; Siesky, Brent A

2013-01-01

To discuss the role of mathematical modeling in studying ocular hemodynamics, with a focus on glaucoma. We reviewed recent literature on glaucoma, ocular blood flow, autoregulation, the optic nerve head, and the use of mathematical modeling in ocular circulation. Many studies suggest that alterations in ocular hemodynamics play a significant role in the development, progression, and incidence of glaucoma. Although there is currently a limited number of studies involving mathematical modeling of ocular blood flow, regulation, and diseases (such as glaucoma), preliminary modeling work shows the potential of mathematical models to elucidate the mechanisms that contribute most significantly to glaucoma progression. Mathematical modeling is a useful tool when used synergistically with clinical and laboratory data in the study of ocular blood flow and glaucoma. The development of models to investigate the relationship between ocular hemodynamic alterations and glaucoma progression will provide a unique and useful method for studying the pathophysiology of glaucoma.

Consumer Economics and Consumer Mathematics Textbooks.

Science.gov (United States)

Eastern Michigan Univ., Ypsilanti. National Inst. for Consumer Education.

This publication lists a selection of consumer economics and consumer mathematics textbooks available for review from the National Institute for Consumer Education. Twenty-six textbooks for the secondary level are cited. Nine advanced level texts are also listed. These texts are generally considered college level texts but could be adapted for…

Mathematical Modelling Approach in Mathematics Education

Science.gov (United States)

Arseven, Ayla

2015-01-01

The topic of models and modeling has come to be important for science and mathematics education in recent years. The topic of "Modeling" topic is especially important for examinations such as PISA which is conducted at an international level and measures a student's success in mathematics. Mathematical modeling can be defined as using…

Mathematics Underground

Science.gov (United States)

Luther, Kenneth H.

2012-01-01

Mathematical modeling of groundwater flow is a topic at the intersection of mathematics and geohydrology and is rarely encountered in undergraduate mathematics. However, this subject is full of interesting and meaningful examples of truly "applied" mathematics accessible to undergraduates, from the pre-calculus to advanced mathematics levels. This…

Mathematical bridges

CERN Document Server

Andreescu, Titu; Tetiva, Marian

2017-01-01

Building bridges between classical results and contemporary nonstandard problems, Mathematical Bridges embraces important topics in analysis and algebra from a problem-solving perspective. Blending old and new techniques, tactics and strategies used in solving challenging mathematical problems, readers will discover numerous genuine mathematical gems throughout that will heighten their appreciation of the inherent beauty of mathematics. Most of the problems are original to the authors and are intertwined in a well-motivated exposition driven by representative examples. The book is structured to assist the reader in formulating and proving conjectures, as well as devising solutions to important mathematical problems by making connections between various concepts and ideas from different areas of mathematics. Instructors and educators teaching problem-solving courses or organizing mathematics clubs, as well as motivated mathematics students from high school juniors to college seniors, will find Mathematical Bri...

Exploring mathematics anxiety and attitude: Mathematics students' experiences

Science.gov (United States)

Sahri, Nurul Ashikin; Kamaruzaman, Wan Nur Farahdalila Wan; Jamil, Jastini Mohd.; Shaharanee, Izwan Nizal Mohd.

2017-11-01

A quantitative and correlational, survey methods were used to investigate the relationships among mathematical anxiety and attitude toward student's mathematics performance. Participants were 100 students volunteer to enroll in undergraduate Industrial Statistics, Decision Sciences and Business Mathematics at one of northern university in Malaysia. Survey data consisted of demographic items and Likert scale items. The collected data was analyzed by using the idea of correlation and regression analysis. The results indicated that there was a significant positive relationship between students' attitude and mathematics anxiety. Results also indicated that a substantial positive effect of students' attitude and mathematics anxiety in students' achievement. Further study can be conducted on how mathematical anxiety and attitude toward mathematics affects can be used to predict the students' performance in the class.

Mathematical concepts of optical superresolution

International Nuclear Information System (INIS)

Lindberg, Jari

2012-01-01

Optical imaging beyond the diffraction limit, i.e., optical superresolution, has been studied extensively in various contexts. This paper presents an overview of some mathematical concepts relevant to superresolution in linear optical systems. Properties of bandlimited functions are surveyed and are related to both instrumental and computational aspects of superresolution. The phenomenon of superoscillation and its relation to superresolution are discussed. (review article)

Special issue on cluster algebras in mathematical physics

Science.gov (United States)

Di Francesco, Philippe; Gekhtman, Michael; Kuniba, Atsuo; Yamazaki, Masahito

2014-02-01

This is a call for contributions to a special issue of Journal of Physics A: Mathematical and Theoretical dedicated to cluster algebras in mathematical physics. Over the ten years since their introduction by Fomin and Zelevinsky, the theory of cluster algebras has witnessed a spectacular growth, first and foremost due to the many links that have been discovered with a wide range of subjects in mathematics and, increasingly, theoretical and mathematical physics. The main motivation of this special issue is to gather together reviews, recent developments and open problems, mainly from a mathematical physics viewpoint, into a single comprehensive issue. We expect that such a special issue will become a valuable reference for the broad scientific community working in mathematical and theoretical physics. The issue will consist of invited review articles and contributed papers containing new results on the interplays of cluster algebras with mathematical physics. Editorial policy The Guest Editors for this issue are Philippe Di Francesco, Michael Gekhtman, Atsuo Kuniba and Masahito Yamazaki. The areas and topics for this issue include, but are not limited to: discrete integrable systems arising from cluster mutations cluster structure on Poisson varieties cluster algebras and soliton interactions cluster positivity conjecture Y-systems in the thermodynamic Bethe ansatz and Zamolodchikov's periodicity conjecture T-system of transfer matrices of integrable lattice models dilogarithm identities in conformal field theory wall crossing in 4d N = 2 supersymmetric gauge theories 4d N = 1 quiver gauge theories described by networks scattering amplitudes of 4d N = 4 theories 3d N = 2 gauge theories described by flat connections on 3-manifolds integrability of dimer/Ising models on graphs. All contributions will be refereed and processed according to the usual procedure of the journal. Guidelines for preparation of contributions The deadline for contributed papers is 31 March

A Capstone Mathematics Course for Prospective Secondary Mathematics Teachers

Science.gov (United States)

Artzt, Alice F.; Sultan, Alan; Curcio, Frances R.; Gurl, Theresa

2012-01-01

This article describes an innovative capstone mathematics course that links college mathematics with school mathematics and pedagogy. It describes how college juniors in a secondary mathematics teacher preparation program engage in leadership experiences that enable them to learn mathematics for teaching while developing student-centered…

On Mathematical Understanding: Perspectives of Experienced Chinese Mathematics Teachers

Science.gov (United States)

Cai, Jinfa; Ding, Meixia

2017-01-01

Researchers have long debated the meaning of mathematical understanding and ways to achieve mathematical understanding. This study investigated experienced Chinese mathematics teachers' views about mathematical understanding. It was found that these mathematics teachers embrace the view that understanding is a web of connections, which is a result…

Hands-On Mathematics: Two Cases from Ancient Chinese Mathematics

Science.gov (United States)

Wang, Youjun

2009-01-01

In modern mathematical teaching, it has become increasingly emphasized that mathematical knowledge should be taught by problem-solving, hands-on activities, and interactive learning experiences. Comparing the ideas of modern mathematical education with the development of ancient Chinese mathematics, we find that the history of mathematics in…

Theoretical Mathematics

Science.gov (United States)

Stöltzner, Michael

Answering to the double-faced influence of string theory on mathematical practice and rigour, the mathematical physicists Arthur Jaffe and Frank Quinn have contemplated the idea that there exists a `theoretical' mathematics (alongside `theoretical' physics) whose basic structures and results still require independent corroboration by mathematical proof. In this paper, I shall take the Jaffe-Quinn debate mainly as a problem of mathematical ontology and analyse it against the backdrop of two philosophical views that are appreciative towards informal mathematical development and conjectural results: Lakatos's methodology of proofs and refutations and John von Neumann's opportunistic reading of Hilbert's axiomatic method. The comparison of both approaches shows that mitigating Lakatos's falsificationism makes his insights about mathematical quasi-ontology more relevant to 20th century mathematics in which new structures are introduced by axiomatisation and not necessarily motivated by informal ancestors. The final section discusses the consequences of string theorists' claim to finality for the theory's mathematical make-up. I argue that ontological reductionism as advocated by particle physicists and the quest for mathematically deeper axioms do not necessarily lead to identical results.

Exploring Differential Effects of Mathematics Courses on Mathematics Achievement

Science.gov (United States)

Ma, Xin; McIntyre, Laureen J.

2005-01-01

Using data from the Longitudinal Study of Mathematics Participation (N = 1,518 students from 34 schools), we investigated the effects of pure and applied mathematics courses on mathematics achievement, controlling for prior mathematics achievement. Results of multilevel modelling showed that the effects of pure mathematics were significant after…

A study of rural preschool practitioners' views on young children's mathematical thinking

Science.gov (United States)

Hunting, Robert P.; Mousley, Judith A.; Perry, Bob

2012-03-01

The project Mathematical Thinking of Preschool Children in Rural and Regional Australia: Research and Practice aimed to investigate views of preschool practitioners about young children's mathematical thinking and development. Structured individual interviews were conducted with 64 preschool practitioners from rural areas of three Australian states. The questions focused on five broad themes: children's mathematics learning, support for mathematics teaching, technology and computers, attitudes and feelings, and assessment and record keeping. We review results from the interview data for each of these themes, discuss their importance, and outline recommendations related to teacher education as well as resource development and research.

Mathematics Curriculum, the Philosophy of Mathematics and its ...

African Journals Online (AJOL)

It is my observation that the current school mathematics curriculum in Ethiopia is not producing competent mathematics students. Many mathematicians in Ethiopia and other part of the world have often expressed grief that the majority of students do not understand mathematical concepts, or do not see why mathematical ...

Gifted Education in Korea: Three Korean High Schools for the Mathematically Gifted

Science.gov (United States)

Choi, Kyong Mi; Hon, Dae Sik

2009-01-01

This article presents a brief history of three Korean high schools for mathematically gifted students. It describes how these schools operate, how their mathematics curricula differ compared to those of regular high schools, the admissions criteria, curriculum offered, and the student and teacher population. This review of specialized, science,…

Mathematics, the Computer, and the Impact on Mathematics Education.

Science.gov (United States)

Tooke, D. James

2001-01-01

Discusses the connection between mathematics and the computer; mathematics curriculum; mathematics instruction, including teachers learning to use computers; and the impact of the computer on learning mathematics. (LRW)

Finite Mathematics and Discrete Mathematics: Is There a Difference?

Science.gov (United States)

Johnson, Marvin L.

Discrete mathematics and finite mathematics differ in a number of ways. First, finite mathematics has a longer history and is therefore more stable in terms of course content. Finite mathematics courses emphasize certain particular mathematical tools which are useful in solving the problems of business and the social sciences. Discrete mathematics…

Mathematical Models of Tuberculosis Reactivation and Relapse

Directory of Open Access Journals (Sweden)

Robert Steven Wallis

2016-05-01

Full Text Available The natural history of human infection with Mycobacterium tuberculosis (Mtb is highly variable, as is the response to treatment of active tuberculosis. There is presently no direct means to identify individuals in whom Mtb infection has been eradicated, whether by a bactericidal immune response or sterilizing antimicrobial chemotherapy. Mathematical models can assist in such circumstances by measuring or predicting events that cannot be directly observed. The 3 models discussed in this review illustrate instances in which mathematical models were used to identify individuals with innate resistance to Mtb infection, determine the etiology of tuberculosis in patients treated with tumor necrosis factor antagonists, and predict the risk of relapse in persons undergoing tuberculosis treatment. These examples illustrate the power of various types of mathematic models to increase knowledge and thereby inform interventions in the present global tuberculosis epidemic.

Mathematical Intelligence and Mathematical Creativity: A Causal Relationship

Science.gov (United States)

Tyagi, Tarun Kumar

2017-01-01

This study investigated the causal relationship between mathematical creativity and mathematical intelligence. Four hundred thirty-nine 8th-grade students, age ranged from 11 to 14 years, were included in the sample of this study by random cluster technique on which mathematical creativity and Hindi adaptation of mathematical intelligence test…

Learning Mathematics for Teaching Mathematics: Non-Specialist Teachers' Mathematics Teacher Identity

Science.gov (United States)

Crisan, Cosette; Rodd, Melissa

2017-01-01

A non-specialist teacher of mathematics is a school teacher who qualified to teach in a subject other than mathematics yet teaches mathematics to students in secondary school. There is an emerging interest internationally in this population, a brief report of which is given in the paper. Because of concerns about the quality of non-specialists'…

Challenge and Thrill of Pre-College Mathematics

Indian Academy of Sciences (India)

Home; Journals; Resonance – Journal of Science Education; Volume 2; Issue 5. Challenge and Thrill of Pre-College Mathematics-A Treasure House for Students. A M Vaidya. Book Review Volume 2 Issue 5 May 1997 pp 86-87. Fulltext. Click here to view fulltext PDF. Permanent link:

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

Science.gov (United States)

Sriraman, Bharath, Ed.

2012-01-01

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

Discrete Mathematics

DEFF Research Database (Denmark)

Sørensen, John Aasted

2011-01-01

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

Mathematical Literacy: A new literacy or a new mathematics?

Directory of Open Access Journals (Sweden)

Renuka Vithal

2006-10-01

Full Text Available Mathematical Literacy is a ‘hot’ topic at present in most countries, whether it is referred to by that name, or in some cases as Numeracy, or Quantitative Literacy, or Matheracy, or as some part of Ethnomathematics, or related to Mathematics in Society. Questions continue to be asked about what is meant by mathematics in any concept of Mathematical Literacy and the use of the very word ‘Literacy’ in its association with Mathematics has been challenged. Its importance, however, lies in changing our perspective on mathematics teaching, away from the elitism so often associated with much mathematics education, and towards a more equitable, accessible and genuinely educational ideal.

The Relationship of Mathematics Anxiety and Mathematical Knowledge to the Learning of Mathematical Pedagogy by Preservice Elementary Teachers.

Science.gov (United States)

Battista, Michael T.

1986-01-01

Examined how preservice elementary teachers' (N=38) mathematical knowledge and mathematics anxiety affect their success in a mathematics methods course. Also examined the hypothesis that a mathematics methods course can reduce the mathematics anxiety of these teachers. One finding is that mathematics anxiety does not inhibit their learning of…

The Relationships among Mathematics Teaching Efficacy, Mathematics Self-Efficacy, and Mathematical Beliefs for Elementary Pre-Service Teachers

Science.gov (United States)

Briley, Jason S.

2012-01-01

Ninety-five elementary pre-service teachers enrolled in a mathematics content course for elementary school teachers completed 3 surveys to measure mathematics teaching efficacy, mathematics self-efficacy, and mathematical beliefs. The pre-service teachers who reported stronger beliefs in their capabilities to teach mathematics effectively were…

Mathematical modeling in wound healing, bone regeneration and tissue engineering.

Science.gov (United States)

Geris, Liesbet; Gerisch, Alf; Schugart, Richard C

2010-12-01

The processes of wound healing and bone regeneration and problems in tissue engineering have been an active area for mathematical modeling in the last decade. Here we review a selection of recent models which aim at deriving strategies for improved healing. In wound healing, the models have particularly focused on the inflammatory response in order to improve the healing of chronic wound. For bone regeneration, the mathematical models have been applied to design optimal and new treatment strategies for normal and specific cases of impaired fracture healing. For the field of tissue engineering, we focus on mathematical models that analyze the interplay between cells and their biochemical cues within the scaffold to ensure optimal nutrient transport and maximal tissue production. Finally, we briefly comment on numerical issues arising from simulations of these mathematical models.

Mathematical model comparing of the multi-level economics systems

Science.gov (United States)

Brykalov, S. M.; Kryanev, A. V.

2017-12-01

The mathematical model (scheme) of a multi-level comparison of the economic system, characterized by the system of indices, is worked out. In the mathematical model of the multi-level comparison of the economic systems, the indicators of peer review and forecasting of the economic system under consideration can be used. The model can take into account the uncertainty in the estimated values of the parameters or expert estimations. The model uses the multi-criteria approach based on the Pareto solutions.

Writing about Class and Race Differences and Similarities in Early Childhood Mathematics: The Case of One Monograph

Science.gov (United States)

Parks, Amy Noelle

2015-01-01

This article reports on a literature review of 49 articles that cited a single monograph East Lansing written in 1981 about early learning in mathematics to make claims of similarity or difference across lines of race and class in early mathematics. The review found that while about two-thirds of the articles cited the monograph to make claims of…

Mathematical modelling

DEFF Research Database (Denmark)

Blomhøj, Morten

2004-01-01

Developing competences for setting up, analysing and criticising mathematical models are normally seen as relevant only from and above upper secondary level. The general belief among teachers is that modelling activities presuppose conceptual understanding of the mathematics involved. Mathematical...... roots for the construction of important mathematical concepts. In addition competences for setting up, analysing and criticising modelling processes and the possible use of models is a formative aim in this own right for mathematics teaching in general education. The paper presents a theoretical...... modelling, however, can be seen as a practice of teaching that place the relation between real life and mathematics into the centre of teaching and learning mathematics, and this is relevant at all levels. Modelling activities may motivate the learning process and help the learner to establish cognitive...

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...

From Patient-Specific Mathematical Neuro-Oncology to Precision Medicine

Directory of Open Access Journals (Sweden)

Anne eBaldock

2013-04-01

Full Text Available Gliomas are notoriously aggressive, malignant brain tumors that have variable response to treatment. These patients often have poor prognosis, informed primarily by histopathology. Mathematical neuro-oncology (MNO is a young and burgeoning field that leverages mathematical models to predict and quantify response to therapies. These mathematical models can form the basis of modern precision medicine approaches to tailor therapy in a patient-specific manner. Patient specific models (PSMs can be used to overcome imaging limitations, improve prognostic predictions, stratify patients and assess treatment response in silico. The information gleaned from such models can aid in the construction and efficacy of clinical trials and treatment protocols, accelerating the pace of clinical research in the war on cancer. This review focuses on the growing translation of PSM to clinical neuro-oncology. It will also provide a forward-looking view on a new era of patient-specific mathematical neuro-oncology.

Discrete Mathematics and the Secondary Mathematics Curriculum.

Science.gov (United States)

Dossey, John

Discrete mathematics, the mathematics of decision making for finite settings, is a topic of great interest in mathematics education at all levels. Attention is being focused on resolving the diversity of opinion concerning the exact nature of the subject, what content the curriculum should contain, who should study that material, and how that…

The Place of Problem Solving in Contemporary Mathematics Curriculum Documents

Science.gov (United States)

Stacey, Kaye

2005-01-01

This paper reviews the presentation of problem solving and process aspects of mathematics in curriculum documents from Australia, UK, USA and Singapore. The place of problem solving in the documents is reviewed and contrasted, and illustrative problems from teachers' support materials are used to demonstrate how problem solving is now more often…

Meeting in mathematics

DEFF Research Database (Denmark)

Mogensen, Arne; Georgiev, Vladimir; Ulovec, Andreas

To encourage many more young people to appreciate the real nature and spirit of mathematics and possibly to be enrolled in mathematics study it is important to involve them in doing mathematics (not just learning about mathematics). This goal could be achieved if mathematics teachers are prepared...... to identify and work with mathematically gifted students (without loosing the rest). The book offers chapters on gifted students, mathematical competences and other issues....

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

Science.gov (United States)

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

2015-01-01

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

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.

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

Directory of Open Access Journals (Sweden)

Yinghui Lai

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

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

Science.gov (United States)

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

2015-01-01

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

The Relationships among Pre-Service Mathematics Teachers' Beliefs about Mathematics, Mathematics Teaching, and Use of Technology in China

Science.gov (United States)

Yang, Xinrong; Leung, Frederick K. S.

2015-01-01

This paper investigated pre-service mathematics teachers' mathematics beliefs, beliefs about information and communication technology (ICT), and their relationships. 787 pre-service mathematics teachers in China completed a survey questionnaire measuring their beliefs about the nature of mathematics, beliefs about mathematics learning and…

mathematical modelling of atmospheric dispersion of pollutants

International Nuclear Information System (INIS)

Mohamed, M.E.

2002-01-01

the main objectives of this thesis are dealing with environmental problems adopting mathematical techniques. in this respect, atmospheric dispersion processes have been investigated by improving the analytical models to realize the realistic physical phenomena. to achieve these aims, the skeleton of this work contained both mathematical and environmental topics,performed in six chapters. in chapter one we presented a comprehensive review study of most important informations related to our work such as thermal stability , plume rise, inversion, advection , dispersion of pollutants, gaussian plume models dealing with both radioactive and industrial contaminants. chapter two deals with estimating the decay distance as well as the decay time of either industrial or radioactive airborne pollutant. further, highly turbulent atmosphere has been investigated as a special case in the three main thermal stability classes namely, neutral, stable, and unstable atmosphere. chapter three is concerned with obtaining maximum ground level concentration of air pollutant. the variable effective height of pollutants has been considered throughout the mathematical treatment. as a special case the constancy of effective height has been derived mathematically and the maximum ground level concentration as well as its location have been established

Pre-Service Teachers' Mathematics Self-Efficacy and Mathematics Teaching Self-Efficacy

Science.gov (United States)

Zuya, Habila Elisha; Kwalat, Simon Kevin; Attah, Bala Galle

2016-01-01

Pre-service mathematics teachers' mathematics self-efficacy and mathematics teaching self-efficacy were investigated in this study. The purpose was to determine the confidence levels of their self-efficacy in mathematics and mathematics teaching. Also, the study was aimed at finding whether their mathematics self-efficacy and teaching…

The Impact of Virtual Simulations, Communication and Peer Reviewing on Spatial Intelligence and Mathematical Achievements

Directory of Open Access Journals (Sweden)

Esther Zaretsky

2011-12-01

Full Text Available The research is aimed at enabling special education pupils to use computers in everyday life, and improving spatial intelligence and mathematical achievements through computers. The method of training focuses on enabling pupils to create computer simulations, communicate by electronic mail while evaluating each other’s products and navigate Internet sites. The creation of such simulations is based on manipulations of the virtual environment similar to the real world as much as possible in order to utilize the unique characteristics of the computer such as spatial visualization. The researcher taught the teachers the basics of the use of computer and trained them how to use the method in their classroom. Then the teachers used the method with their special education pupils in accordance with their cognitive and motor abilities. The objects were taken from the pupils’ everyday environment. The teachers trained the pupils in pairs. Such procedures were held among different populations. The teachers improved their mastery of computers. In spite of their lack of experience before the experiment, they built high-level PowerPoint presentations and used them with their pupils in the classroom including even virtual simulations. They sent their products by Electronic mail (E-Mail for the peer reviewing process and navigated relevant Internet sites. The teachers reported pupils’ high motivation and their success in the various virtual activities. As a result, the spatial intelligence and mathematical achievements of the pupils were improved. The teacher-pupil interaction and the social relationships between the pupils were also improved.

Mathematics Teachers' Perceptions of Their Students' Mathematical Competence: Relations to Mathematics Achievement, Affect, and Engagement in Singapore and Australia

Science.gov (United States)

Areepattamannil, Shaljan; Kaur, Berinderjeet

2013-01-01

This study, drawing on data from the Trends in International Mathematics and Science Study (TIMSS) 2011, examined whether mathematics teachers' perceptions of their students' mathematical competence were related to mathematics achievement, affect toward mathematics, and engagement in mathematics lessons among Grade 8 students in Singapore and…

Mathematics education a spectrum of work in mathematical sciences departments

CERN Document Server

Hsu, Pao-sheng; Pollatsek, Harriet

2016-01-01

Many in the mathematics community in the U.S. are involved in mathematics education in various capacities. This book highlights the breadth of the work in K-16 mathematics education done by members of US departments of mathematical sciences. It contains contributions by mathematicians and mathematics educators who do work in areas such as teacher education, quantitative literacy, informal education, writing and communication, social justice, outreach and mentoring, tactile learning, art and mathematics, ethnomathematics, scholarship of teaching and learning, and mathematics education research. Contributors describe their work, its impact, and how it is perceived and valued. In addition, there is a chapter, co-authored by two mathematicians who have become administrators, on the challenges of supporting, evaluating, and rewarding work in mathematics education in departments of mathematical sciences. This book is intended to inform the readership of the breadth of the work and to encourage discussion of its val...

Developing teaching material based on realistic mathematics andoriented to the mathematical reasoning and mathematical communication

Directory of Open Access Journals (Sweden)

Fitria Habsah

2017-05-01

Full Text Available This research aims to produce mathematics textbook for grade VII junior high school students based on realistic mathematics and oriented to the mathematical reasoning and mathematical communication. The quality is determined based on Nieveen criteria, including validity, practicality, and effectiveness.This study was a research and development and used Borg & Gall model. The subject of this research were the students of SMPN 2 Pujon-Kabupaten Malang, that is 30 students in an experimental class (using the developed textbook and 29 students in a control class (using BSE book from the government. The teaching material was categorized valid if the expert's judgment at least is categorized as “good”. The teaching material was categorized practical if both of teachers and students assessment at least categorized as “good”. The teaching material was categorized effectively if minimum 75% of student scores at least is categorized as “good” for the mathematical reasoning test and mathematical communication test. This research resulted in a valid, practical, and effective teaching material. The resulted of the validation show that material teaching is valid. The resulted of teachers and students assessment show that the product is practical. The tests scores show that the product is effective. Percentage of students who categorized at least as “good” is 83,33% for the mathematical reasoning and 86,67% for the mathematical communication. The resulted of statistic test shows that the product more effective than the BSE book from the government in terms of mathematical reasoning and mathematical communication.

Mathematical Modeling in Mathematics Education: Basic Concepts and Approaches

Science.gov (United States)

Erbas, Ayhan Kürsat; Kertil, Mahmut; Çetinkaya, Bülent; Çakiroglu, Erdinç; Alacaci, Cengiz; Bas, Sinem

2014-01-01

Mathematical modeling and its role in mathematics education have been receiving increasing attention in Turkey, as in many other countries. The growing body of literature on this topic reveals a variety of approaches to mathematical modeling and related concepts, along with differing perspectives on the use of mathematical modeling in teaching and…

3rd International Conference on Computational Mathematics and Computational Geometry

CERN Document Server

Ravindran, Anton

2016-01-01

This volume presents original research contributed to the 3rd Annual International Conference on Computational Mathematics and Computational Geometry (CMCGS 2014), organized and administered by Global Science and Technology Forum (GSTF). Computational Mathematics and Computational Geometry are closely related subjects, but are often studied by separate communities and published in different venues. This volume is unique in its combination of these topics. After the conference, which took place in Singapore, selected contributions chosen for this volume and peer-reviewed. The section on Computational Mathematics contains papers that are concerned with developing new and efficient numerical algorithms for mathematical sciences or scientific computing. They also cover analysis of such algorithms to assess accuracy and reliability. The parts of this project that are related to Computational Geometry aim to develop effective and efficient algorithms for geometrical applications such as representation and computati...

Using Mathematics in Science: Working with Your Mathematics Department

Science.gov (United States)

Lyon, Steve

2014-01-01

Changes to the mathematics and science curriculums are designed to increase rigour in mathematics, and place greater emphasis on mathematical content in science subjects at key stages 3, 4 and 5 (ages 11-18). One way to meet the growing challenge of providing increased emphasis on mathematics in the science curriculum is greater collaboration…

Applied mathematical sciences research at Argonne, April 1, 1981-March 31, 1982

International Nuclear Information System (INIS)

Pieper, G.W.

1982-01-01

This report reviews the research activities in Applied Mathematical Sciences at Argonne National Laboratory for the period April 1, 1981, through March 31, 1982. The body of the report discusses various projects carried out in three major areas of research: applied analysis, computational mathematics, and software engineering. Information on section staff, visitors, workshops, and seminars is found in the appendices

Proofs of the Cantor-Bernstein theorem a mathematical excursion

CERN Document Server

Hinkis, Arie

2013-01-01

This book offers an excursion through the developmental area of research mathematics. It presents some 40 papers, published between the 1870s and the 1970s, on proofs of the Cantor-Bernstein theorem and the related Bernstein division theorem. While the emphasis is placed on providing accurate proofs, similar to the originals, the discussion is broadened to include aspects that pertain to the methodology of the development of mathematics and to the philosophy of mathematics. Works of prominent mathematicians and logicians are reviewed, including Cantor, Dedekind, Schröder, Bernstein, Borel, Zermelo, Poincaré, Russell, Peano, the Königs, Hausdorff, Sierpinski, Tarski, Banach, Brouwer and several others mainly of the Polish and the Dutch schools. In its attempt to present a diachronic narrative of one mathematical topic, the book resembles Lakatos’ celebrated book Proofs and Refutations. Indeed, some of the observations made by Lakatos are corroborated herein. The analogy between the two books is clearly an...

Developing Mathematics Problems Based on Pisa Level

Directory of Open Access Journals (Sweden)

Shahibul Ahyan

2014-01-01

Full Text Available This research aims to produce mathematics problems based on PISA level with valid and practical content of change and relationships and has potential effect for Junior High School students. A development research method developed by Akker, Gravemeijer, McKenney and Nieveen is used this research. In the first stage, the researcher analyzed students, algebra material in school-based curricula (KTSP and mathematics problems of PISA 2003 of change and relationships content. The second stage, the researcher designed 13 problems with content of change and relationships. The last, the researcher used formative evaluation design developed by Tessmer which includes self evaluation, one-to-one, expert review, small group, and field test. The data collect by walk through, interview, and questionnaire. The result of this research indicated that 12 mathematical problems based on PISA level of change and relationships content that developed have validity, practically, and potential effects for Junior High School students.

The pragmatics of mathematics education vagueness and mathematical discourse

CERN Document Server

Rowland, Tim

2003-01-01

Drawing on philosophy of language and recent linguistic theory, Rowland surveys several approaches to classroom communication in mathematics. Are students intimidated by the nature of mathematics teaching? Many students appear fearful of voicing their understanding - is fear of error part of the linguistics of mathematics? The approaches explored here provide a rationale and a method for exploring and understanding speakers'' motives in classroom mathematics talk. Teacher-student interactions in mathematics are analysed, and this provides a toolkit that teachers can use to respond to the intellectual vulnerability of their students.

Lakatos and Hersh on Mathematical Proof

Directory of Open Access Journals (Sweden)

Hossein Bayat

2015-12-01

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

Developing Teaching Material Based on Realistic Mathematics Andoriented to the Mathematical Reasoning and Mathematical Communication

OpenAIRE

Habsah, Fitria

2017-01-01

This research aims to produce mathematics textbook for grade VII junior high school students based on realistic mathematics and oriented to the mathematical reasoning and mathematical communication. The quality is determined based on Nieveen criteria, including validity, practicality, and effectiveness.This study was a research and development and used Borg & Gall model. The subject of this research were the students of SMPN 2 Pujon-Kabupaten Malang, that is 30 students in an experimental cla...

INTERSUBJECT CONNECTIONS OF COURSE OF MATHEMATICAL LOGIC AND OTHER MATHEMATICAL COURSES AT PREPARATION OF FUTURE TEACHER OF MATHEMATICS

Directory of Open Access Journals (Sweden)

Yu.I. Sinko

2012-03-01

Full Text Available In this article the interconnections of course of mathematical logic with other mathematical courses – geometry, algebra and theory of numbers, mathematical analysis, and also with the courses of mathematics teaching methodology, history of mathematics in the system of preparation of teachers of mathematics in pedagogical Institute of higher education are analyzed. The presence of connections between the elements of the system and their quality is the important description of the pedagogical system.

Mathematics Connection

African Journals Online (AJOL)

MATHEMATICS CONNECTION aims at providing a forum topromote the development of Mathematics Education in Ghana. Articles that seekto enhance the teaching and/or learning of mathematics at all levels of theeducational system are welcome.

Chern-Simons terms and cocycles in physics and mathematics

Energy Technology Data Exchange (ETDEWEB)

Jackiw, R.

1984-12-01

Contemporary topological research in Yang-Mills theory is reviewed, emphasizing the Chern-Simons terms and their relatives. Three applications of the Chern-Simons terms in physical theory are described: to help understanding gauge theories in even dimensional space-time; gauge field dynamics in odd dimensional space-time; and mathematically coherent description of even-dimensional gauge theories with chiral fermions that are apparently inconsistent due to chiral anomalies. Discussion of these applications is preceded by explanation of the mathematical preliminaries and examples in simple quantum mechanical settings. 24 refs. (LEW)

The Mathematics of Infinity A Guide to Great Ideas

CERN Document Server

Faticoni, Theodore G

2012-01-01

Praise for the First Edition ". . . an enchanting book for those people in computer science or mathematics who are fascinated by the concept of infinity."—Computing Reviews ". . . a very well written introduction to set theory . . . easy to read and well suited for self-study . . . highly recommended."—Choice The concept of infinity has fascinated and confused mankind for centuries with theories and ideas that cause even seasoned mathematicians to wonder. The Mathematics of Infinity: A Guide to Great Ideas, Second Edition uniquely explores how we can manipulate these ideas when

VEDIC MATHEMATICS

Directory of Open Access Journals (Sweden)

Sead Rešić

2015-09-01

Full Text Available It is very difficult to motivate students when it comes to a school subject like Mathematics. Teachers spend a lot of time trying to find something that will arouse interest in students. It is particularly difficult to find materials that are motivating enough for students that they eagerly wait for the next lesson. One of the solutions may be found in Vedic Mathematics. Traditional methods of teaching Mathematics create fear of this otherwise interesting subject in the majority of students. Fear increases failure. Often the traditional, conventional mathematical methods consist of very long lessons which are difficult to understand. Vedic Mathematics is an ancient system that is very flexible and encourages the development of intuition and innovation. It is a mental calculating tool that does not require a calculator because the calculator is embedded in each of us. Starting from the above problems of fear and failure in Mathematics, the goal of this paper is to do research with the control and the experimental group and to compare the test results. Two tests should be done for each of the groups. The control group would do the tests in the conventional way. The experimental group would do the first test in a conventional manner and then be subjected to different treatment, that is to say, be taught on the basis of Vedic Mathematics. After that, the second group would do the second test according to the principles of Vedic Mathematics. Expectations are that after short lectures on Vedic mathematics results of the experimental group would improve and that students will show greater interest in Mathematics.

Mathematical modeling for novel cancer drug discovery and development.

Science.gov (United States)

Zhang, Ping; Brusic, Vladimir

2014-10-01

Mathematical modeling enables: the in silico classification of cancers, the prediction of disease outcomes, optimization of therapy, identification of promising drug targets and prediction of resistance to anticancer drugs. In silico pre-screened drug targets can be validated by a small number of carefully selected experiments. This review discusses the basics of mathematical modeling in cancer drug discovery and development. The topics include in silico discovery of novel molecular drug targets, optimization of immunotherapies, personalized medicine and guiding preclinical and clinical trials. Breast cancer has been used to demonstrate the applications of mathematical modeling in cancer diagnostics, the identification of high-risk population, cancer screening strategies, prediction of tumor growth and guiding cancer treatment. Mathematical models are the key components of the toolkit used in the fight against cancer. The combinatorial complexity of new drugs discovery is enormous, making systematic drug discovery, by experimentation, alone difficult if not impossible. The biggest challenges include seamless integration of growing data, information and knowledge, and making them available for a multiplicity of analyses. Mathematical models are essential for bringing cancer drug discovery into the era of Omics, Big Data and personalized medicine.

Understanding the Program Effectiveness of Early Mathematics Interventions for Prekindergarten and Kindergarten Environments: A Meta-Analytic Review

Science.gov (United States)

Wang, Aubrey H.; Firmender, Janine M.; Power, Joshua R.; Byrnes, James P.

2016-01-01

Research Findings: The early childhood years are critical in developing early mathematics skills, but the opportunities one has to learn mathematics tend to be limited, preventing the development of significant mathematics learning. By conducting a meta-analysis of 29 experimental and quasi-experimental studies that have been published since 2000,…

The Mathematical Intelligence Seen through the Lens of the Montessori Theory of the Human Tendencies.

Science.gov (United States)

Baker, Kay M.

1996-01-01

Contextualizes the mathematical intelligence as revealed in the human tendencies, as supported by the extended family, and facilitated by choice within a responsive environment. Reviews the function of Montessori materials, including mathematical materials, and emphasizes that the personal intelligences are integral to all activities simply…

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.

The Magic of Mathematics Discovering the Spell of Mathematics

CERN Document Server

Pappas, Theoni

2011-01-01

Delves into the world of ideas, explores the spell mathematics casts on our lives, and helps you discover mathematics where you least expect it. Be spellbound by the mathematical designs found in nature. Learn how knots may untie the mysteries of life. Be mesmerized by the computer revolution. Discover how the hidden forces of mathematics hold architectural structures together connect your telephone calls help airplanes get off the ground solve the mysteries of the living cell. See how some artists use a mathematical palette in their works and how many writers draw upon the wealth of its ideas

Guide to mathematical concepts of quantum theory

International Nuclear Information System (INIS)

Heinosaari, T.; Ziman, M.

2008-01-01

Quantum Theory is one of the pillars of modern science developed over the last hundred years. In this review we introduce, step by step, the quantum theory understood as a mathematical model describing quantum experiments. We start with splitting the experiment into two parts: a preparation process and a measurement process leading to a registration of a particular outcome. These two ingredients of the experiment are represented by states and effects, respectively. Further, the whole picture of quantum measurement will be developed and concepts of observables, instruments and measurement models representing the three different descriptions on experiments will be introduced. In the second stage, we enrich the model of the experiment by introducing the concept of quantum channel describing the system changes between preparations and measurements. At the very end we review the elementary properties of quantum entanglement. The text contains many examples and exercise covering also many topics from quantum information theory and quantum measurement theory. The goal is to give a mathematically clear and self-containing explanation of the main concepts of the modern language of quantum theory (Authors)

Guide to mathematical concepts of quantum theory

International Nuclear Information System (INIS)

Heinosaari, T.; Ziman, M.

2008-01-01

Quantum Theory is one of the pillars of modern science developed over the last hundred years. In this review paper we introduce, step by step, the quantum theory understood as a mathematical model describing quantum experiments. We start with splitting the experiment into two parts: a preparation process and a measurement process leading to a registration of a particular outcome. These two ingredients of the experiment are represented by states and effects, respectively. Further, the whole picture of quantum measurement will be developed and concepts of observables, instruments and measurement models representing the three different descriptions on experiments will be introduced. In the second stage, we enrich the model of the experiment by introducing the concept of quantum channel describing the system changes between preparations and measurements. At the very end we review the elementary properties of quantum entanglement. The text contains many examples and exercise covering also many topics from quantum information theory and quantum measurement theory. The goal is to give a mathematically clear and self-containing explanation of the main concepts of the modern language of quantum theory. (author)

Effectiveness of Computer-Assisted Mathematics Education (CAME) over Academic Achievement: A Meta-Analysis Study

Science.gov (United States)

Demir, Seda; Basol, Gülsah

2014-01-01

The aim of the current study is to determine the overall effects of Computer-Assisted Mathematics Education (CAME) on academic achievement. After an extensive review of the literature, studies using Turkish samples and observing the effects of Computer-Assisted Education (CAE) on mathematics achievement were examined. As a result of this…

PREFACE: International Conference on Advancement in Science and Technology 2012 (iCAST): Contemporary Mathematics, Mathematical Physics and their Applications

Science.gov (United States)

Ganikhodjaev, Nasir; Mukhamedov, Farrukh; Hee, Pah Chin

2013-04-01

The 4th International Conference on the Advancement of Science and Technology 2012 (iCAST 2012), with theme 'Contemporary Mathematics, Mathematical Physics and their Applications', took place in Kuantan, Malaysia, from Wednesday 7 to Friday 9 November 2012. The conference was attended by more than 100 participants, and hosted about 160 oral and poster papers by more than 140 pre-registered authors. The key topics of the 4th iCAST 2012 include Pure Mathematics, Applied Mathematics, Theoretical/Mathematical Physics, Dynamical Systems, Statistics and Financial Mathematics. The scientific program was rather full since after the Keynote and Invited Talks in the morning, four parallel sessions ran every day. However, according to all attendees, the program was excellent with a high level of talks and the scientific environment was fruitful; thus all attendees had a creative time. The conference aimed to promote the knowledge and development of high-quality research in mathematical fields concerned with the application of other scientific fields as well as modern technological trends in physics, chemistry, biology, medicine, economics, sociology and environmental sciences. We would like to thank the Keynote and the Invited Speakers for their significant contributions to 4th iCAST 2012. We would also like to thank the members of the International Scientific Committee and the members of the Organizing Committee. We cannot end without expressing our many thanks to International Islamic University Malaysia and our sponsors for their financial support . This volume presents selected papers which have been peer-reviewed. The editors hope that it may be useful and fruitful for scholars, researchers, and advanced technical members of the industrial laboratory facilities for developing new tools and products. Guest Editors Nasir Ganikhodjaev, Farrukh Mukhamedov and Pah Chin Hee The PDF contains the committee lists, board list and biographies of the plenary speakers.

Interest in mathematics and science among students having high mathematics aptitude

Science.gov (United States)

Ely, Jane Alice

The study investigates why men and women differ in their interest in mathematics and science and in the pursuit of careers in mathematics and science. The most persistent gender differential in educational standard testing is the scores in mathematics achievement. The mean Scholastic Aptitude Test (Mathematics) scores for women are consistently below that of men by about 40 points. One result of this gender differential in mathematics is that few women entertain a career requiring a robust knowledge of higher mathematics (i.e. engineering, computing, or the physical sciences). A large body of literature has been written attempting to explain why this is happening. Biological, cultural, structural and psychological explanations have been suggested and empirically examined. Controlling for mathematical ability is one method of sorting out these explanations. Eliminating mathematical ability as a factor, this dissertation reports the results of a study of men and women college students who all had high mathematics ability. Thus, any differences we found among them would have to be a result of other variables. Using a Mathematics Placement Exam and the SAT-M, forty-two students (12 males and 30 females) with high scores in both were interviewed. Student were asked about their experiences in high school and college mathematics, their career choices, and their attitudes toward mathematics. The findings, that there were no gender differences in the course selection, attitudes towards mathematics, and career choice, differed from my initial expectations. This negative finding suggests that women with high ability in mathematics are just as likely as men to pursue interests in mathematics and related courses in college and in selecting careers.

Mathematical Thinking and Creativity through Mathematical Problem Posing and Solving

Directory of Open Access Journals (Sweden)

María F. Ayllón

2016-04-01

Full Text Available This work shows the relationship between the development of mathematical thinking and creativity with mathematical problem posing and solving. Creativity and mathematics are disciplines that do not usually appear together. Both concepts constitute complex processes sharing elements, such as fluency (number of ideas, flexibility (range of ideas, novelty (unique idea and elaboration (idea development. These factors contribute, among others, to the fact that schoolchildren are competent in mathematics. The problem solving and posing are a very powerful evaluation tool that shows the mathematical reasoning and creative level of a person. Creativity is part of the mathematics education and is a necessary ingredient to perform mathematical assignments. This contribution presents some important research works about problem posing and solving related to the development of mathematical knowledge and creativity. To that end, it is based on various beliefs reflected in the literature with respect to notions of creativity, problem solving and posing.

Mathematical thinking styles of undergraduate students and their achievement in mathematics

Science.gov (United States)

Risnanosanti

2017-08-01

The main purpose of this study is to analyze the role of mathematical thinking styles in students' achievement in mathematics. On the basis of this study, it is also to generate recommendation for classroom instruction. The two specific aims are; first to observe students' mathematical thinking styles during problem solving, the second to asses students' achievement in mathematics. The data were collected by using Mathematical Thinking Styles questionnaires and test of students' achievement in mathematics. The subject in this study was 35 students from third year at mathematics study program of Muhammadiyah University of Bengkulu in academic year 2016/2017. The result of this study was that the students have three mathematical thinking styles (analytic, visual, and integrated), and the students who have analytic styles have better achievement than those who have visual styles in mathematics.

Quotable Quotes in Mathematics

Science.gov (United States)

Lo, Bruce W. N.

1983-01-01

As a way to dispel negative feelings toward mathematics, a variety of quotations are given. They are categorized by: what mathematics is, mathematicians, mathematics and other disciplines, different areas of mathematics, mathematics and humor, applications of mathematics, and pure versus applied mathematics. (MNS)

Elementary Mathematics Teachers' Perceptions and Lived Experiences on Mathematical Communication

Science.gov (United States)

Kaya, Defne; Aydin, Hasan

2016-01-01

Mathematical thinking skills and meaningful mathematical understanding are among the goals of current mathematics education. There is a wide consensus among scholars about the purpose of developing mathematical understanding and higher order thinking skills in students. However, how to develop those skills in classroom settings is an area that…

Understanding in mathematics

CERN Document Server

Sierpinska, Anna

1994-01-01

The concept of understanding in mathematics with regard to mathematics education is considered in this volume, the main problem for mathematics teachers being how to facilitate their students'' understanding of the mathematics being taught.

Figures of thought mathematics and mathematical texts

CERN Document Server

Reed, David

2003-01-01

Examines the ways in which mathematical works can be read as texts, examines their textual strategiesand demonstrates that such readings provide a rich source of philosophical debate regarding mathematics.

Front tracking for hyperbolic conservation laws

CERN Document Server

Holden, Helge

2002-01-01

Hyperbolic conservation laws are central in the theory of nonlinear partial differential equations and in science and technology. The reader is given a self-contained presentation using front tracking, which is also a numerical method. The multidimensional scalar case and the case of systems on the line are treated in detail. A chapter on finite differences is included. "It is already one of the few best digests on this topic. The present book is an excellent compromise between theory and practice. Students will appreciate the lively and accurate style." D. Serre, MathSciNet "I have read the book with great pleasure, and I can recommend it to experts as well as students. It can also be used for reliable and very exciting basis for a one-semester graduate course." S. Noelle, Book review, German Math. Soc. "Making it an ideal first book for the theory of nonlinear partial differential equations...an excellent reference for a graduate course on nonlinear conservation laws." M. Laforest, Comp. Phys. Comm.

Predicting Success in College Mathematics from High School Mathematics Preparation

OpenAIRE

Shepley, Richard A.

1983-01-01

The purpose of this study was to develop a model to predict the college mathematics courses a freshman could expect to pass by considering their high school mathematics preparation. The high school information that was used consisted of the student's sex, the student's grade point average in mathematics, the highest level of high school mathematics courses taken, and the number of mathematics courses taken in high school. The high school sample was drawn from graduated Seniors in the State...

Mathematical Chemistry

OpenAIRE

Trinajstić, Nenad; Gutman, Ivan

2002-01-01

A brief description is given of the historical development of mathematics and chemistry. A path leading to the meeting of these two sciences is described. An attempt is made to define mathematical chemistry, and journals containing the term mathematical chemistry in their titles are noted. In conclusion, the statement is made that although chemistry is an experimental science aimed at preparing new compounds and materials, mathematics is very useful in chemistry, among other things, to produc...

Using Financial Calculators in a Business Mathematics Course.

Science.gov (United States)

Heller, William H.; Taylor, Monty B.

2000-01-01

Discusses the authors' experiences with integrating financial calculators into a business mathematics course. Presents a brief overview of the operation of financial calculators, reviews some of the more common models, discusses how to use the equation solver utility on other calculators to emulate a financial calculator, and explores the…

Role of mathematics in cancer research: attitudes and training of Japanese mathematicians.

Science.gov (United States)

Kudô, A

1979-01-01

An extensive survey of attitude towards scientific information of scientists in Japan was conducted in Japan. It was published in a technical report, and this survey is reviewed in this paper, with the hope that this will furnish findings important in working out the plan for promoting exploitation of mathematical talent in biomedical research. Findings are concordant with the impression of foreign visitors: (1) pure mathematicians tend to concentrate on mathematics only; (2) applied mathematics and statistics are heavily oriented toward industry; (3) mathematicians and pharmacologists are very different in their attitudes to scientific information. Based on the personal experience of the author, difficulties to be circumvented in utilizing aptitudes for mathematics and/or statistics in biomedical research are discussed. PMID:540605

Role of mathematics in cancer research: attitudes and training of Japanese mathematicians.

Science.gov (United States)

Kudô, A

1979-10-01

An extensive survey of attitude towards scientific information of scientists in Japan was conducted in Japan. It was published in a technical report, and this survey is reviewed in this paper, with the hope that this will furnish findings important in working out the plan for promoting exploitation of mathematical talent in biomedical research. Findings are concordant with the impression of foreign visitors: (1) pure mathematicians tend to concentrate on mathematics only; (2) applied mathematics and statistics are heavily oriented toward industry; (3) mathematicians and pharmacologists are very different in their attitudes to scientific information. Based on the personal experience of the author, difficulties to be circumvented in utilizing aptitudes for mathematics and/or statistics in biomedical research are discussed.

Error Analysis in Mathematics. Technical Report #1012

Science.gov (United States)

Lai, Cheng-Fei

2012-01-01

Error analysis is a method commonly used to identify the cause of student errors when they make consistent mistakes. It is a process of reviewing a student's work and then looking for patterns of misunderstanding. Errors in mathematics can be factual, procedural, or conceptual, and may occur for a number of reasons. Reasons why students make…

Elementary Pre-Service Teachers' Mathematics Anxiety and Mathematics Teaching Anxiety

Science.gov (United States)

Haciomeroglu, Guney

2014-01-01

The present study examined the structure of elementary pre-service teachers' mathematics anxiety and mathematics teaching anxiety by asking whether the two systems of anxiety are related. The Turkish Mathematics Anxiety Rating Scale Short Version and the Mathematics Teaching Anxiety Scale were administered to 260 elementary pre-service teachers.…

Mathematics across cultures the history of non-Western mathematics

CERN Document Server

2000-01-01

Mathematics Across Cultures: A History of Non-Western Mathematics consists of essays dealing with the mathematical knowledge and beliefs of cultures outside the United States and Europe. In addition to articles surveying Islamic, Chinese, Native American, Aboriginal Australian, Inca, Egyptian, and African mathematics, among others, the book includes essays on Rationality, Logic and Mathematics, and the transfer of knowledge from East to West. The essays address the connections between science and culture and relate the mathematical practices to the cultures which produced them. Each essay is well illustrated and contains an extensive bibliography. Because the geographic range is global, the book fills a gap in both the history of science and in cultural studies. It should find a place on the bookshelves of advanced undergraduate students, graduate students, and scholars, as well as in libraries serving those groups.

Should I take Further Mathematics? Physics undergraduates’ experiences of post-compulsory Mathematics

Science.gov (United States)

Bowyer, Jessica; Darlington, Ellie

2017-01-01

It is essential that physics undergraduates are appropriately prepared for the mathematical demands of their course. This study investigated physics students’ perceptions of post-compulsory mathematics as preparation for their degree course. 494 physics undergraduates responded to an online questionnaire about their experiences of A-level Mathematics and Further Mathematics. The findings suggest that physics undergraduates would benefit from studying Further Mathematics and specialising in mechanics during their A-level studies. As both A-level Mathematics and Further Mathematics are being reformed, universities should look closely at the benefits of Further Mathematics as preparation for their physics courses and either increase their admissions requirements, or recommend that students take Further Mathematics.

New Avenues for History in Mathematics Education: Mathematical Competencies and Anchoring

DEFF Research Database (Denmark)

Jankvist, U. T.; Kjeldsen, T. H.

2011-01-01

. The first scenario occurs when history is used as a ‘tool’ for the learning and teaching of mathematics, the second when history of mathematics as a ‘goal’ is pursued as an integral part of mathematics education. We introduce a multiple-perspective approach to history, and suggest that research on history......The paper addresses the apparent lack of impact of ‘history in mathematics education’ in mathematics education research in general, and proposes new avenues for research. We identify two general scenarios of integrating history in mathematics education that each gives rise to different problems...... in mathematics education follows one of two different avenues in dealing with these scenarios. The first is to focus on students’ development of mathematical competencies when history is used a tool for the learning of curriculum-dictated mathematical in-issues. A framework for this is described. Secondly, when...

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

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.

Mathematical marriages: intercourse between mathematics and Semiotic choice.

Science.gov (United States)

Wagner, Roy

2009-04-01

This paper examines the interaction between Semiotic choices and the presentation and solution of a family of contemporary mathematical problems centred around the so-called 'stable marriage problem'. I investigate how a socially restrictive choice of signs impacts mathematical production both in terms of problem formation and of solutions. I further note how the choice of gendered language ends up constructing a reality, which duplicates the very structural framework that it imported into mathematical analysis in the first place. I go on to point out some semiotic lines of flight from this interlocking grip of mathematics and gendered language.

Structural Equation Model to Validate: Mathematics-Computer Interaction, Computer Confidence, Mathematics Commitment, Mathematics Motivation and Mathematics Confidence

Science.gov (United States)

Garcia-Santillán, Arturo; Moreno-Garcia, Elena; Escalera-Chávez, Milka E.; Rojas-Kramer, Carlos A.; Pozos-Texon, Felipe

2016-01-01

Most mathematics students show a definite tendency toward an attitudinal deficiency, which can be primarily understood as intolerance to the matter, affecting their scholar performance adversely. In addition, information and communication technologies have been gradually included within the process of teaching mathematics. Such adoption of…

Potential of mathematical modeling in fruit quality | Vazquez-Cruz ...

African Journals Online (AJOL)

A review of mathematical modeling applied to fruit quality showed that these models ranged inresolution from simple yield equations to complex representations of processes as respiration, photosynthesis and assimilation of nutrients. The latter models take into account complex genotype environment interactions to ...

Application of mathematical modeling in sustained release delivery systems.

Science.gov (United States)

Grassi, Mario; Grassi, Gabriele

2014-08-01

This review, presenting as starting point the concept of the mathematical modeling, is aimed at the physical and mathematical description of the most important mechanisms regulating drug delivery from matrix systems. The precise knowledge of the delivery mechanisms allows us to set up powerful mathematical models which, in turn, are essential for the design and optimization of appropriate drug delivery systems. The fundamental mechanisms for drug delivery from matrices are represented by drug diffusion, matrix swelling, matrix erosion, drug dissolution with possible recrystallization (e.g., as in the case of amorphous and nanocrystalline drugs), initial drug distribution inside the matrix, matrix geometry, matrix size distribution (in the case of spherical matrices of different diameter) and osmotic pressure. Depending on matrix characteristics, the above-reported variables may play a different role in drug delivery; thus the mathematical model needs to be built solely on the most relevant mechanisms of the particular matrix considered. Despite the somewhat diffident behavior of the industrial world, in the light of the most recent findings, we believe that mathematical modeling may have a tremendous potential impact in the pharmaceutical field. We do believe that mathematical modeling will be more and more important in the future especially in the light of the rapid advent of personalized medicine, a novel therapeutic approach intended to treat each single patient instead of the 'average' patient.

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.

Mathematical methods in time series analysis and digital image processing

CERN Document Server

Kurths, J; Maass, P; Timmer, J

2008-01-01

The aim of this volume is to bring together research directions in theoretical signal and imaging processing developed rather independently in electrical engineering, theoretical physics, mathematics and the computer sciences. In particular, mathematically justified algorithms and methods, the mathematical analysis of these algorithms, and methods as well as the investigation of connections between methods from time series analysis and image processing are reviewed. An interdisciplinary comparison of these methods, drawing upon common sets of test problems from medicine and geophysical/enviromental sciences, is also addressed. This volume coherently summarizes work carried out in the field of theoretical signal and image processing. It focuses on non-linear and non-parametric models for time series as well as on adaptive methods in image processing.

The materiality of mathematics: presenting mathematics at the blackboard.

Science.gov (United States)

Greiffenhagen, Christian

2014-09-01

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

Engineering Mathematics I : Electromagnetics, Fluid Mechanics, Material Physics and Financial Engineering

CERN Document Server

Rančić, Milica

2016-01-01

This book highlights the latest advances in engineering mathematics with a main focus on the mathematical models, structures, concepts, problems and computational methods and algorithms most relevant for applications in modern technologies and engineering. In particular, it features mathematical methods and models of applied analysis, probability theory, differential equations, tensor analysis and computational modelling used in applications to important problems concerning electromagnetics, antenna technologies, fluid dynamics, material and continuum physics and financial engineering. The individual chapters cover both theory and applications, and include a wealth of figures, schemes, algorithms, tables and results of data analysis and simulation. Presenting new methods and results, reviews of cutting-edge research, and open problems for future research, they equip readers to develop new mathematical methods and concepts of their own, and to further compare and analyse the methods and results discussed. The ...

The role of mathematical models in the optimization of radiopharmaceutical therapy

International Nuclear Information System (INIS)

Divgi, C.

2001-01-01

Mathematical models have been used in radiopharmaceutical therapy for over five decades. These have served to determine the amount of radioactivity required to treat disease, as in the therapy of hyperthyroidism with iodine-131, or, more frequently, to determine the largest amount of radioactivity that can be safely administered. Mathematical models are especially useful in the determination of fractionated radiopharmaceutical therapy. This review will briefly outline the historical development and current utility of mathematical models in radiopharmaceutical therapy, including thyroid disorders and radioimmunotherapy; and describe the potential of modeling in fractionated therapy. The extended application of such models to currently used radiopharmaceutical therapy based on indices of body mass or surface area, to alleviate toxicity and increase radiation dose to tumour, will be proposed. Finally, future applications of mathematical models in radiopharmaceutical therapy will be outlined. (author)

The Effect of an Augmented Reality Enhanced Mathematics Lesson on Student Achievement and Motivation

Science.gov (United States)

Estapa, Anne; Nadolny, Larysa

2015-01-01

The purpose of the study was to assess student achievement and motivation during a high school augmented reality mathematics activity focused on dimensional analysis. Included in this article is a review of the literature on the use of augmented reality in mathematics and the combination of print with augmented reality, also known as interactive…

Using Logo in the teaching and learning of mathematics: a research bibliography

OpenAIRE

Jones, Keith

2005-01-01

This review suggests that students working with Logo, by creating and interacting with objects that are visible, quantifiable, and adhere to conventional mathematics, build connections between spatial and numeric/algebraic thinking. Using Logo can help students make mathematics more concrete, while simultaneously supporting algebraic formalisation of actions as Logo “procedures". Working with Logo affords students opportunities to try out ideas and modify plans, elements that are key to mathe...

Applied Mathematical Sciences research at Argonne, October 1, 1978-March 31, 1980

Energy Technology Data Exchange (ETDEWEB)

Pieper, G. W. [ed.

1980-01-01

This report reviews the research activities of the Applied Mathematical Sciences Section for the period October 1, 1978, through March 31, 1980. The body of the report discusses various projects carried out in four major areas of research: applied analysis, computational mathematics, software engineering, and software clinics. Information on section staff, visitors, workshops, and seminars is found in the appendices. Descriptions of individual research topics are very brief.

Using a Card Trick to Teach Discrete Mathematics

Science.gov (United States)

Simonson, Shai; Holm, Tara S.

2003-01-01

We present a card trick that can be used to review or teach a variety of topics in discrete mathematics. We address many subjects, including permutations, combinations, functions, graphs, depth first search, the pigeonhole principle, greedy algorithms, and concepts from number theory. Moreover, the trick motivates the use of computers in…

Rainforest Mathematics

Science.gov (United States)

Kilpatrick, Jeremy

2014-01-01

This paper addresses the contested way that ethnomathematics has sometimes been received by mathematicians and others and what that disagreement might suggest about issues in mathematics education; namely, (a) the relation of ethnomathematics to academic mathematics; (b) recent efforts to reform secondary school mathematics so that it prepares…

Mathematical scandals

CERN Document Server

Pappas, Theoni

1997-01-01

In this highly readable volume of vignettes of mathematical scandals and gossip, Theoni Pappas assembles 29 fascinating stories of intrigue and the bizarre ? in short, the human background of the history of mathematics. Might a haberdasher have changed Einstein's life? Why was the first woman mathematician murdered? How come there's no Nobel Prize in mathematics?Mathematics is principally about numbers, equations, and solutions, all of them precise and timeless. But, behind this arcane matter lies the sometimes sordid world of real people, whose rivalries and deceptions

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...

High school mathematics teachers' perspectives on the purposes of mathematical proof in school mathematics

Science.gov (United States)

Dickerson, David S.; Doerr, Helen M.

2014-12-01

Proof serves many purposes in mathematics. In this qualitative study of 17 high school mathematics teachers, we found that these teachers perceived that two of the most important purposes for proof in school mathematics were (a) to enhance students' mathematical understanding and (b) to develop generalized thinking skills that were transferable to other fields of endeavor. We found teachers were divided on the characteristics (or features) of proofs that would serve these purposes. Teachers with less experience tended to believe that proofs in the high school should adhere to strict standards of language and reasoning while teachers with more experience tended to believe that proofs based on concrete or visual features were well suited for high school mathematics. This study has implications for teacher preparation because it appears that there is a wide variation in how teachers think about proof. It seems likely that students would experience proof very differently merely because they were seated in different classrooms.

Cluster algebras in mathematical physics

International Nuclear Information System (INIS)

Francesco, Philippe Di; Gekhtman, Michael; Kuniba, Atsuo; Yamazaki, Masahito

2014-01-01

This special issue of Journal of Physics A: Mathematical and Theoretical contains reviews and original research articles on cluster algebras and their applications to mathematical physics. Cluster algebras were introduced by S Fomin and A Zelevinsky around 2000 as a tool for studying total positivity and dual canonical bases in Lie theory. Since then the theory has found diverse applications in mathematics and mathematical physics. Cluster algebras are axiomatically defined commutative rings equipped with a distinguished set of generators (cluster variables) subdivided into overlapping subsets (clusters) of the same cardinality subject to certain polynomial relations. A cluster algebra of rank n can be viewed as a subring of the field of rational functions in n variables. Rather than being presented, at the outset, by a complete set of generators and relations, it is constructed from the initial seed via an iterative procedure called mutation producing new seeds successively to generate the whole algebra. A seed consists of an n-tuple of rational functions called cluster variables and an exchange matrix controlling the mutation. Relations of cluster algebra type can be observed in many areas of mathematics (Plücker and Ptolemy relations, Stokes curves and wall-crossing phenomena, Feynman integrals, Somos sequences and Hirota equations to name just a few examples). The cluster variables enjoy a remarkable combinatorial pattern; in particular, they exhibit the Laurent phenomenon: they are expressed as Laurent polynomials rather than more general rational functions in terms of the cluster variables in any seed. These characteristic features are often referred to as the cluster algebra structure. In the last decade, it became apparent that cluster structures are ubiquitous in mathematical physics. Examples include supersymmetric gauge theories, Poisson geometry, integrable systems, statistical mechanics, fusion products in infinite dimensional algebras, dilogarithm

Mathematical and statistical applications in life sciences and engineering

CERN Document Server

Adhikari, Mahima; Chaubey, Yogendra

2017-01-01

The book includes articles from eminent international scientists discussing a wide spectrum of topics of current importance in mathematics and statistics and their applications. It presents state-of-the-art material along with a clear and detailed review of the relevant topics and issues concerned. The topics discussed include message transmission, colouring problem, control of stochastic structures and information dynamics, image denoising, life testing and reliability, survival and frailty models, analysis of drought periods, prediction of genomic profiles, competing risks, environmental applications and chronic disease control. It is a valuable resource for researchers and practitioners in the relevant areas of mathematics and statistics.

International Summer School on Mathematical Systems Theory and Economics

CERN Document Server

Szegö, G

1969-01-01

The International Summer School on Mathematical Systems Theory and Economics was held at the Villa Monastero in Varenna, Italy, from June 1 through June 12, 1967. The objective of this Summer School was to review the state of the art and the prospects for the application of the mathematical theory of systems to the study and the solution of economic problems. Particular emphasis was given to the use of the mathematical theory of control for the solution of problems in economics. It was felt that the publication of a volume collecting most of the lectures given at the school would show the current status of the application of these methods. The papers are organized into four sections arranged into two volumes: basic theories and optimal control of economic systems which appear in the first volume, and special mathematical problems and special applications which are contained in the second volume. Within each section the papers follow in alphabetical order by author. The seven papers on basic theories are a rat...

Financial mathematics

CERN Document Server

Jothi, A Lenin

2009-01-01

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

Mathematics everywhere

CERN Document Server

Aigner, Martin; Spain, Philip G

2010-01-01

Mathematics is all around us. Often we do not realize it, though. Mathematics Everywhere is a collection of presentations on the role of mathematics in everyday life, through science, technology, and culture. The common theme is the unique position of mathematics as the art of pure thought and at the same time as a universally applicable science. The authors are renowned mathematicians; their presentations cover a wide range of topics. From compact discs to the stock exchange, from computer tomography to traffic routing, from electronic money to climate change, they make the "math inside" unde

Engineering mathematics

CERN Document Server

Stroud, K A

2013-01-01

A groundbreaking and comprehensive reference that's been a bestseller since it first debuted in 1970, the new seventh edition of Engineering Mathematics has been thoroughly revised and expanded. Providing a broad mathematical survey, this innovative volume covers a full range of topics from the very basic to the advanced. Whether you're an engineer looking for a useful on-the-job reference or want to improve your mathematical skills, or you are a student who needs an in-depth self-study guide, Engineering Mathematics is sure to come in handy time and time again.

Use of mathematical modelling to assess the impact of vaccines on antibiotic resistance.

Science.gov (United States)

Atkins, Katherine E; Lafferty, Erin I; Deeny, Sarah R; Davies, Nicholas G; Robotham, Julie V; Jit, Mark

2017-11-13

Antibiotic resistance is a major global threat to the provision of safe and effective health care. To control antibiotic resistance, vaccines have been proposed as an essential intervention, complementing improvements in diagnostic testing, antibiotic stewardship, and drug pipelines. The decision to introduce or amend vaccination programmes is routinely based on mathematical modelling. However, few mathematical models address the impact of vaccination on antibiotic resistance. We reviewed the literature using PubMed to identify all studies that used an original mathematical model to quantify the impact of a vaccine on antibiotic resistance transmission within a human population. We reviewed the models from the resulting studies in the context of a new framework to elucidate the pathways through which vaccination might impact antibiotic resistance. We identified eight mathematical modelling studies; the state of the literature highlighted important gaps in our understanding. Notably, studies are limited in the range of pathways represented, their geographical scope, and the vaccine-pathogen combinations assessed. Furthermore, to translate model predictions into public health decision making, more work is needed to understand how model structure and parameterisation affects model predictions and how to embed these predictions within economic frameworks. Copyright © 2017 Elsevier Ltd. All rights reserved.

Apps for Mathematics Learning: A Review of "Educational" Apps from the iTunes App Store

Science.gov (United States)

Highfield, Kate; Goodwin, Kristy

2013-01-01

Increasingly iPads™ are being used in schools and prior-to-school settings, with a plethora of Apps available for mathematics learning. Despite the growing number of Apps available in the iTunes App Store, there has been limited systematic analysis of the pedagogic design of Apps designed for mathematics learning. This paper describes a content…

Brain stimulation, mathematical, and numerical training: Contribution of core and noncore skills.

Science.gov (United States)

Looi, C Y; Cohen Kadosh, R

2016-01-01

Mathematical abilities that are correlated with various life outcomes vary across individuals. One approach to improve mathematical abilities is by understanding the underlying cognitive functions. Theoretical and experimental evidence suggest that mathematical abilities are subserved by "core" and "noncore" skills. Core skills are commonly regarded as the "innate" capacity to attend to and process numerical information, while noncore skills are those that are important for mathematical cognition, but are not exclusive to the mathematical domain such as executive functions, spatial skills, and attention. In recent years, mathematical training has been combined with the application of noninvasive brain stimulation to further enhance training outcomes. However, the development of more strategic training paradigms is hindered by the lack of understanding on the contributory nature of core and noncore skills and their neural underpinnings. In the current review, we will examine the effects of brain stimulation with focus on transcranial electrical stimulation on core and noncore skills, and its impact on mathematical and numerical training. We will conclude with a discussion on the theoretical and experimental implications of these studies and directions for further research. © 2016 Elsevier B.V. All rights reserved.

Hipatia: a hypermedia learning environment in mathematics

Directory of Open Access Journals (Sweden)

Marisol Cueli

2016-01-01

Full Text Available Literature revealed the benefits of different instruments for the development of mathematical competence, problem solving, self-regulated learning, affective-motivational aspects and intervention in students with specific difficulties in mathematics. However, no one tool combined all these variables. The aim of this study is to present and describe the design and development of a hypermedia tool, Hipatia. Hypermedia environments are, by definición, adaptive learning systems, which are usually a web-based application program that provide a personalized learning environment. This paper describes the principles on which Hipatia is based as well as a review of available technologies developed in different academic subjects. Hipatia was created to boost self-regulated learning, develop specific math skills, and promote effective problem solving. It was targeted toward fifth and sixth grade students with and without learning difficulties in mathematics. After the development of the tool, we concluded that it aligned well with the logic underlying the principles of self-regulated learning. Future research is needed to test the efficacy of Hipatia with an empirical methodology.

Mathematical Modeling: Challenging the Figured Worlds of Elementary Mathematics

Science.gov (United States)

Wickstrom, Megan H.

2017-01-01

This article is a report on a teacher study group that focused on three elementary teachers' perceptions of mathematical modeling in contrast to typical mathematics instruction. Through the theoretical lens of figured worlds, I discuss how mathematics instruction was conceptualized across the classrooms in terms of artifacts, discourse, and…

Mathematics Teachers' Ideas about Mathematical Models: A Diverse Landscape

Science.gov (United States)

Bautista, Alfredo; Wilkerson-Jerde, Michelle H.; Tobin, Roger G.; Brizuela, Bárbara M.

2014-01-01

This paper describes the ideas that mathematics teachers (grades 5-9) have regarding mathematical models of real-world phenomena, and explores how teachers' ideas differ depending on their educational background. Participants were 56 United States in-service mathematics teachers. We analyzed teachers' written responses to three open-ended…

Tutorials in mathematical biosciences

CERN Document Server

2008-01-01

The book offers an easy introduction to fast growing research areas in evolution of species, population genetics, ecological models, and population dynamics. The first two chapters review the concept and methodologies of phylogenetic trees; computational schemes and illustrations are given, including applications such as tracing the origin of SARS and influenza. The third chapter introduces the reader to ecological models, including predator-prey models. This chapter includes and introduction to reaction-diffusion equations, which are used to analyze the ecological models. The next chapter reviews a broad range of ongoing research in population dynamics, including evolution of dispersal models; it also features interesting mathematical theorems and lists open problems. The final chapter deals with gene frequencies under the action of migration and selection. The book is addressed to readers at the level of grad students and researchers. A background in PDEs is provided.

Mathematical Modelling Plant Signalling Networks

KAUST Repository

Muraro, D.

2013-01-01

During the last two decades, molecular genetic studies and the completion of the sequencing of the Arabidopsis thaliana genome have increased knowledge of hormonal regulation in plants. These signal transduction pathways act in concert through gene regulatory and signalling networks whose main components have begun to be elucidated. Our understanding of the resulting cellular processes is hindered by the complex, and sometimes counter-intuitive, dynamics of the networks, which may be interconnected through feedback controls and cross-regulation. Mathematical modelling provides a valuable tool to investigate such dynamics and to perform in silico experiments that may not be easily carried out in a laboratory. In this article, we firstly review general methods for modelling gene and signalling networks and their application in plants. We then describe specific models of hormonal perception and cross-talk in plants. This mathematical analysis of sub-cellular molecular mechanisms paves the way for more comprehensive modelling studies of hormonal transport and signalling in a multi-scale setting. © EDP Sciences, 2013.

Mathematics and engineering in real life through mathematical competitions

Science.gov (United States)

More, M.

2018-02-01

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

Discrete Mathematics

DEFF Research Database (Denmark)

Sørensen, John Aasted

2011-01-01

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

Mathematical modeling of cancer metabolism.

Science.gov (United States)

Medina, Miguel Ángel

2018-04-01

Systemic approaches are needed and useful for the study of the very complex issue of cancer. Modeling has a central position in these systemic approaches. Metabolic reprogramming is nowadays acknowledged as an essential hallmark of cancer. Mathematical modeling could contribute to a better understanding of cancer metabolic reprogramming and to identify new potential ways of therapeutic intervention. Herein, I review several alternative approaches to metabolic modeling and their current and future impact in oncology. Copyright © 2018 Elsevier B.V. All rights reserved.

Mathematics Anxiety in Young Children: Concurrent and Longitudinal Associations with Mathematical Performance

Science.gov (United States)

Vukovic, Rose K.; Kieffer, Michael J.; Bailey, Sean P.; Harari, Rachel R.

2013-01-01

This study explored mathematics anxiety in a longitudinal sample of 113 children followed from second to third grade. We examined how mathematics anxiety related to different types of mathematical performance concurrently and longitudinally and whether the relations between mathematics anxiety and mathematical performance differed as a function of…

Introducing philosophy of mathematics

CERN Document Server

Friend, Michele

2014-01-01

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

Mathematical Modelling in the Junior Secondary Years: An Approach Incorporating Mathematical Technology

Science.gov (United States)

Lowe, James; Carter, Merilyn; Cooper, Tom

2018-01-01

Mathematical models are conceptual processes that use mathematics to describe, explain, and/or predict the behaviour of complex systems. This article is written for teachers of mathematics in the junior secondary years (including out-of-field teachers of mathematics) who may be unfamiliar with mathematical modelling, to explain the steps involved…

DEVELOPING STUDENTS’ ABILITY OF MATHEMATICAL CONNECTION THROUGH USING OUTDOOR MATHEMATICS LEARNING

Directory of Open Access Journals (Sweden)

Saleh Haji

2017-01-01

Full Text Available The Purpose of this study is to determine the achievement and improvement of students’ mathematical connectionability through using outdoor mathematics learning. 64 students from the fifth grade of Primary School at SDN 65 and SDN 67 Bengkulu City were taken as the sample of this study. While the method of the research used in this research is experiment with quasi-experimental designs non-equivalent control group. The results of the study are as follows: (1 There is an increasing ability found in mathematical connection of students whom taught by using outdoors mathematics learning is 0,53; (2 Based on statical computation that achievement of students’ ability of mathematical connection is taught by using outdoor mathematics learning score is 71,25. It is higher than the students score 66,25 which were taught by using the conventional learning. So as to improve students’ mathematical connection, teachers are suggested to use the outdoors mathematics learning

Loving + hating mathematics challenging the myths of mathematical life

CERN Document Server

Hersh, Reuben

2011-01-01

Mathematics is often thought of as the coldest expression of pure reason. But few subjects provoke hotter emotions--and inspire more love and hatred--than mathematics. And although math is frequently idealized as floating above the messiness of human life, its story is nothing if not human; often, it is all too human. Loving and Hating Mathematics is about the hidden human, emotional, and social forces that shape mathematics and affect the experiences of students and mathematicians. Written in a lively, accessible style, and filled with gripping stories and anecdotes, Loving and Hating Mathema

Dilemma in Teaching Mathematics

Science.gov (United States)

Md Kamaruddin, Nafisah Kamariah; Md Amin, Zulkarnain

2012-01-01

The challenge in mathematics education is finding the best way to teach mathematics. When students learn the reasoning and proving in mathematics, they will be proficient in mathematics. Students must know mathematics before they can apply it. Symbolism and logic is the key to both the learning of mathematics and its effective application to…

Introductory discrete mathematics

CERN Document Server

Balakrishnan, V K

2010-01-01

This concise text offers an introduction to discrete mathematics for undergraduate students in computer science and mathematics. Mathematics educators consider it vital that their students be exposed to a course in discrete methods that introduces them to combinatorial mathematics and to algebraic and logical structures focusing on the interplay between computer science and mathematics. The present volume emphasizes combinatorics, graph theory with applications to some stand network optimization problems, and algorithms to solve these problems.Chapters 0-3 cover fundamental operations involv

Fatou, Julia, Montel the great prize of mathematical sciences of 1918, and beyond

CERN Document Server

Audin, Michèle

2011-01-01

How did Pierre Fatou and Gaston Julia create what we now call Complex Dynamics, in the context of the early twentieth century and especially of the First World War? The book is based partly on new, unpublished sources.Who were Pierre Fatou, Gaston Julia, Paul Montel? New biographical information is given on the little known mathematician that was Pierre Fatou. How did the serious WW1 injury of Julia influence mathematical life in France? From the reviews of the French edition: "Audin’s book is indeed filled with marvelous biographical information and analysis, dealing not just with the men mentioned in the book’s title but a large number of other players, too … . the book under review addresses itself to scholars for whom the history of mathematics has a particular resonance and especially to mathematicians active, or even with merely an interest in, complex dynamics. … presents it all to the reader in a very appealing form." (Michael Berg, The Mathematical Association of America, October 2009)

Mathematics and Engineering in Real Life through Mathematical Competitions

Science.gov (United States)

More, M.

2018-01-01

We bring out an experience of organizing mathematical competitions that can be used as a medium to motivate the student and teacher minds in new directions of thinking. This can contribute to fostering research, innovation and provide a hands-on experience of mathematical concepts with the real world. Mathematical competitions can be used to build…

Secondary School Mathematics Teachers' Attitude in Teaching Mathematics

OpenAIRE

Mulugeta Atnafu

2014-01-01

The purpose of this study was to examine Addis Ababa secondary school mathematics teachers’ attitude in teaching mathematics. 148 mathematics teachers were selected using cluster sampling from Addis Ababa administration region. The study used survey method of data collection and it includes both quantitative and qualitative research methods. From the independent t-test, ANOVA, tukey test and regression analysis, some of the results obtained were: the majority of the secondary school mathemati...

An Investigation of Mathematical Modeling with Pre-Service Secondary Mathematics Teachers

Science.gov (United States)

Thrasher, Emily Plunkett

2016-01-01

The goal of this thesis was to investigate and enhance our understanding of what occurs while pre-service mathematics teachers engage in a mathematical modeling unit that is broadly based upon mathematical modeling as defined by the Common Core State Standards for Mathematics (National Governors Association Center for Best Practices & Council…

Prevalence of Mixed Methods Research in Mathematics Education

Science.gov (United States)

Ross, Amanda A.; Onwuegbuzie, Anthony J.

2012-01-01

In wake of federal legislation such as the No Child Left Behind Act of 2001 that have called for "scientifically based research in education," this study examined the possible trends in mixed methods research articles published in 2 peer-reviewed mathematics education journals (n = 87) from 2002 to 2006. The study also illustrates how…

Review of Street-Fighting Mathematics: The Art of Educated Guessing and Opportunistic Problem Solving by Sanjoy Mahajan

OpenAIRE

Thomas J. Pfaff

2015-01-01

Mahajan, Sanjoy. Street-Fighting Mathematics: The Art of Educated Guessing and Opportunistic Problem Solving (The MIT Press, Cambridge, Massachusetts, 2010). 152 pp. ISBN 978--0--262--51429--3 Street-Fighting Mathematics is an engaging collection of problem-solving techniques. The book is not for a general audience, as it requires a significant level of mathematical and scientific background knowledge. In particular, most of the book requires knowledge of Calculus I and there are examples ...

Panel Debate: Technics and technology in mathematics and mathematics education

DEFF Research Database (Denmark)

Misfeldt, Morten

2015-01-01

The use of computer technology for teaching and learning of mathematics has several consequences and does sometimes give rise to both controversies and misunderstandings. We address these problems by both a philosophical and a historical approach, investigating what it actually is that goes on when...... guidelines and conclusions regarding the use of computer technology in mathematics education....... new technologies enter mathematics as a discipline and mathematics education as a societal practice. Our analysis suggests a focus on continuities in time and place in the sense that it is necessary to understand the history of “tool use” in mathematics and the various ways that scholastic and non...

Improving students’ creative mathematical reasoning ability students through adversity quotient and argument driven inquiry learning

Science.gov (United States)

Hidayat, W.; Wahyudin; Prabawanto, S.

2018-01-01

This study aimed to investigate the role factors of Adversity Quotient (AQ) and Argument-Driven Inquiry (ADI) instruction in improving mathematical creative reasoning ability from students’ who is a candidate for a math teacher. The study was designed in the form of experiments with a pretest-posttest control group design that aims to examine the role of Adversity Quotient (AQ) and Argument-Driven Inquiry (ADI) learning on improving students’ mathematical creative reasoning abilities. The population in this research was the student of mathematics teacher candidate in Cimahi City, while the sample of this research was 90 students of the candidate of the teacher of mathematics specified purposively then determined randomly which belong to experiment class and control class. Based on the results and discussion, it was concluded that: (1) Improvement the ability of mathematical creative reasoning of students’ who was a candidate for a math teacher who received Argument-Driven Inquiry (ADI) instruction is better than those who received direct instruction is reviewed based on the whole; (2) There was no different improvement the ability of mathematical creative reasoning of students’ who is a candidate for a math teacher who received Argument-Driven Inquiry (ADI) instruction and direct instruction was reviewed based on the type of Adversity Quotient (Quitter / AQ Low, Champer / AQ Medium, and the Climber / AQ High); (3) Learning factors and type of Adversity Quotient (AQ) affected the improvement of students’ mathematical creative reasoning ability. In addition, there was no interaction effect between learning and AQ together in developing of students’ mathematical creative reasoning ability; (4) mathematical creative reasoning ability of students’ who is a candidate for math teacher had not been achieved optimally on the indicators novelty.

Mathematical Models of Breast and Ovarian Cancers

Science.gov (United States)

Botesteanu, Dana-Adriana; Lipkowitz, Stanley; Lee, Jung-Min; Levy, Doron

2016-01-01

Women constitute the majority of the aging United States (US) population, and this has substantial implications on cancer population patterns and management practices. Breast cancer is the most common women's malignancy, while ovarian cancer is the most fatal gynecological malignancy in the US. In this review we focus on these subsets of women's cancers, seen more commonly in postmenopausal and elderly women. In order to systematically investigate the complexity of cancer progression and response to treatment in breast and ovarian malignancies, we assert that integrated mathematical modeling frameworks viewed from a systems biology perspective are needed. Such integrated frameworks could offer innovative contributions to the clinical women's cancers community, since answers to clinical questions cannot always be reached with contemporary clinical and experimental tools. Here, we recapitulate clinically known data regarding the progression and treatment of the breast and ovarian cancers. We compare and contrast the two malignancies whenever possible, in order to emphasize areas where substantial contributions could be made by clinically inspired and validated mathematical modeling. We show how current paradigms in the mathematical oncology community focusing on the two malignancies do not make comprehensive use of, nor substantially reflect existing clinical data, and we highlight the modeling areas in most critical need of clinical data integration. We emphasize that the primary goal of any mathematical study of women's cancers should be to address clinically relevant questions. PMID:27259061

The Joy of Mathematics Discovering Mathematics All Around You

CERN Document Server

Pappas, Theoni

1993-01-01

Part of the joy of mathematics is that it is everywhere-in soap bubbles, electricity, da Vinci's masterpieces, even in an ocean wave. Written by the well-known mathematics teacher consultant, this volume's collection of over 200 clearly illustrated mathematical ideas, concepts, puzzles, and games shows where they turn up in the "real" world. You'll find out what a googol is, visit hotel infinity, read a thorny logic problem that was stumping them back in the 8th century. THE JOY OF MATHEMATICS is designed to be opened at random…it's mini essays are self-contained providing the reader

Grounded Blends and Mathematical Gesture Spaces: Developing Mathematical Understandings via Gestures

Science.gov (United States)

Yoon, Caroline; Thomas, Michael O. J.; Dreyfus, Tommy

2011-01-01

This paper examines how a person's gesture space can become endowed with mathematical meaning associated with mathematical spaces and how the resulting mathematical gesture space can be used to communicate and interpret mathematical features of gestures. We use the theory of grounded blends to analyse a case study of two teachers who used gestures…

Mathematics through Millenia

DEFF Research Database (Denmark)

Hansen, Vagn Lundsgaard

2005-01-01

A brief tour through the history of mathematics from the very beginnings to modern times, with an emphasis on the main contributions and important periods of mathematics in various civilizations.......A brief tour through the history of mathematics from the very beginnings to modern times, with an emphasis on the main contributions and important periods of mathematics in various civilizations....

Mathematics through millenia

DEFF Research Database (Denmark)

Hansen, Vagn Lundsgaard

A brief tour through the history of mathematics from the very beginnings to modern times, with an emphasis on the main contributions and important periods of mathematics in various civilizations.......A brief tour through the history of mathematics from the very beginnings to modern times, with an emphasis on the main contributions and important periods of mathematics in various civilizations....

Mathematical biology

CERN Document Server

Murray, James D

1993-01-01

The book is a textbook (with many exercises) giving an in-depth account of the practical use of mathematical modelling in the biomedical sciences. The mathematical level required is generally not high and the emphasis is on what is required to solve the real biological problem. The subject matter is drawn, e.g. from population biology, reaction kinetics, biological oscillators and switches, Belousov-Zhabotinskii reaction, reaction-diffusion theory, biological wave phenomena, central pattern generators, neural models, spread of epidemics, mechanochemical theory of biological pattern formation and importance in evolution. Most of the models are based on real biological problems and the predictions and explanations offered as a direct result of mathematical analysis of the models are important aspects of the book. The aim is to provide a thorough training in practical mathematical biology and to show how exciting and novel mathematical challenges arise from a genuine interdisciplinary involvement with the biosci...

Mathematics unbound

CERN Document Server

Parshall, Karen Hunger

2002-01-01

Although today's mathematical research community takes its international character very much for granted, this "global nature" is relatively recent, having evolved over a period of roughly 150 years-from the beginning of the nineteenth century to the middle of the twentieth century. During this time, the practice of mathematics changed from being centered on a collection of disparate national communities to being characterized by an international group of scholars for whom the goal of mathematical research and cooperation transcended national boundaries. Yet, the development of an international community was far from smooth and involved obstacles such as war, political upheaval, and national rivalries. Until now, this evolution has been largely overlooked by historians and mathematicians alike. This book addresses the issue by bringing together essays by twenty experts in the history of mathematics who have investigated the genesis of today's international mathematical community. This includes not only develo...

Developing non-routine problems for assessing students’ mathematical literacy

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Murdiyani, N. M.

2018-03-01

The purpose of this study is to develop non-routine problems for assessing the mathematics literacy skills of students, which is valid, practical, and effective. It is based on the previous research said that Indonesian students’ mathematical literacy is still low. The results of this study can be used as a guide in developing the evaluation questions that can train students to improve the ability of solving non-routine problems in everyday life. This research type is formative evaluation that consists of preliminary, self evaluation, expert reviews, one-to-one, small group, and field test. The sample of this research is grade 8 students at one of Junior High School in Yogyakarta. This study results in mathematics literacy problems prototype consisting of level 1 to level 6 problems similar to PISA problems. This study also discusses the examples of students’ answer and their reasoning.

Implementing a new mathematics curriculum: Mathematics teachers’ beliefs and practices

OpenAIRE

Ernest Ampadu

2013-01-01

Mathematics has become a ‘critical filter’ in the social, economic and professional development of individuals and forms a core component of the school curriculum in most countries. It is upon this utilitarian nature of mathematics to the individual and the society as a whole that the school mathematics curriculum has been undergoing a number of restructuring over the last three decades. In Ghana, a new mathematics curriculum was introduced in September 2007 which aims at shifting the teachin...

Mathematics for physicists

CERN Document Server

Martin, B R

2015-01-01

Mathematics for Physicists is a relatively short volume covering all the essential mathematics needed for a typical first degree in physics, from a starting point that is compatible with modern school mathematics syllabuses. Early chapters deliberately overlap with senior school mathematics, to a degree that will depend on the background of the individual reader, who may quickly skip over those topics with which he or she is already familiar. The rest of the book covers the mathematics that is usually compulsory for all students in their first two years of a typical university physics degree, plus a little more. There are worked examples throughout the text, and chapter-end problem sets. Mathematics for Physicists features: * Interfaces with modern school mathematics syllabuses * All topics usually taught in the first two years of a physics degree * Worked examples throughout * Problems in every chapter, with answers to selected questions at the end of the book and full solutions on a website This text will ...

International Conference on Recent Trends in Mathematical Analysis and its Applications 2014

CERN Document Server

Mohapatra, R; Singh, Uaday; Srivastava, H

2015-01-01

This book discusses recent developments in and the latest research on mathematics, statistics and their applications. All contributing authors are eminent academics, scientists, researchers and scholars in their respective fields, hailing from around the world. The book presents roughly 60 unpublished, high-quality and peer-reviewed research papers that cover a broad range of areas including approximation theory, harmonic analysis, operator theory, fixed-point theory, functional differential equations, dynamical and control systems, complex analysis, special functions, function spaces, summability theory, Fourier and wavelet analysis, and numerical analysis – all of which are topics of great interest to the research community – while further papers highlight important applications of mathematical analysis in science, engineering and related areas. This conference aims at bringing together experts and young researchers in mathematics from all over the world to discuss the latest advances in mathematical an...

An Alternative to Piagetian Psychology for Science and Mathematics Education

Science.gov (United States)

Novak, Joseph D.

1978-01-01

Reviews the basic precepts of the learning theories of Piaget and Ausubel. Although Piaget is credited for his contributions to educational psychology, the author supports Ausubel's theory of meaningful learning as more significant for future contributions in science and mathematics education. (CP)

Semiotic Scaffolding in Mathematics

DEFF Research Database (Denmark)

Johansen, Mikkel Willum; Misfeldt, Morten

2015-01-01

This paper investigates the notion of semiotic scaffolding in relation to mathematics by considering its influence on mathematical activities, and on the evolution of mathematics as a research field. We will do this by analyzing the role different representational forms play in mathematical...... cognition, and more broadly on mathematical activities. In the main part of the paper, we will present and analyze three different cases. For the first case, we investigate the semiotic scaffolding involved in pencil and paper multiplication. For the second case, we investigate how the development of new...... in both mathematical cognition and in the development of mathematics itself, but mathematical cognition cannot itself be reduced to the use of semiotic scaffolding....

Mathematical modeling of renal hemodynamics in physiology and pathophysiology.

Science.gov (United States)

Sgouralis, Ioannis; Layton, Anita T

2015-06-01

In addition to the excretion of metabolic waste and toxin, the kidney plays an indispensable role in regulating the balance of water, electrolyte, acid-base, and blood pressure. For the kidney to maintain proper functions, hemodynamic control is crucial. In this review, we describe representative mathematical models that have been developed to better understand the kidney's autoregulatory processes. We consider mathematical models that simulate glomerular filtration, and renal blood flow regulation by means of the myogenic response and tubuloglomerular feedback. We discuss the extent to which these modeling efforts have expanded the understanding of renal functions in health and disease. Copyright © 2015 Elsevier Inc. All rights reserved.

Mathematical and Statistical Methods for Actuarial Sciences and Finance

CERN Document Server

Legros, Florence; Perna, Cira; Sibillo, Marilena

2017-01-01

This volume gathers selected peer-reviewed papers presented at the international conference "MAF 2016 – Mathematical and Statistical Methods for Actuarial Sciences and Finance”, held in Paris (France) at the Université Paris-Dauphine from March 30 to April 1, 2016. The contributions highlight new ideas on mathematical and statistical methods in actuarial sciences and finance. The cooperation between mathematicians and statisticians working in insurance and finance is a very fruitful field, one that yields unique  theoretical models and practical applications, as well as new insights in the discussion of problems of national and international interest. This volume is addressed to academicians, researchers, Ph.D. students and professionals.

TIMSS 2003: Relating dimensions of mathematics attitude to mathematics achievement

Directory of Open Access Journals (Sweden)

Kadijević Đorđe

2008-01-01

Full Text Available This study, which used a sample of 137,346 students from thirty three countries that participated in the TIMSS 2003 project in the eighth grade, examined the features of the individual and collective relations of three dimensions of mathematics attitude to mathematics achievement (MA, searching for the dimension mostly related to that achievement. The three dimensions of mathematics attitude were self-confidence in learning mathematics (SCLM, liking mathematics (LM and usefulness of mathematics (UM. By utilizing psychometrically valid and reliable measures of the three dimensions, it was found that: (1 each dimension of mathematics attitude alone was positively related to MA for almost all thirty three countries; (2 SCLM was primarily related to MA for thirty one countries; (3 when the two other dimensions were held constant, SCLM was positively related to MA for thirty three countries, LM was negatively related to MA for thirty countries, whereas UM was not related to MA for twenty one countries; (4 positive collective relationships of SCLM, LM and UM to MA considerably varied from country to country. Implications for research and practice are included.

Mathematical E-Learning: State of the Art and Experiences at the Open University of Catalonia

Science.gov (United States)

Juan, A.; Huertas, A.; Steegmann, C.; Corcoles, C.; Serrat, C.

2008-01-01

In this article we present a review of the state of the art in mathematical e-learning and some personal experiences on this area developed during the last eleven years at the Open University of Catalonia (UOC), a completely online university located in Spain. The article discusses important aspects related to online mathematics courses offered in…

Philosophy of mathematics

CERN Document Server

Gabbay, Dov M; Woods, John

2009-01-01

One of the most striking features of mathematics is the fact that we are much more certain about the mathematical knowledge we have than about what mathematical knowledge is knowledge of. Are numbers, sets, functions and groups physical entities of some kind? Are they objectively existing objects in some non-physical, mathematical realm? Are they ideas that are present only in the mind? Or do mathematical truths not involve referents of any kind? It is these kinds of questions that have encouraged philosophers and mathematicians alike to focus their attention on issues in the philosophy of mat

Mathematical Models of Elementary Mathematics Learning and Performance. Final Report.

Science.gov (United States)

Suppes, Patrick

This project was concerned with the development of mathematical models of elementary mathematics learning and performance. Probabilistic finite automata and register machines with a finite number of registers were developed as models and extensively tested with data arising from the elementary-mathematics strand curriculum developed by the…

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:

Mathematical Creativity and Mathematical Aptitude: A Cross-Lagged Panel Analysis

Science.gov (United States)

Tyagi, Tarun Kumar

2016-01-01

Cross-lagged panel correlation (CLPC) analysis has been used to identify causal relationships between mathematical creativity and mathematical aptitude. For this study, 480 8th standard students were selected through a random cluster technique from 9 intermediate and high schools of Varanasi, India. Mathematical creativity and mathematical…

A synthesis of mathematical and cognitive performances of students with mathematics learning disabilities.

Science.gov (United States)

Shin, Mikyung; Bryant, Diane Pedrotty

2015-01-01

The purpose of this study was to synthesize the findings from 23 articles that compared the mathematical and cognitive performances of students with mathematics learning disabilities (LD) to (a) students with LD in mathematics and reading, (b) age- or grade-matched students with no LD, and (c) mathematical-ability-matched younger students with no LD. Overall results revealed that students with mathematics LD exhibited higher word problem-solving abilities and no significant group differences on working memory, long-term memory, and metacognition measures compared to students with LD in mathematics and reading. Findings also revealed students with mathematics LD demonstrated significantly lower performance compared to age- or grade-matched students with no LD on both mathematical and cognitive measures. Comparison between students with mathematics LD and younger students with no LD revealed mixed outcomes on mathematical measures and generally no significant group differences on cognitive measures. © Hammill Institute on Disabilities 2013.

Effects of Gender, Mathematics Anxiety and Achievement Motivation on College Students’ Achievement in Mathematics

Directory of Open Access Journals (Sweden)

Ajogbeje Oke James

2013-07-01

Full Text Available The urge to excel or perform maximally in mathematics varies from individual to individual because achievement motivation is often developed or learnt during socialization and learning experiences. The study examined the relationship between College of Education students’ achievement motivation and mathematics achievement, correlation coefficient between mathematics anxiety and college students’ achievement motivation as well as mathematics anxiety and mathematics achievement. The sample, 268 College of Education students offering mathematics as one of their subject combination, was selected using purposive sampling techniques. Three research instruments namely: Mathematics Anxiety Scale (MAS, Achievement Motivation Scale (AMS and Mathematics Achievement Test (MAT were used to collect data for the study. Data collected for the study were analyzed using correlational analysis and ANOVA. The results showed that a significantly low negative correlation coefficient existed between mathematics anxiety and mathematics achievement. There is a negative and significant correlation coefficient between mathematics anxiety and achievement motivation. Similarly, a positive and significant correlation coefficient also exists between achievement motivation and mathematics achievement. Based on the findings of the study, it was recommended that mathematics teachers should adopt activity based strategies and conducive learning environment in order to reduce college students’ anxieties in mathematics learning.

The Mathematics Education Debates: Preparing Students to Become Professionally Active Mathematics Teachers

Science.gov (United States)

Munakata, Mika

2010-01-01

The Mathematics Education Debate is an assignment designed for and implemented in an undergraduate mathematics methods course for prospective secondary school mathematics teachers. For the assignment, students read and analyze current research and policy reports related to mathematics education, prepare and present their positions, offer…

Mathematical Thinking and Creativity through Mathematical Problem Posing and Solving

Science.gov (United States)

Ayllón, María F.; Gómez, Isabel A.; Ballesta-Claver, Julio

2016-01-01

This work shows the relationship between the development of mathematical thinking and creativity with mathematical problem posing and solving. Creativity and mathematics are disciplines that do not usually appear together. Both concepts constitute complex processes sharing elements, such as fluency (number of ideas), flexibility (range of ideas),…

"Mathematics Is Like a Lion": Elementary Students' Beliefs about Mathematics

Science.gov (United States)

Markovits, Zvia; Forgasz, Helen

2017-01-01

The aim of this study was to explore the beliefs of elementary school students about mathematics and about themselves as mathematics learners. The participants, Israeli grade 4 and grade 6 students, completed questionnaires. Using an "animal metaphor" to tap beliefs, some students perceived mathematics as difficult and complicated, while…

Ordinary Mathematical Models in Calculating the Aviation GTE Parameters

Directory of Open Access Journals (Sweden)

E. A. Khoreva

2017-01-01

Full Text Available The paper presents the analytical review results of the ordinary mathematical models of the operating process used to study aviation GTE parameters and characteristics at all stages of its creation and operation. Considers the mathematical models of the zero and the first level, which are mostly used when solving typical problems in calculating parameters and characteristics of engines.Presents a number of practical problems arising in designing aviation GTE for various applications.The application of mathematical models of the zero-level engine can be quite appropriate when the engine is considered as a component in the aircraft system to estimate its calculated individual flight performance or when modeling the flight cycle of the aircrafts of different purpose.The paper demonstrates that introduction of correction functions into the first-level mathematical models in solving typical problems (influence of the Reynolds number, characteristics deterioration of the units during the overhaul period of engine, as well as influence of the flow inhomogeneity at the inlet because of manufacturing tolerance, etc. enables providing a sufficient engineering estimate accuracy to reflect a realistic operating process in the engine and its elements.

Authenticity of Mathematical Modeling

Science.gov (United States)

Tran, Dung; Dougherty, Barbara J.

2014-01-01

Some students leave high school never quite sure of the relevancy of the mathematics they have learned. They fail to see links between school mathematics and the mathematics of everyday life that requires thoughtful decision making and often complex problem solving. Is it possible to bridge the gap between school mathematics and the mathematics in…

Mathematics interventions for children and adolescents with Down syndrome: a research synthesis.

Science.gov (United States)

Lemons, C J; Powell, S R; King, S A; Davidson, K A

2015-08-01

Many children and adolescents with Down syndrome fail to achieve proficiency in mathematics. Researchers have suggested that tailoring interventions based on the behavioural phenotype may enhance efficacy. The research questions that guided this review were (1) what types of mathematics interventions have been empirically evaluated with children and adolescents with Down syndrome?; (2) do the studies demonstrate sufficient methodological rigor?; (3) is there evidence of efficacy for the evaluated mathematics interventions?; and (4) to what extent have researchers considered aspects of the behavioural phenotype in selecting, designing and/or implementing mathematics interventions for children and adolescents with Down syndrome? Nine studies published between 1989 and 2012 were identified for inclusion. Interventions predominantly focused on early mathematics skills and reported positive outcomes. However, no study met criteria for methodological rigor. Further, no authors explicitly considered the behavioural phenotype. Additional research using rigorous experimental designs is needed to evaluate the efficacy of mathematics interventions for children and adolescents with Down syndrome. Suggestions for considering the behavioural phenotype in future research are provided. © 2015 MENCAP and International Association of the Scientific Study of Intellectual and Developmental Disabilities and John Wiley & Sons Ltd.

Pre-Service Secondary Mathematics Teachers' Reflections on Good and Bad Mathematics Teaching

Science.gov (United States)

Dayal, Hem Chand

2013-01-01

Researchers suggest that teachers' beliefs about teaching are strongly influenced by their personal experiences with mathematics. This study aimed to explore Pacific Island pre-service secondary mathematics teachers' perceptions about good and bad mathematics teachers. Thirty pre-service teachers, enrolled in a mathematics teaching methods course…

iPad Apps That Promote Mathematical Knowledge? "Yes, They Exist!"

Science.gov (United States)

Larkin, Kevin

2014-01-01

Having trouble finding the right app? In this article, Kevin Larkin discusses the difficulties teachers encounter when searching the App Store for high quality, appropriate apps that support students' mathematical learning. Kevin provides a useful link to a collection of over 100 app reviews.

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

Mathematical Modeling in Combustion Science

CERN Document Server

Takeno, Tadao

1988-01-01

An important new area of current research in combustion science is reviewed in the contributions to this volume. The complicated phenomena of combustion, such as chemical reactions, heat and mass transfer, and gaseous flows, have so far been studied predominantly by experiment and by phenomenological approaches. But asymptotic analysis and other recent developments are rapidly changing this situation. The contributions in this volume are devoted to mathematical modeling in three areas: high Mach number combustion, complex chemistry and physics, and flame modeling in small scale turbulent flow combustion.

The Effect of Realistic Mathematics Education Approach on Students' Achievement And Attitudes Towards Mathematics

Directory of Open Access Journals (Sweden)

Effandi Zakaria

2017-02-01

Full Text Available This study was conducted to determine the effect of Realistic Mathematics Education Approach on mathematics achievement and student attitudes towards mathematics. This study also sought determine the relationship between student achievement and attitudes towards mathematics. This study used a quasi-experimental design conducted on 61 high school students at SMA Unggul Sigli. Students were divided into two groups, the treatment group $(n = 30$ namely, the Realistic Mathematics Approach group (PMR and the control group $(n = 31$ namely, the traditional group. This study was conducted for six weeks. The instruments used in this study were the achievement test and the attitudes towards mathematics questionnaires. Data were analyzed using SPSS. To determine the difference in mean achievement and attitudes between the two groups, data were analyzed using one-way ANOVA test. The result showed significant differences between the Realistic Mathematics Approach and the traditional approach in terms of achievement. The study showed no significant difference between the Realistic Mathematics Approach and the traditional approach in term of attitudes towards mathematics. It can be concluded that the use of realistic mathematics education approach enhanced students' mathematics achievement, but not attitudes towards mathematics. The Realistic Mathematics Education Approach encourage students to participate actively in the teaching and learning of mathematics. Thus, Realistic Mathematics Education Approach is an appropriate methods to improve the quality of teaching and learning process.

Experiencing mathematics what do we do, when we do mathematics?

CERN Document Server

Hersh, Reuben

2014-01-01

The question "What am I doing?" haunts many creative people, researchers, and teachers. Mathematics, poetry, and philosophy can look from the outside sometimes as ballet en pointe, and at other times as the flight of the bumblebee. Reuben Hersh looks at mathematics from the inside; he collects his papers written over several decades, their edited versions, and new chapters in his book Experiencing Mathematics, which is practical, philosophical, and in some places as intensely personal as Swann's madeleine. -Yuri Manin, Max Planck Institute, Bonn, Germany What happens when mid-career a mathemat

Aspects of Mathematical Modelling of Pressure Retarded Osmosis

Science.gov (United States)

Anissimov, Yuri G.

2016-01-01

In power generating terms, a pressure retarded osmosis (PRO) energy generating plant, on a river entering a sea or ocean, is equivalent to a hydroelectric dam with a height of about 60 meters. Therefore, PRO can add significantly to existing renewable power generation capacity if economical constrains of the method are resolved. PRO energy generation relies on a semipermeable membrane that is permeable to water and impermeable to salt. Mathematical modelling plays an important part in understanding flows of water and salt near and across semipermeable membranes and helps to optimize PRO energy generation. Therefore, the modelling can help realizing PRO energy generation potential. In this work, a few aspects of mathematical modelling of the PRO process are reviewed and discussed. PMID:26848696

Measurement and the mathematical apparatus of quantum physics

International Nuclear Information System (INIS)

Slavnov, D.A.

2007-01-01

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

A review of mathematical functions for the analysis of growth in poultry

NARCIS (Netherlands)

Darmani Kuhi, H.; Porter, T.; Lopez, S.; Kebreab, E.; Strathe, A.B.; Dumas, A.; Dijkstra, J.; France, J.

2010-01-01

Poultry industries face various decisions in the production cycle that affect the profitability of an operation. Predictions of growth when the birds are ready for sale are important factors that contribute to the economy of poultry operations. Mathematical functions called ‘growth functions’ have

Racial Differences in Mathematics Test Scores for Advanced Mathematics Students

Science.gov (United States)

Minor, Elizabeth Covay

2016-01-01

Research on achievement gaps has found that achievement gaps are larger for students who take advanced mathematics courses compared to students who do not. Focusing on the advanced mathematics student achievement gap, this study found that African American advanced mathematics students have significantly lower test scores and are less likely to be…

Primary School Pre-Service Mathematics Teachers' Views on Mathematical Modeling

Science.gov (United States)

Karali, Diren; Durmus, Soner

2015-01-01

The current study aimed to identify the views of pre-service teachers, who attended a primary school mathematics teaching department but did not take mathematical modeling courses. The mathematical modeling activity used by the pre-service teachers was developed with regards to the modeling activities utilized by Lesh and Doerr (2003) in their…

Mathematical physics applied mathematics for scientists and engineers

CERN Document Server

Kusse, Bruce R

2006-01-01

What sets this volume apart from other mathematics texts is its emphasis on mathematical tools commonly used by scientists and engineers to solve real-world problems. Using a unique approach, it covers intermediate and advanced material in a manner appropriate for undergraduate students. Based on author Bruce Kusse's course at the Department of Applied and Engineering Physics at Cornell University, Mathematical Physics begins with essentials such as vector and tensor algebra, curvilinear coordinate systems, complex variables, Fourier series, Fourier and Laplace transforms, differential and integral equations, and solutions to Laplace's equations

Why do early mathematics skills predict later reading? The role of mathematical language.

Science.gov (United States)

Purpura, David J; Logan, Jessica A R; Hassinger-Das, Brenna; Napoli, Amy R

2017-09-01

A growing body of evidence indicates that the development of mathematics and literacy skills is highly related. The importance of literacy skills-specifically language-for mathematics development has been well rationalized. However, despite several prominent studies indicating that mathematics skills are highly predictive of literacy development, the reason for this relation is not well understood. The purpose of this study was to identify how and why early mathematics is predictive of early literacy development. Participants included 125 preschool children 3-5 years old (M = 4 years 3 months). Participants were assessed on mathematics, literacy, and cognitive measures in both the fall and spring of their preschool year. Mediation analyses indicated that the relation between early mathematics and literacy skills is mediated by children's mathematical language skills. These findings suggest that, in prior research identifying mathematical performance as a significant predictor of later literacy skills, mathematical performance may have acted only as a proxy measure for more complex language skills such as those assessed on a mathematical language measure. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

An Invitation to Mathematics

CERN Document Server

Schleicher, Dierk

2011-01-01

This "Invitation to Mathematics" consists of 14 contributions, many from the world's leading mathematicians, which introduce the readers to exciting aspects of current mathematical research. The contributions are as varied as the personalities of active mathematicians, but together they show mathematics as a rich and lively field of research. The contributions are written for interested students at the age of transition between high school and university who know high school mathematics and perhaps competition mathematics and who want to find out what current research mathematics is

The Mathematical Event: Mapping the Axiomatic and the Problematic in School Mathematics

Science.gov (United States)

de Freitas, Elizabeth

2013-01-01

Traditional philosophy of mathematics has been concerned with the nature of mathematical objects rather than events. This traditional focus on reified objects is reflected in dominant theories of learning mathematics whereby the learner is meant to acquire familiarity with ideal mathematical objects, such as number, polygon, or tangent. I argue…

Interventions for Primary School Children With Difficulties in Mathematics.

Science.gov (United States)

Dowker, Ann

2017-01-01

Difficulty with arithmetic is a common problem for children and adults, though there has been some work on the topic for a surprisingly long time. This chapter will review some of the research that has been done over the years on interventions with primary school children. Interventions can be of various levels of intensiveness, ranging from whole-class approaches that take account of individual differences through small-group and limited-time individual interventions to extended-time individual interventions. Interventions discussed here include those involving peer tuition and group collaboration; those involving board and computer games; and those that involve assessing children's strengths and weaknesses in different components of mathematics; and targeting remedial activities to the assessed weaknesses. Most of the interventions discussed in this chapter specifically involve mathematics (usually mainly arithmetic), but there is also some discussion of attempts to improve mathematics by training children in domain-general skills, including Piagetian operations, metacognition, and executive functions. © 2017 Elsevier Inc. All rights reserved.

Magical mathematics the mathematical ideas that animate great magic tricks

CERN Document Server

Diaconis, Persi

2012-01-01

Magical Mathematics reveals the secrets of amazing, fun-to-perform card tricks--and the profound mathematical ideas behind them--that will astound even the most accomplished magician. Persi Diaconis and Ron Graham provide easy, step-by-step instructions for each trick, explaining how to set up the effect and offering tips on what to say and do while performing it. Each card trick introduces a new mathematical idea, and varying the tricks in turn takes readers to the very threshold of today's mathematical knowledge. For example, the Gilbreath Principle--a fantastic effect where the cards remain in control despite being shuffled--is found to share an intimate connection with the Mandelbrot set. Other card tricks link to the mathematical secrets of combinatorics, graph theory, number theory, topology, the Riemann hypothesis, and even Fermat's last theorem.

"Survivor" Math: Using Pop Culture to Enhance Learning Mathematics

Science.gov (United States)

Burks, Robert

2011-01-01

This article describes a modification of the popular TV game show, "Survivor," as conducted in an undergraduate first semester mathematics precalculus course. The objective of this game is a group-based competitive drill and practice activity to help students prepare and review for the fundamental concepts exam. The results of this activity…

Mathematical modelling

CERN Document Server

2016-01-01

This book provides a thorough introduction to the challenge of applying mathematics in real-world scenarios. Modelling tasks rarely involve well-defined categories, and they often require multidisciplinary input from mathematics, physics, computer sciences, or engineering. In keeping with this spirit of modelling, the book includes a wealth of cross-references between the chapters and frequently points to the real-world context. The book combines classical approaches to modelling with novel areas such as soft computing methods, inverse problems, and model uncertainty. Attention is also paid to the interaction between models, data and the use of mathematical software. The reader will find a broad selection of theoretical tools for practicing industrial mathematics, including the analysis of continuum models, probabilistic and discrete phenomena, and asymptotic and sensitivity analysis.

Mathematical modeling

CERN Document Server

Eck, Christof; Knabner, Peter

2017-01-01

Mathematical models are the decisive tool to explain and predict phenomena in the natural and engineering sciences. With this book readers will learn to derive mathematical models which help to understand real world phenomena. At the same time a wealth of important examples for the abstract concepts treated in the curriculum of mathematics degrees are given. An essential feature of this book is that mathematical structures are used as an ordering principle and not the fields of application. Methods from linear algebra, analysis and the theory of ordinary and partial differential equations are thoroughly introduced and applied in the modeling process. Examples of applications in the fields electrical networks, chemical reaction dynamics, population dynamics, fluid dynamics, elasticity theory and crystal growth are treated comprehensively.

Secondary Teachers’ Mathematics-related Beliefs and Knowledge about Mathematical Problem-solving

Science.gov (United States)

E Siswono, T. Y.; Kohar, A. W.; Hartono, S.

2017-02-01

This study investigates secondary teachers’ belief about the three mathematics-related beliefs, i.e. nature of mathematics, teaching mathematics, learning mathematics, and knowledge about mathematical problem solving. Data were gathered through a set of task-based semi-structured interviews of three selected teachers with different philosophical views of teaching mathematics, i.e. instrumental, platonist, and problem solving. Those teachers were selected from an interview using a belief-related task from purposively selected teachers in Surabaya and Sidoarjo. While the interviews about knowledge examine teachers’ problem solving content and pedagogical knowledge, the interviews about beliefs examine their views on several cases extracted from each of such mathematics-related beliefs. Analysis included the categorization and comparison on each of beliefs and knowledge as well as their interaction. Results indicate that all the teachers did not show a high consistency in responding views of their mathematics-related beliefs, while they showed weaknesses primarily on problem solving content knowledge. Findings also point out that teachers’ beliefs have a strong relationship with teachers’ knowledge about problem solving. In particular, the instrumental teacher’s beliefs were consistent with his insufficient knowledge about problem-solving, while both platonist and problem-solving teacher’s beliefs were consistent with their sufficient knowledge of either content or pedagogical problem solving.

Mathematics Connection: Contact

African Journals Online (AJOL)

Principal Contact. Dr. Kofi Mereku Executive Editor Department of Mathematics Education, UCE Mathematical Association of Ghana, C/o Department of Mathematics Education University College of Education of Winneba P. O. Box 25, Winneba, Ghana Phone: +233244961318. Email: dkmereku@uew.edu.gh ...

Middle School Mathematics Students' Perspectives on the Study of Mathematics

Science.gov (United States)

Vaughn, Christy H.

2012-01-01

This qualitative study addressed the perceptions toward the study of mathematics by middle school students who had formerly been in a remedial mathematics program. The purpose of the study was to explore the past experiences of nine students in order to determine what is needed for them to feel successful in mathematics. The conceptual framework…

Mathematics disorder

Science.gov (United States)

... this page: //medlineplus.gov/ency/article/001534.htm Mathematics disorder To use the sharing features on this page, please enable JavaScript. Mathematics disorder is a condition in which a child's ...

Mathematical models of viscous friction

CERN Document Server

Buttà, Paolo; Marchioro, Carlo

2015-01-01

In this monograph we present a review of a number of recent results on the motion of a classical body immersed in an infinitely extended medium and subjected to the action of an external force. We investigate this topic in the framework of mathematical physics by focusing mainly on the class of purely Hamiltonian systems, for which very few results are available. We discuss two cases: when the medium is a gas and when it is a fluid. In the first case, the aim is to obtain microscopic models of viscous friction. In the second, we seek to underline some non-trivial features of the motion. Far from giving a general survey on the subject, which is very rich and complex from both a phenomenological and theoretical point of view, we focus on some fairly simple models that can be studied rigorously, thus providing a first step towards a mathematical description of viscous friction. In some cases, we restrict ourselves to studying the problem at a heuristic level, or we present the main ideas, discussing only some as...

1st Joint India-AMS Meeting in Mathematics : History of Indian Mathematics at the AMS-India Mathematics Conference

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Sridharan, R; Srinivas, M

2005-01-01

This volume consists of a collection of articles based on lectures given by scholars from India, Europe and USA at the sessions on 'History of Indian Mathematics' at the AMS-India mathematics conference in Bangalore during December 2003. These articles cover a wide spectrum of themes in Indian mathematics. They begin with the mathematics of the ancient period dealing with Vedic Prosody and Buddhist Logic, move on to the work of Brahmagupta, of Bhaskara, and that of the mathematicians of the Kerala school of the classical and medieval period, and end with the work of Ramanaujan, and Indian contributions to Quantum Statistics during the modern era. The volume should be of value to those interested in the history of mathematics.

Mathematical concepts

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Jost, Jürgen

2015-01-01

The main intention of this book is to describe and develop the conceptual, structural and abstract thinking of mathematics. Specific mathematical structures are used to illustrate the conceptual approach; providing a deeper insight into mutual relationships and abstract common features. These ideas are carefully motivated, explained and illustrated by examples so that many of the more technical proofs can be omitted. The book can therefore be used: ·         simply as an overview of the panorama of mathematical structures and the relations between them, to be supplemented by more detailed texts whenever you want to acquire a working knowledge of some structure ·         by itself as a first introduction to abstract mathematics ·         together with existing textbooks, to put their results into a more general perspective ·         to gain a new and hopefully deeper perspective after having studied such textbooks Mathematical Concepts has a broader scope and is less detaile...

The Mathematical Formalism of a Particle in a Magnetic Field

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Mantoiu, M

2005-01-01

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

Mathematics without boundaries surveys in interdisciplinary research

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Rassias, Themistocles

2014-01-01

This volume consists of chapters written by eminent scientists and engineers from the international community and presents significant advances in several theories, and applications of an interdisciplinary research. These contributions focus on both old and recent developments of Global Optimization Theory, Convex Analysis, Calculus of Variations, and Discrete Mathematics and Geometry, as well as several applications to a large variety of concrete problems, including  applications of computers  to the study of smoothness and analyticity of functions, applications to epidemiological diffusion, networks, mathematical models of elastic and piezoelectric fields, optimal algorithms, stability of neutral type vector functional differential equations, sampling and rational interpolation for non-band-limited signals, recurrent neural network for convex optimization problems, and experimental design.  The book also contains some review works, which could prove particularly useful for a broader audience of readers i...

Teaching secondary mathematics

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Rock, David

2013-01-01

Solidly grounded in up-to-date research, theory and technology,?Teaching Secondary Mathematics?is a practical, student-friendly, and popular text for secondary mathematics methods courses. It provides clear and useful approaches for mathematics teachers, and shows how concepts typically found in a secondary mathematics curriculum can be taught in a positive and encouraging way. The thoroughly revised fourth edition combines this pragmatic approach with truly innovative and integrated technology content throughout. Synthesized content between the book and comprehensive companion websi

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.

XIV International Conference on Mathematical Programming

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Pardalos, Panos; Rapcsák, Tamás

2001-01-01

This volume contains refereed papers based on the lectures presented at the XIV International Conference on Mathematical Programming held at Matrahaza, Hungary, between 27-31 March 1999. This conference was organized by the Laboratory of Operations Research and Deci­ sion Systems at the Computer and Automation Institute, Hungarian Academy of Sciences. The editors hope this volume will contribute to the theory and applications of mathematical programming. As a tradition of these events, the main purpose of the confer­ ence was to review and discuss recent advances and promising research trends concerning theory, algorithms and applications in different fields of Optimization Theory and related areas such as Convex Analysis, Complementarity Systems and Variational Inequalities. The conference is traditionally held in the Matra Mountains, and housed by the resort house of the Hungarian Academy of Sciences. This was the 14th event of the long lasting series of conferences started in 1973. The organizers wish to...

Review of Street-Fighting Mathematics: The Art of Educated Guessing and Opportunistic Problem Solving by Sanjoy Mahajan

Directory of Open Access Journals (Sweden)

Thomas J. Pfaff

2015-07-01

Full Text Available Mahajan, Sanjoy. Street-Fighting Mathematics: The Art of Educated Guessing and Opportunistic Problem Solving (The MIT Press, Cambridge, Massachusetts, 2010. 152 pp. ISBN 978--0--262--51429--3 Street-Fighting Mathematics is an engaging collection of problem-solving techniques. The book is not for a general audience, as it requires a significant level of mathematical and scientific background knowledge. In particular, most of the book requires knowledge of Calculus I and there are examples that will require knowledge of Physics. At the same time, there are parts of the book that don't require this much background. While the title of the book may be misleading, as it is really street-fighting mathematics for people with a fair amount of training in the subject, there is a lot to be gained from reading this book, and calculus teachers may find it to be a useful resource.

DISCRETE MATHEMATICS/NUMBER THEORY

OpenAIRE

Mrs. Manju Devi*

2017-01-01

Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics such as integers, graphs, and statements do not vary smoothly in this way, but have distinct, separated values. Discrete mathematics therefore excludes topics in "continuous mathematics" such as calculus and analysis. Discrete objects can often be enumerated by ...

Does chess instruction improve mathematical problem-solving ability? Two experimental studies with an active control group.

Science.gov (United States)

Sala, Giovanni; Gobet, Fernand

2017-12-01

It has been proposed that playing chess enables children to improve their ability in mathematics. These claims have been recently evaluated in a meta-analysis (Sala & Gobet, 2016, Educational Research Review, 18, 46-57), which indicated a significant effect in favor of the groups playing chess. However, the meta-analysis also showed that most of the reviewed studies used a poor experimental design (in particular, they lacked an active control group). We ran two experiments that used a three-group design including both an active and a passive control group, with a focus on mathematical ability. In the first experiment (N = 233), a group of third and fourth graders was taught chess for 25 hours and tested on mathematical problem-solving tasks. Participants also filled in a questionnaire assessing their meta-cognitive ability for mathematics problems. The group playing chess was compared to an active control group (playing checkers) and a passive control group. The three groups showed no statistically significant difference in mathematical problem-solving or metacognitive abilities in the posttest. The second experiment (N = 52) broadly used the same design, but the Oriental game of Go replaced checkers in the active control group. While the chess-treated group and the passive control group slightly outperformed the active control group with mathematical problem solving, the differences were not statistically significant. No differences were found with respect to metacognitive ability. These results suggest that the effects (if any) of chess instruction, when rigorously tested, are modest and that such interventions should not replace the traditional curriculum in mathematics.

Mathematics Teaching Today

Science.gov (United States)

Martin, Tami S.; Speer, William R.

2009-01-01

This article describes features, consistent messages, and new components of "Mathematics Teaching Today: Improving Practice, Improving Student Learning" (NCTM 2007), an updated edition of "Professional Standards for Teaching Mathematics" (NCTM 1991). The new book describes aspects of high-quality mathematics teaching; offers a model for observing,…

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

Developmental Mathematics Students: Who are They and What is Their Mathematics Self-Efficacy?

OpenAIRE

Baxter, Ryan; Bates, Alan; Al-Bataineh, Adel Tawfig

2017-01-01

The purpose of this quantitative study was to determine differences indevelopmental mathematics students’ self-efficacy within the demographic datafrom the survey. Data from a sample of 240 Intermediate Algebra students at asingle four-year university using the Mathematics Self-Efficacy Resultsindicate that males possess higher levels of mathematics self-efficacy andconfidence with their mathematical abilities than females. Students whocompleted a lower developmental mathematics course prior ...

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…

Algorithmic mathematics

CERN Document Server

Hougardy, Stefan

2016-01-01

Algorithms play an increasingly important role in nearly all fields of mathematics. This book allows readers to develop basic mathematical abilities, in particular those concerning the design and analysis of algorithms as well as their implementation. It presents not only fundamental algorithms like the sieve of Eratosthenes, the Euclidean algorithm, sorting algorithms, algorithms on graphs, and Gaussian elimination, but also discusses elementary data structures, basic graph theory, and numerical questions. In addition, it provides an introduction to programming and demonstrates in detail how to implement algorithms in C++. This textbook is suitable for students who are new to the subject and covers a basic mathematical lecture course, complementing traditional courses on analysis and linear algebra. Both authors have given this "Algorithmic Mathematics" course at the University of Bonn several times in recent years.

Handbook of mathematics

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Kuipers, L

1969-01-01

International Series of Monographs in Pure and Applied Mathematics, Volume 99: Handbook of Mathematics provides the fundamental mathematical knowledge needed for scientific and technological research. The book starts with the history of mathematics and the number systems. The text then progresses to discussions of linear algebra and analytical geometry including polar theories of conic sections and quadratic surfaces. The book then explains differential and integral calculus, covering topics, such as algebra of limits, the concept of continuity, the theorem of continuous functions (with examp

REJECTION TO LEARNING OF MATHEMATICS BECAUSE OF VIOLENCE IN THE TECHNOLOGICAL BACCALAUREATE

Directory of Open Access Journals (Sweden)

Francisco Caballero-Jiménez

2016-01-01

Full Text Available This paper corresponds the first theoretical and applied results in the thesis of the author and director, and aims to make a conceptual review of school education and its importance in society and the study of mathematics and as these are rejected and stigmatized. In turn, we study, how it manifests itself direct, structural and cultural violence in learning math to finally propose peace education as alternative in order to influence the rejection and stigma regarding mathematics, trying to improve their learning.

Developmental Mathematics Students: Who are They and What is Their Mathematics Self-Efficacy?

OpenAIRE

Ryan Baxter; Alan Bates; Adel Tawfig Al-Bataineh

2016-01-01

The purpose of this quantitative study was to determine differences in developmental mathematics students’ self-efficacy within the demographic data from the survey. Data from a sample of 240 Intermediate Algebra students at a single four-year university using the Mathematics Self-Efficacy Results indicate that males possess higher levels of mathematics self-efficacy and confidence with their mathematical abilities than females. Students who completed a lower developmental mathematics course ...

Mathematical physics

CERN Document Server

Geroch, Robert

1985-01-01

Mathematical Physics is an introduction to such basic mathematical structures as groups, vector spaces, topological spaces, measure spaces, and Hilbert space. Geroch uses category theory to emphasize both the interrelationships among different structures and the unity of mathematics. Perhaps the most valuable feature of the book is the illuminating intuitive discussion of the ""whys"" of proofs and of axioms and definitions. This book, based on Geroch's University of Chicago course, will be especially helpful to those working in theoretical physics, including such areas as relativity, particle

Speed mathematics

CERN Document Server

Handley, Bill

2012-01-01

This new, revised edition of the bestselling Speed Mathematics features new chapters on memorising numbers and general information, calculating statistics and compound interest, square roots, logarithms and easy trig calculations. Written so anyone can understand, this book teaches simple strategies that will enable readers to make lightning-quick calculations. People who excel at mathematics use better strategies than the rest of us; they are not necessarily more intelligent. With Speed Mathematics you'll discover methods to make maths easy and fun. This book is perfect for stud

Masculinities in mathematics

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Mendick, Heather

2006-01-01

The study of mathematics, with other ''gendered'' subjects such as science and engineering, usually attracts more male than female pupils. This book explores this phenomenon, addressing the important question of why more boys than girls choose to study mathematics. It illuminates what studying mathematics means for both students and teachers.

Mathematics at University

DEFF Research Database (Denmark)

Winsløw, Carl

2015-01-01

Mathematics is studied in universities by a large number of students. At the same time it is a field of research for a (smaller) number of university teachers. What relations, if any, exist between university research and teaching of mathematics? Can research “support” teaching? What research...... and what teaching? In this presentation we propose a theoretical framework to study these questions more precisely, based on the anthropological theory of didactics. As a main application, the links between the practices of mathematical research and university mathematics teaching are examined...

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

Mathematics in India

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Plofker, Kim

2009-01-01

Based on extensive research in Sanskrit sources, Mathematics in India chronicles the development of mathematical techniques and texts in South Asia from antiquity to the early modern period. Kim Plofker reexamines the few facts about Indian mathematics that have become common knowledge--such as the Indian origin of Arabic numerals--and she sets them in a larger textual and cultural framework. The book details aspects of the subject that have been largely passed over in the past, including the relationships between Indian mathematics and astronomy, and their cross-fertilizations with Islamic sc

Meaning in mathematics

CERN Document Server

2011-01-01

Is mathematics a highly sophisticated intellectual game in which the adepts display their skill by tackling invented problems, or are mathematicians engaged in acts of discovery as they explore an independent realm of mathematical reality? Why does this seemingly abstract discipline provide the key to unlocking the deep secrets of the physical universe? How one answers these questions will significantly influence metaphysical thinking about reality. This book is intended to fill a gap between popular 'wonders of mathematics' books and the technical writings of the philosophers of mathematics.

The Use of the History of Mathematics in the Teaching Pre-Service Mathematics Teachers

Science.gov (United States)

Galante, Dianna

2014-01-01

Many scholars have written about using the history of mathematics in the teaching of pre-service mathematics teachers. For this study, pre-service mathematics teachers developed an electronic journal of reflections based on presentations in the history of mathematics in a secondary mathematics education course. The main purpose of the…

Construction of mathematical knowledge using graphic calculators (CAS) in the mathematics classroom

Science.gov (United States)

Hitt, Fernando

2011-09-01

Mathematics education researchers are asking themselves about why technology has impacted heavily on the social environment and not in the mathematics classroom. The use of technology in the mathematics classroom has not had the expected impact, as it has been its use in everyday life (i.e. cell phone). What about teachers' opinions? Mathematics teachers can be divided into three categories: those with a boundless overflow (enthusiasm) who want to use the technology without worrying much about the construction of mathematical concepts, those who reject outright the use of technology because they think that their use inhibits the development of mathematical skills and others that reflect on the balance that must exist between paper-pencil activities and use of technology. The mathematics teacher, by not having clear examples that support this last option about the balance of paper-pencil activities and technology, opt for one of the extreme positions outlined above. In this article, we show the results of research on a methodology based on collaborative learning (ACODESA) in the training of mathematics teachers in secondary schools and implementation of activities in an environment of paper-pencil and CAS in the mathematics classroom. We also note that with the development of technology on the use of electronic tablets and interactive whiteboards, these activities will take on greater momentum in the near future.

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.

Empowering Mathematical Practices

Science.gov (United States)

Coomes, Jacqueline; Lee, Hyung Sook

2017-01-01

Mathematics teachers want to empower students as mathematical thinkers and doers (NCTM 2000). Specific ways of thinking and doing mathematics were described in the Process Standards (NCTM 2000); they were further characterized as habits of mind (Mark, Goldenberg, and Sword 2010); and more recently, they were detailed in the Common Core's Standards…

Learners with learning difficulties in mathematics : attitudes, curriculum and methods of teaching mathematics

OpenAIRE

2012-01-01

D.Ed. The aim of this theses is to find out whether there is any relationship between learners' attitudes and learning difficulties in mathematics: To investigate whether learning difficulties in mathematics are associated with learners' gender. To establish the nature of teachers' perceptions of the learning problem areas in the mathematics curriculum. To find out about the teachers' views on the methods of teaching mathematics, resources, learning of mathematics, extra curricular activit...

Studies in Mathematics, Volume X. Applied Mathematics in the High School.

Science.gov (United States)

Schiffer, Max M.

This publication contains a sequence of lectures given to high school mathematics teachers by the author. Applications of mathematics emphasized are elementary algebra, geometry, and matrix algebra. Included are: (1) an introduction concerning teaching applications of mathematics; (2) Chapter 1: Mechanics for the High School Student; (3) Chapter…

Mathematics for the liberal arts

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Bindner, Donald; Hemmeter, Joe

2014-01-01

Presents a clear bridge between mathematics and the liberal arts Mathematics for the Liberal Arts provides a comprehensible and precise introduction to modern mathematics intertwined with the history of mathematical discoveries. The book discusses mathematical ideas in the context of the unfolding story of human thought and highlights the application of mathematics in everyday life. Divided into two parts, Mathematics for the Liberal Arts first traces the history of mathematics from the ancient world to the Middle Ages, then moves on to the Renaissance and finishes with the development of modern mathematics. In the second part, the book explores major topics of calculus and number theory, including problem-solving techniques and real-world applications. This book emphasizes learning through doing, presents a practical approach, and features: A detailed explanation of why mathematical principles are true and how the mathematical processes workNumerous figures and diagrams as well as hundreds of worked example...

Advances in Reactor physics, mathematics and computation. Volume 3

Energy Technology Data Exchange (ETDEWEB)

1987-01-01

These proceedings of the international topical meeting on advances in reactor physics, mathematics and computation, volume 3, are divided into sessions bearing on: - poster sessions on benchmark and codes: 35 conferences - review of status of assembly spectrum codes: 9 conferences - Numerical methods in fluid mechanics and thermal hydraulics: 16 conferences - stochastic transport and methods: 7 conferences.

Engineering mathematics

CERN Document Server

Bird, John

2014-01-01

A practical introduction to the core mathematics required for engineering study and practiceNow in its seventh edition, Engineering Mathematics is an established textbook that has helped thousands of students to succeed in their exams.John Bird's approach is based on worked examples and interactive problems. This makes it ideal for students from a wide range of academic backgrounds as the student can work through the material at their own pace. Mathematical theories are explained in a straightforward manner, being supported by practical engineering examples and applications in order to ensure

Preservice Elementary Mathematics Teachers' Level of Relating Mathematical Concepts in Daily Life Contexts

Science.gov (United States)

Akkus, Oylum

2008-01-01

The purpose of this study was to investigate preservice elementary mathematics teachers' ability of relating mathematical concepts and daily life context. Two research questions were set; what is the preservice elementary mathematics teachers' level of relating mathematical concepts and daily life context regarding to their education year and…

Secondary Mathematics Coaching: The Components of Effective Mathematics Coaching and Implications

Science.gov (United States)

Bengo, Priscilla

2016-01-01

Mathematics coaching, which can be defined broadly as job-embedded learning for mathematics teachers with someone who can help, is being used in Canada to improve teaching practice and increase student achievement. Mathematics coaching research is quite new with little written on the components of effective coaching. The paper attempts to…

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...

Structural Modeling for Influence of Mathematics Self-Concept, Motivation to Learn Mathematics and Self-Regulation Learning on Mathematics Academic Achievement

OpenAIRE

Hamideh Jafari Koshkouei; Ahmad Shahvarani; Mohammad Hassan Behzadi; Mohsen Rostamy-Malkhalifeh

2016-01-01

The present study was carried out to investigate the influence of mathematics self-concept (MSC), motivation to learn mathematics (SMOT) and self-regulation learning (SRL) on students' mathematics academic achievement. This study is of a descriptive survey type. 300 female students at the first grade of high school (the second period) in City Qods, were selected by multiple step cluster sampling method and completed MSC, SMOT and SRL questionnaires. Mathematics academic achievement was measur...

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? 

Making Sense of Mathematics

Science.gov (United States)

Umphrey, Jan

2011-01-01

The National Council of Teachers of Mathematics (NCTM) is a voice and advocate for mathematics educators, working to ensure that all students receive equitable mathematics learning of the highest quality. To help teachers and school leaders understand the Common Core State Standards for Mathematics (CCSSM) and to point out how the CCSSM can be…

Where mathematics come from how the embodied mind brings mathematics into being

CERN Document Server

Lakoff, George

2001-01-01

This book is about mathematical ideas, about what mathematics means-and why. Abstract ideas, for the most part, arise via conceptual metaphor-metaphorical ideas projecting from the way we function in the everyday physical world. Where Mathematics Comes From argues that conceptual metaphor plays a central role in mathematical ideas within the cognitive unconscious-from arithmetic and algebra to sets and logic to infinity in all of its forms.

Pluralism in mathematics a new position in philosophy of mathematics

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Friend, Michèle

2014-01-01

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

Mathematics for physical chemistry

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Mortimer, Robert G

2013-01-01

Mathematics for Physical Chemistry is the ideal supplementary text for practicing chemists and students who want to sharpen their mathematics skills while enrolled in general through physical chemistry courses. This book specifically emphasizes the use of mathematics in the context of physical chemistry, as opposed to being simply a mathematics text. This 4e includes new exercises in each chapter that provide practice in a technique immediately after discussion or example and encourage self-study. The early chapters are constructed around a sequence of mathematical topics, wit

Secondary School Mathematics Teachers' Knowledge Levels and Use of History of Mathematics

Science.gov (United States)

Bütüner, Suphi Önder

2018-01-01

This study describes secondary school mathematics teachers' use of history of mathematics in their classes and their knowledge levels in this field. The study population included a total of 58 secondary school mathematics teachers working at the secondary schools located in Yozgat city center, and the sample included 32 mathematics teachers from…

Mathematical mind-benders

CERN Document Server

Winkler, Peter

2007-01-01

Peter Winkler is at it again. Following the enthusiastic reaction to Mathematical Puzzles: A Connoisseur's Collection, Peter has compiled a new collection of elegant mathematical puzzles to challenge and entertain the reader. The original puzzle connoisseur shares these puzzles, old and new, so that you can add them to your own anthology. This book is for lovers of mathematics, lovers of puzzles, lovers of a challenge. Most of all, it is for those who think that the world of mathematics is orderly, logical, and intuitive-and are ready to learn otherwise! A pdf with errata is updated by the aut

Mathematical knowledge for teaching: Making the tacit more explicit in mathematics teacher education

Science.gov (United States)

Abdullah, Mohd Faizal Nizam Lee; Vimalanandan, Lena

2017-05-01

Teaching practice during school based experiences, afford an opportunity for pre service teachers to put into practice their knowledge for teaching mathematics. Like all knowledge, Mathematical Knowledge for Teaching (MKT) is held in both tacit and explicit form, making it especially difficult to study and map during instruction. This study investigates the tacit and explicit nature of MKT held by pre service teachers in a Malaysian Teacher Education Program and how it impacts the Mathematical Quality of their instruction (MQI). This study of three mathematics pre-service teachers (PSTs), utilised videos of mathematics lessons, reflective debriefs and interviews. The findings suggest that factors such as reflecting, peer-sharing, conferencing with mentors and observing support in making tacit knowledge more explicit during planning and instruction. Implications for preparation of mathematics teachers capable of high Mathematical Quality of Instruction are also discussed.

Teaching mathematics using excel

OpenAIRE

Bonello, Mary Rose; Camilleri, Silvana

2004-01-01

'Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning.' (Principles and Standards for School Mathematics-NCTM April 2000)

2016 Annual Meeting of the Canadian Society for History and Philosophy of Mathematics

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Schlimm, Dirk

2017-01-01

This volume contains fourteen papers that were presented at the 2016 Annual Meeting of the Canadian Society for History and Philosophy of Mathematics/La Société Canadienne d’Histoire et de Philosophie des Mathématiques, held at the University of Calgary in Alberta, Canada. In addition to showcasing rigorously reviewed modern scholarship on an interesting variety of topics in the history and philosophy of mathematics, this meeting also honored the life and work of the logician and philosopher of mathematics Aldo Antonelli (1962-2015). The first four papers in this book are part of that remembrance and have a philosophical focus. Included in these are a discussion of Bolzano’s objections to Kant’s philosophy of mathematics and an examination of the influence of rhetorical and poetic aesthetics on the development of symbols in the 16th and 17thCenturies. The remaining papers deal with the history of mathematics and cover such subjects as Early schemes for polar ordinates in the work of L’Hôpital, bas...

Perception determinants in learning mathematics

Science.gov (United States)

Mokhtar, Siti Fairus; Ali, Noor Rasidah; Rashid, Nurazlina Abdul

2015-05-01

This article described a statistical study of students' perception in mathematics. The objective of this study is to identify factors related to perception about learning mathematics among non mathematics' student. This study also determined the relationship between of these factors among non mathematics' student. 43 items questionnaires were distributed to one hundred students in UiTM Kedah who enrolled in the Business Mathematics course. These items were measured by using a semantic scale with the following anchors: 1 = strongly disagree to 7 = strongly agree. A factor analysis of respondents were identified into five factors that influencing the students' perception in mathematics. In my study, factors identified were attitude, interest, role of the teacher, role of peers and usefulness of mathematics that may relate to the perception about learning mathematics among non mathematics' student.

Construction mathematics

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Virdi, Surinder; Virdi, Narinder Kaur

2014-01-01

Construction Mathematics is an introductory level mathematics text, written specifically for students of construction and related disciplines. Learn by tackling exercises based on real-life construction maths. Examples include: costing calculations, labour costs, cost of materials and setting out of building components. Suitable for beginners and easy to follow throughout. Learn the essential basic theory along with the practical necessities. The second edition of this popular textbook is fully updated to match new curricula, and expanded to include even more learning exercises. End of chapter exercises cover a range of theoretical as well as practical problems commonly found in construction practice, and three detailed assignments based on practical tasks give students the opportunity to apply all the knowledge they have gained. Construction Mathematics addresses all the mathematical requirements of Level 2 construction NVQs from City & Guilds/CITB and Edexcel courses, including the BTEC First Diploma in...

Attitudes of Mathematics Teachers toward Using Smart Board in Teaching Mathematics

Science.gov (United States)

Muhanna, Wafa; Nejem, Khamis Mousa

2013-01-01

This study aimed at investigating the attitudes of mathematics teachers toward using a smart board in teaching mathematics and also to determine the effect of gender, experience, and qualification of teachers on their attitudes. The sample of this study consisted of 74 mathematics teachers--35 males and 39 females--from private schools in Amman…

The role of mathematics in politics as an issue for mathematics teaching

DEFF Research Database (Denmark)

Sánchez, Mario; Blomhøj, Morten

2010-01-01

This paper presents analyses of some examples of mathematical models used in the Mexican society of today. We seek to justify why and illustrate how such examples can be included in mathematics teaching and in teacher education.......This paper presents analyses of some examples of mathematical models used in the Mexican society of today. We seek to justify why and illustrate how such examples can be included in mathematics teaching and in teacher education....

Metacognition Process of Students with High Mathematics Anxiety in Mathematics Problem-Solving

OpenAIRE

Patrisius Afrisno Udil; Tri Atmojo Kusmayadi; Riyadi Riyadi

2017-01-01

This study aims to find out students’ metacognition process while solving the mathematics problem. It focuses on analyzing the metacognition process of students with high mathematics anxiety based on Polya’s problem solving phases. This study uses qualitative research with case study strategy. The subjects consist of 8 students of 7th grade selected through purposive sampling. Data in the form of Mathematics Anxiety Scale (MAS) result and recorded interview while solving mathematics problems ...

Mathematics for the imagination

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Higgins, Peter

2002-01-01

Mathematics for the Imagination provides an accessible and entertaining investigation into mathematical problems in the world around us. From world navigation, family trees, and calendars to patterns, tessellations, and number tricks, this informative and fun new book helps you to understand the maths behind real-life questions and rediscover your arithmetical mind.This is a follow-up to the popular Mathematics for the Curious, Peter Higgins's first investigation into real-life mathematical problems.A highly involving book which encourages the reader to enter into the spirit of mathematical ex

What is mathematical logic?

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

2010-01-01

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

The nature of mathematics

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Jourdain, Philip E B

2007-01-01

Anyone with an interest in mathematics will welcome the republication of this little volume by a remarkable mathematician who was also a logician, a philosopher, and an occasional writer of fiction and poetry. Originally published in 1913, and later included in the acclaimed anthology The World of Mathematics, Jourdain's survey shows how and why the methods of mathematics were developed, traces the development of mathematical science from the earliest to modern times, and chronicles the application of mathematics to natural science.Starting with the ancient Egyptians and Greeks, the author p

Fundamental concepts of mathematics

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Goodstein, R L

Fundamental Concepts of Mathematics, 2nd Edition provides an account of some basic concepts in modern mathematics. The book is primarily intended for mathematics teachers and lay people who wants to improve their skills in mathematics. Among the concepts and problems presented in the book include the determination of which integral polynomials have integral solutions; sentence logic and informal set theory; and why four colors is enough to color a map. Unlike in the first edition, the second edition provides detailed solutions to exercises contained in the text. Mathematics teachers and people

The development of mathematics

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Bell, Eric Temple

1945-01-01

""This important book . . . presents a broad account of the part played by mathematics in the evolution of civilization, describing clearly the main principles, methods, and theories of mathematics that have survived from about 4000 BC to 1940.""― BooklistIn this time-honored study, one of the 20th century's foremost scholars and interpreters of the history and meaning of mathematics masterfully outlines the development of its leading ideas, and clearly explains the mathematics involved in each. According to the author, a professor of mathematics at the California Institute of Technology from

Mathematics in ancient Greece

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Dantzig, Tobias

2006-01-01

More than a history of mathematics, this lively book traces mathematical ideas and processes to their sources, stressing the methods used by the masters of the ancient world. Author Tobias Dantzig portrays the human story behind mathematics, showing how flashes of insight in the minds of certain gifted individuals helped mathematics take enormous forward strides. Dantzig demonstrates how the Greeks organized their precursors' melange of geometric maxims into an elegantly abstract deductive system. He also explains the ways in which some of the famous mathematical brainteasers of antiquity led

The Mathematical Aspects of Quantum Maps

International Nuclear Information System (INIS)

Berkolaiko, G

2003-01-01

The book represents the collected lectures given at the Summer School on Mathematical Aspects of Quantum Maps held at Bologna University in September 2001. Quantum maps gained their prominence as a testing ground for mathematical understanding of various concepts in quantum chaos, such as the spectral statistics, quantum ergodicity, scarring of the eigenfunctions and the connection to algebraic number theory. The book is nicely structured. It begins by reviewing the relevant concepts and results from dynamical systems (a contribution by A Knauf) and number theory (by Z Rudnick). A contribution by the editors, M Degli Esposti and S Graffi, explains the quantization procedure for the quantum maps and proceeds to discuss some properties of the quantized maps, such as ergodicity and scarring, and the number theoretical techniques involved in proving these properties. The contribution by A Baeacker discusses the numerical methods used to study quantum chaotic systems. It contains both the mathematical background and a detailed explanation of the numerical techniques, possible pitfalls at the implementation stage and how to avoid them. It even contains a computer program in Python used by the author to compute the eigenvalues of a perturbed cat map. The last contribution, by R Artuso, while very interesting in itself, feels somewhat disconnected from the rest of the book. It deals with deterministic transport in hyperbolic and weakly chaotic systems, where one can observe normal and anomalous diffusion respectively. Although being a collection of contributions from various authors, the book feels very much like a well-coordinated team effort, with frequent cross-contributional references underlying the connections between different facets of the discussed subjects. I consider it an invaluable reference for researchers in the field of quantum chaos and would recommend it as a first read for people just entering the field. It contains both the necessary background

3rd International Symposium Mathematical Progress in Expressive Image Synthesis

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Ochiai, Hiroyuki

2016-01-01

“Progress in Expressive Image Synthesis” (MEIS2015), was held in Fukuoka, Japan, September 25–27, 2015. The aim of the symposium was to provide a unique venue where various issues in computer graphics (CG) application fields could be discussed by mathematicians, CG researchers, and practitioners. Through the previous symposiums MEIS2013 and MEIS2014, mathematicians as well as CG researchers have recognized that CG is a specific and practical activity derived from mathematical theories. Issues found in CG broaden the field of mathematics and vice versa, and CG visualizes mathematical theories in an aesthetic manner. In this volume, the editors aim to provoke interdisciplinary research projects through the peer-reviewed papers and poster presentations at the this year’s symposium. This book captures interactions among mathematicians, CG researchers, and practitioners sharing important, state-of-the-art issues in graphics and visual perception. The book is suitable for all CG researchers seeking open pro...

International Conference on $p$-Adic Mathematical Physics and its Applications

CERN Document Server

2015-01-01

Since 1987, there have been many interesting and promissing applications of p-adic (non-Archimedean, ultrametric) analysis to some problems of modern mathematical and theoretical physics, and also to some other related fields of sciences. As a result, it emerged a new field of research called p-adic mathematical physics. During this time, there has been permanent interest in investigation of relevant mathematical tools, as well as of possible applications -- from strings to the universe as a whole. In particular, there have been remarkable achievements in some complex biosystems with hierarchy. Enthusiastic researchers believe that application of p-adic analysis and ultrametric methods becomes one of scientific challenges of the 21st century. For the progress in this field in period 1987-2008 one can see review paper http://arxiv.org/abs/0904.4205. For an insight to investigations after 2008 one can look at publications of the journal p-Adic Numbers, Ultrametric Analysis and Applications. To promote this fiel...

Meaning in mathematics education

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Valero, Paola; Hoyles, Celia; Skovsmose, Ole

2005-01-01

What does it mean to know mathematics? How does meaning in mathematics education connect to common sense or to the meaning of mathematics itself? How are meanings constructed and communicated and what are the dilemmas related to these processes? There are many answers to these questions, some of which might appear to be contradictory. Thus understanding the complexity of meaning in mathematics education is a matter of huge importance. There are twin directions in which discussions have developed - theoretical and practical - and this book seeks to move the debate forward along both dimensions while seeking to relate them where appropriate. A discussion of meaning can start from a theoretical examination of mathematics and how mathematicians over time have made sense of their work. However, from a more practical perspective, anybody involved in teaching mathematics is faced with the need to orchestrate the myriad of meanings derived from multiple sources that students develop of mathematical knowledge.

An introduction to the history of algebra solving equations from Mesopotamian times to the Renaissance

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Sesiano, Jacques

2009-01-01

This text should not be viewed as a comprehensive history of algebra before 1600, but as a basic introduction to the types of problems that illustrate the earliest forms of algebra. It would be particularly useful for an instructor who is looking for examples to help enliven a course on elementary algebra with problems drawn from actual historical texts. -Warren Van Egmond about the French edition for MathSciNet This book does not aim to give an exhaustive survey of the history of algebra up to early modern times but merely to present some significant steps in solving equations and, wherever

Philosophical dimensions in mathematics education

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Francois, Karen

2007-01-01

This book brings together diverse recent developments exploring the philosophy of mathematics in education. The unique combination of ethnomathematics, philosophy, history, education, statistics and mathematics offers a variety of different perspectives from which existing boundaries in mathematics education can be extended. The ten chapters in this book offer a balance between philosophy of and philosophy in mathematics education. Attention is paid to the implementation of a philosophy of mathematics within the mathematics curriculum.

Women in mathematics celebrating the centennial of the Mathematical Association of America

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Greenwald, Sarah; Jensen-Vallin, Jacqueline; Mast, Maura

2017-01-01

This collection of refereed papers celebrates the contributions, achievements, and progress of female mathematicians, mostly in the 20th and 21st centuries. Emerging from the themed paper session “The Contributions of Women to Mathematics: 100 Years and Counting” at MAA's 2015 MathFest, this volume contains a diverse mix of current scholarship and exposition on women and mathematics, including biographies, histories, and cultural discussions. The multiplicity of authors also ensures a wide variety of perspectives. In inspiring and informative chapters, the authors featured in this volume reflect on the accomplishments of women in mathematics, showcasing the changes in mathematical culture that resulted as more women obtained tenure-track and tenured academic positions, received prestigious awards and honors, served in leadership roles in professional societies, and became more visibly active in the mathematical community. Readers will find discussions of mathematical excellence at Girton College, Cambridg...

Emotions and Motivation in Mathematics Education: Theoretical Considerations and Empirical Contributions

Science.gov (United States)

Schukajlow, Stanislaw; Rakoczy, K.; Pekrun, R.

2017-01-01

Emotions and motivation are important prerequisites, mediators, and outcomes of learning and achievement. In this article, we first review major theoretical approaches and empirical findings in research on students' emotions and motivation in mathematics, including a discussion of how classroom instruction can support emotions and motivation.…

Relationships of Mathematics Anxiety, Mathematics Self-Efficacy and Mathematics Performance of Adult Basic Education Students

Science.gov (United States)

Watts, Beverly Kinsey

2011-01-01

Competent mathematical skills are needed in the workplace as well as in the college setting. Adults in Adult Basic Education classes and programs generally perform below high school level competency, but very few studies have been performed investigating the predictors of mathematical success for adults. The current study contributes to the…

Improving University Students' Perception of Mathematics and Mathematics Ability

Directory of Open Access Journals (Sweden)

Shelly L. Wismath

2015-01-01

Full Text Available Although mathematical and quantitative reasoning skills are an essential part of adult life in our society, many students arrive at post-secondary education without such skills. Taking a standard mathematics course such as calculus may do little to improve those skills. Using a modification of the Tapia & Marsh questionnaire, we surveyed 62 students taking a broad quantitative reasoning course designed to develop quantitative skills, with respect to two broad attitudinal areas: students’ perception of their own ability, confidence and anxiety, and their perception of the value of mathematics in their studies and their lives. Pre- to post-course comparisons were done by both paired t-tests and Wilcoxon signed-rank tests. Our results showed a significant increase in confidence and decrease in anxiety, while perception of the value of mathematics was already high and changed little by the end of the course.

Mathematical biodescriptors of proteomics maps: background and applications.

Science.gov (United States)

Basak, Subhash C; Gute, Brian D

2008-05-01

This article reviews recent developments in the formulation and application of biodescriptors to characterize proteomics maps. Such biodescriptors can be derived by applying techniques from discrete mathematics (graph theory, linear algebra and information theory). This review focuses on the development of biodescriptors for proteomics maps derived from 2D gel electrophoresis. Preliminary results demonstrated that such descriptors have a reasonable ability to differentiate between proteomics patterns that result from exposure to closely related individual chemicals and complex mixtures, such as the jet fuel JP-8. Further research is required to evaluate the utility of these proteomics-based biodescriptors for drug discovery and predictive toxicology.

Advanced engineering mathematics

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Jeffrey, Alan

2001-01-01

Advanced Engineering Mathematics provides comprehensive and contemporary coverage of key mathematical ideas, techniques, and their widespread applications, for students majoring in engineering, computer science, mathematics and physics. Using a wide range of examples throughout the book, Jeffrey illustrates how to construct simple mathematical models, how to apply mathematical reasoning to select a particular solution from a range of possible alternatives, and how to determine which solution has physical significance. Jeffrey includes material that is not found in works of a similar nature, such as the use of the matrix exponential when solving systems of ordinary differential equations. The text provides many detailed, worked examples following the introduction of each new idea, and large problem sets provide both routine practice, and, in many cases, greater challenge and insight for students. Most chapters end with a set of computer projects that require the use of any CAS (such as Maple or Mathematica) th...

Canadian Mathematical Congress

CERN Document Server

1977-01-01

For two weeks in August, 1975 more than 140 mathematicians and other scientists gathered at the Universite de Sherbrooke. The occasion was the 15th Biennial Seminar of the Canadian Mathematical Congress, entitled Mathematics and the Life Sciences. Participants in this inter­ disciplinary gathering included researchers and graduate students in mathematics, seven different areas of biological science, physics, chemistry and medical science. Geographically, those present came from the United States and the United Kingdom as well as from academic departments and government agencies scattered across Canada. In choosing this particular interdisciplinary topic the programme committee had two chief objectives. These were to promote Canadian research in mathematical problems of the life sciences, and to encourage co-operation and exchanges between mathematical scientists" biologists and medical re­ searchers. To accomplish these objective the committee assembled a stim­ ulating programme of lectures and talks. Six ...

Mathematical quantization

CERN Document Server

Weaver, Nik

2001-01-01

With a unique approach and presenting an array of new and intriguing topics, Mathematical Quantization offers a survey of operator algebras and related structures from the point of view that these objects are quantizations of classical mathematical structures. This approach makes possible, with minimal mathematical detail, a unified treatment of a variety of topics.Detailed here for the first time, the fundamental idea of mathematical quantization is that sets are replaced by Hilbert spaces. Building on this idea, and most importantly on the fact that scalar-valued functions on a set correspond to operators on a Hilbert space, one can determine quantum analogs of a variety of classical structures. In particular, because topologies and measure classes on a set can be treated in terms of scalar-valued functions, we can transfer these constructions to the quantum realm, giving rise to C*- and von Neumann algebras.In the first half of the book, the author quickly builds the operator algebra setting. He uses this ...

Mathematical physiology

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Sneyd, James

2009-01-01

There has been a long history of interaction between mathematics and physiology. This book looks in detail at a wide selection of mathematical models in physiology, showing how physiological problems can be formulated and studied mathematically, and how such models give rise to interesting and challenging mathematical questions. With its coverage of many recent models it gives an overview of the field, while many older models are also discussed, to put the modern work in context. In this second edition the coverage of basic principles has been expanded to include such topics as stochastic differential equations, Markov models and Gibbs free energy, and the selection of models has also been expanded to include some of the basic models of fluid transport, respiration/perfusion, blood diseases, molecular motors, smooth muscle, neuroendrocine cells, the baroreceptor loop, turboglomerular oscillations, blood clotting and the retina. Owing to this extensive coverage, the second edition is published in two volumes. ...

Brain correlates of mathematical competence in processing mathematical representations

Directory of Open Access Journals (Sweden)

Roland H. Grabner

2011-11-01

Full Text Available The ability to extract numerical information from different representation formats (e.g., equations, tables, or diagrams is a key component of mathematical competence but little is known about its neural correlate. Previous studies comparing mathematically less and more competent adults have focused on mental arithmetic and reported differences in left angular gyrus activity which were interpreted to reflect differential reliance on arithmetic fact retrieval during problem solving. The aim of the present functional magnetic resonance imaging (fMRI study was to investigate the brain correlates of mathematical competence in a task requiring the processing of typical mathematical representations. Twenty-eight adults of lower and higher mathematical competence worked on a representation matching task in which they had to evaluate whether the numerical information of a symbolic equation matches that of a bar chart. Two task conditions without and one condition with arithmetic demands were administered. Both competence groups performed equally well in the non-arithmetic conditions and only differed in accuracy in the condition requiring calculation. Activation contrasts between the groups revealed consistently stronger left angular gyrus activation in the more competent individuals across all three task conditions. The finding of competence-related activation differences independently of arithmetic demands suggests that more and less competent individuals differ in a cognitive process other than arithmetic fact retrieval. Specifically, it is argued that the stronger left angular gyrus activity in the more competent adults may reflect their higher proficiency in processing mathematical symbols. Moreover, the study demonstrates competence-related parietal activation differences that were not accompanied by differential experimental performance.

Mathematization in introductory physics

Science.gov (United States)

Brahmia, Suzanne M.

Mathematization is central to STEM disciplines as a cornerstone of the quantitative reasoning that characterizes these fields. Introductory physics is required for most STEM majors in part so that students develop expert-like mathematization. This dissertation describes coordinated research and curriculum development for strengthening mathematization in introductory physics; it blends scholarship in physics and mathematics education in the form of three papers. The first paper explores mathematization in the context of physics, and makes an original contribution to the measurement of physics students' struggle to mathematize. Instructors naturally assume students have a conceptual mastery of algebra before embarking on a college physics course because these students are enrolled in math courses beyond algebra. This paper provides evidence that refutes the validity of this assumption and categorizes some of the barriers students commonly encounter with quantification and representing ideas symbolically. The second paper develops a model of instruction that can help students progress from their starting points to their instructor's desired endpoints. Instructors recognize that the introductory physics course introduces new ideas at an astonishing rate. More than most physicists realize, however, the way that mathematics is used in the course is foreign to a large portion of class. This paper puts forth an instructional model that can move all students toward better quantitative and physical reasoning, despite the substantial variability of those students' initial states. The third paper describes the design and testing of curricular materials that foster mathematical creativity to prepare students to better understand physics reasoning. Few students enter introductory physics with experience generating equations in response to specific challenges involving unfamiliar quantities and units, yet this generative use of mathematics is typical of the thinking involved in

The Effect of Realistic Mathematics Education Approach on Students' Achievement And Attitudes Towards Mathematics

OpenAIRE

Effandi Zakaria; Muzakkir Syamaun

2017-01-01

This study was conducted to determine the effect of Realistic Mathematics Education Approach on mathematics achievement and student attitudes towards mathematics. This study also sought determine the relationship between student achievement and attitudes towards mathematics. This study used a quasi-experimental design conducted on 61 high school students at SMA Unggul Sigli. Students were divided into two groups, the treatment group $(n = 30)$ namely, the Realistic Mathematics Approach group ...

Orientations toward Mathematical Processes of Prospective Secondary Mathematics Teachers as Related to Work with Tasks

Science.gov (United States)

Cannon, Tenille

2016-01-01

Mathematics can be conceptualized in different ways. Policy documents such as the National Council of Teachers of Mathematics (NCTM) (2000) and the Common Core State Standards Initiative (CCSSI) (2010), classify mathematics in terms of mathematical content (e.g., quadratic functions, Pythagorean theorem) and mathematical activity in the form of…

Abandoning mathematics. Reconstructing the process in the context of the social perception of mathematics

Directory of Open Access Journals (Sweden)

Anna Baczko-Dombi

2018-02-01

Full Text Available Mathematics, as no other school subject, evokes conflicting emotions and contradictory attitudes – from “the gate to a career” and “the queen of science” to the widespread acceptance of mathematical ignorance in society. The process of studying mathematics requires systematic work and patience, as mathematical knowledge has a cumulative nature. In the case of mathematics education, some students abandon mathematics at quite early levels of education and begin to consider themselves “humanists”, which results in serious consequences for future educational and career choices. In this paper, I propose a description of the process of escaping from mathematics in the context of students’ perceptions of this subject, using the results of two studies – one qualitative and the other quantitative.

The Effectiveness of Educational Technology Applications for Enhancing Mathematics Achievement in K-12 Classrooms: A Meta-Analysis. Educator's Summary

Science.gov (United States)

Center for Research and Reform in Education, 2012

2012-01-01

This review summarizes research on the effects of technology use on mathematics achievement in K-12 classrooms. The main research questions included: (1) Do education technology applications improve mathematics achievement in K-12 classrooms as compared to traditional teaching methods without education technology?; and (2) What study and research…

Mathematics of the 19th century mathematical logic, algebra, number theory, probability theory

CERN Document Server

Yushkevich, A

1992-01-01

This multi-authored effort, Mathematics of the nineteenth century (to be fol­ lowed by Mathematics of the twentieth century), is a sequel to the History of mathematics fram antiquity to the early nineteenth century, published in three 1 volumes from 1970 to 1972. For reasons explained below, our discussion of twentieth-century mathematics ends with the 1930s. Our general objectives are identical with those stated in the preface to the three-volume edition, i. e. , we consider the development of mathematics not simply as the process of perfecting concepts and techniques for studying real-world spatial forms and quantitative relationships but as a social process as weIl. Mathematical structures, once established, are capable of a certain degree of autonomous development. In the final analysis, however, such immanent mathematical evolution is conditioned by practical activity and is either self-directed or, as is most often the case, is determined by the needs of society. Proceeding from this premise, we intend...

Making Mathematics.

Science.gov (United States)

Huckstep, Peter

2002-01-01

Contends teachers must resist the temptation to suggest that, while children can create stories and melodies, they cannot create mathematics. Quotes mathematician G. H. Hardy: "A mathematician, like a painter or poet, is a 'maker' of patterns." Considers mathematics should be able to stand up for itself. (BT)

The Language of Mathematics: The Importance of Teaching and Learning Mathematical Vocabulary

Science.gov (United States)

Riccomini, Paul J.; Smith, Gregory W.; Hughes, Elizabeth M.; Fries, Karen M.

2015-01-01

Vocabulary understanding is a major contributor to overall comprehension in many content areas, including mathematics. Effective methods for teaching vocabulary in all content areas are diverse and long standing. Teaching and learning the language of mathematics is vital for the development of mathematical proficiency. Students' mathematical…

Reciprocal Relationships between Mathematics Anxiety and Attitude towards Mathematics in Elementary Students

Science.gov (United States)

Haciomeroglu, Guney

2017-01-01

This current study examined the reciprocal relationship between anxiety and attitude towards mathematics in elementary students. Two instruments (attitudes towards mathematics inventory short form [ATMI-Short Form] and the Revised Fennema-Sherman Mathematics Anxiety Scale [Revised-FSMAS]) were administered to 310 fourth grade elementary students.…

Helping Children Learn Mathematics through Multiple Intelligences and Standards for School Mathematics.

Science.gov (United States)

Adams, Thomasenia Lott

2001-01-01

Focuses on the National Council of Teachers of Mathematics 2000 process-oriented standards of problem solving, reasoning and proof, communication, connections, and representation as providing a framework for using the multiple intelligences that children bring to mathematics learning. Presents ideas for mathematics lessons and activities to…

Rescheduling nursing shifts: scoping the challenge and examining the potential of mathematical model based tools.

Science.gov (United States)

Clark, Alistair; Moule, Pam; Topping, Annie; Serpell, Martin

2015-05-01

To review research in the literature on nursing shift scheduling / rescheduling, and to report key issues identified in a consultation exercise with managers in four English National Health Service trusts to inform the development of mathematical tools for rescheduling decision-making. Shift rescheduling is unrecognised as an everyday time-consuming management task with different imperatives from scheduling. Poor rescheduling decisions can have quality, cost and morale implications. A systematic critical literature review identified rescheduling issues and existing mathematic modelling tools. A consultation exercise with nursing managers examined the complex challenges associated with rescheduling. Minimal research exists on rescheduling compared with scheduling. Poor rescheduling can result in greater disruption to planned nursing shifts and may impact negatively on the quality and cost of patient care, and nurse morale and retention. Very little research examines management challenges or mathematical modelling for rescheduling. Shift rescheduling is a complex and frequent management activity that is more challenging than scheduling. Mathematical modelling may have potential as a tool to support managers to minimise rescheduling disruption. The lack of specific methodological support for rescheduling that takes into account its complexity, increases the likelihood of harm for patients and stress for nursing staff and managers. © 2013 John Wiley & Sons Ltd.

Mathematics, substance and surmise views on the meaning and ontology of mathematics