Top Research Papers on Mathematics

Many intellectual endeavors require mathematical problem solving, but this skill remains beyond the capabilities of computers. To measure this ability in machine learning models, we introduce MATH, a new dataset of 12,500 challenging competition mathematics problems. Each problem in MATH has a full step-by-step solution which can be used to teach models to generate answer derivations and explanations. To facilitate future research and increase accuracy on MATH, we also contribute a large auxiliary pretraining dataset which helps teach models the fundamentals of mathematics. Even though we are ...

The findings indicate that children's environments and interactions related to their learning are supported in the specific context of math learning, and the HME represents a setting in which children learn about math through social interactions with their caregivers.

Meta-analyses from the 1990s previously have established a significant, small-to-moderate, and negative correlation between math achievement and math anxiety. Since these publications, research has continued to investigate this relation with more diverse samples and measures. Thus, the goal of the present meta-analysis was to provide an update of the math anxiety-math achievement relation and its moderators. Analyzing 747 effect sizes accumulated from research conducted between 1992 and 2018, we found a small-to-moderate, negative, and statistically significant correlation ( r = -.28) between ...

The third edition of this significant and groundbreaking book summarizes current research into how young children learn mathematics and how best to develop foundational knowledge to realize more effective teaching. Using straightforward, practical language, early math experts Douglas Clements and Julie Sarama show how learning trajectories help teachers understand children's level of mathematical understanding and lead to better teaching. By focusing on the inherent delight and curiosity behind young children's mathematical reasoning, learning trajectories ultimately make teaching more joyous:...

Abstract Math anxiety is widely considered a potential barrier to success in STEM. Current thinking holds that math anxiety is directly linked to avoidance of and underperformance in STEM domains. However, past evidence supporting these claims is limited in important ways. Perhaps most crucially, it is possible that math anxiety predicts STEM outcomes merely as a proxy for poor math skills. Here, we tested the link between math anxiety and subsequent STEM outcomes by measuring math anxiety, math ability, and several covariates in 183 first-semester university students. We then tracked students...

Graph2Tree is proposed, a novel deep learning architecture that combines the merits of the graph-based encoder and tree-based decoder to generate better solution expressions for math word problem (MWP) solution expressions.

Building upon our previous work on the Wilson-Cowan equations with distributed delays, we study the dynamic behavior in a system of two coupled Wilson-Cowan pairs. We focus in particular on understanding the mechanisms that govern the transitions in and out of oscillatory regimes associated with pathological behavior. We investigate these mechanisms under multiple coupling scenarios, and we compare the effects of using discrete delays versus a weak Gamma delay distribution. We found that, in order to trigger and stop oscillations, each kernel emphasizes different critical combinations of coupl...

Abstract This book explores arguments for and against moral realism and mathematical realism, how they interact, and what they can tell us about areas of philosophical interest more generally. It argues that our mathematical beliefs have no better claim to being self-evident or provable than our moral beliefs. Nor do our mathematical beliefs have better claim to being empirically justified. It is also incorrect that reflection on the “genealogy” of our moral beliefs establishes a lack of parity between the cases. In general, if one is a moral anti-realist on the basis of epistemological consi...

This textbook is a comprehensive introduction to computational mathematics and scientific computing suitable for undergraduate and postgraduate courses. It presents both practical and theoretical aspects of the subject, as well as advantages and pitfalls of classical numerical methods alongside with computer code and experiments in Python. Each chapter closes with modern applications in physics, engineering, and computer science. Features: No previous experience in Python is required. Includes simplified computer code for fast-paced learning and transferable skills development. Includes practi...

A metric to measure the lexicon usage diversity of a given MWP corpus is proposed, and it is demonstrated that ASDiv (Academia Sinica Diverse MWP Dataset) is more diverse than existing corpora.

Based on control-value theory (CVT), we examined longitudinal relations between students' control and value appraisals, three activity-related achievement emotions (enjoyment, anger, and boredom), and math achievement (N = 1,716 fifth and seventh grade students).We assessed appraisals and emotions with self-report measures of perceived competence in math, perceived value of math, and math emotions, and achievement with school grades in math.All variables were measured in each of three consecutive annual assessments.Using structural equation modeling, we tested the CVT proposition that appraisa...

This book provides a thorough overview of mathematical physics, highlighting classical topics as well as recent developments.

We investigate the mathematical capabilities of two iterations of ChatGPT (released 9-January-2023 and 30-January-2023) and of GPT-4 by testing them on publicly available datasets, as well as hand-crafted ones, using a novel methodology. In contrast to formal mathematics, where large databases of formal proofs are available (e.g., the Lean Mathematical Library), current datasets of natural-language mathematics, used to benchmark language models, either cover only elementary mathematics or are very small. We address this by publicly releasing two new datasets: GHOSTS and miniGHOSTS. These are t...

Both in science and in practical affairs we reason by combining facts only inconclusively supported by evidence. Building on an abstract understanding of this process of combination, this book constructs a new theory of epistemic probability. The theory draws on the work of A. P. Dempster but diverges from Depster's viewpoint by identifying his as epistemic probabilities and taking his rule for combining upper and lower as fundamental. The book opens with a critique of the well-known Bayesian theory of epistemic probability. It then proceeds to develop an alternative to the additive set functi...

This textbook presents, in a mathematically precise manner, a unified introduction to deterministic control theory. This second edition includes new chapters that introduce a variety of topics, such as controllability with vanishing energy, boundary control systems, and delayed systems.

Classical, Conformal and Topological Field Theory Classical Mechanics Condensed Matter Physics and Optics Differential Geometry Dirac Operators Dynamical Systems Fluid Dynamics Functional Analysis and Variational Techniques Gauge Theory General Relativity Integrable Systems Lie Groups and Lie Algebras Many Particle Systems Noncommutative Geometry Partial Differential Equations and ODEs Path Integrals and Functional Integrals Perturbation Theory Quantization Techniques Quantum Field Theory Quantum Gravity Quantum Groups Quantum Information and Computation Quantum Mechanics Renormalization Scatt...

This encyclopedia is a comprehensive reference text, covering every topic in the field with entries ranging from short descriptions to much longer pieces where the topic warrants more elaboration. This second edition will include additional entries on new ideas in mathematics education.

This paper describes mathlib, a community-driven effort to build a unified library of mathematics formalized in the Lean proof assistant. Among proof assistant libraries, it is distinguished by its dependently typed foundations, focus on classical mathematics, extensive hierarchy of structures, use of large- and small-scale automation, and distributed organization. We explain the architecture and design decisions of the library and the social organization that has led us here.

The different methods of ML, mathematics behind ML, its application in day to day life and future aspects are reviewed.

Current research into the psychology of children's mathematics is extremely diverse. The present volume reflects this diversity; it is unique in its breadth, bringing together accounts of cutting-edge research from widely differing, sometimes opposing viewpoints. The reader with a grounding in developmental psychology but no knowledge of mathematical development will enjoy a wide ranging and challenging summary of current trends. Those already familiar with some of the work may take the opportunity to broaden their knowledge base and to evaluate new methodologies and the insights they offer. T...

"The philosophy of mathematics will naturally be expected to deal with questions at the frontier of knowledge, as to which comparative certainty is not yet attained. But separation of such questions is hardly likely to be fruitful unless the more scientific parts of mathematics are known. A book dealing with those parts may, therefore, claim to be an introduction to mathematical philosophy..." - Bertrand Russell, from the Preface First published in 1919, Introduction to Mathematical Philosophy shows Russell drawing on his formidable knowledge of philosophy and mathematics to write a brilliant ...

This survey provides a brief and selective overview of research in the philosophy of mathematics education. It asks what makes up the philosophy of mathematics education, what it means, what questions it asks and answers, and what is its overall importance and use? It provides overviews of critical mathematics education, and the most relevant modern movements in the philosophy of mathematics. A case study is provided of an emerging research tradition in one country. This is the Hermeneutic strand of research in the philosophy of mathematics education in Brazil. This illustrates one orientation...

This concise volume presents an overview of mathematical physics & generalized functions, an in-depth study of the "generalized" differential equation.

Fundamentals of Mathematical Statistics is meant for a standard one-semester advanced undergraduate or graduate-level course in Mathematical Statistics. It covers all the key topics—statistical models, linear normal models, exponential families, estimation, asymptotics of maximum likelihood, significance testing, and models for tables of counts. It assumes a good background in mathematical analysis, linear algebra, and probability but includes an appendix with basic results from these areas. Throughout the text, there are numerous examples and graduated exercises that illustrate the topics cov...

The current meta-analysis examined the association between K-12 students' motivation to learn mathematics and mathematics anxiety, and explored the effects of potential moderating factors, including different motivation measures, dimensions of mathematics anxiety, students' developmental stages, and cultural contexts. This meta-analysis was conducted with 73 articles (80 independent samples, total N = 95,872) and a total of 142 effect sizes. Results indicated a moderate, negative correlation between students' motivation for mathematics and mathematics anxiety (r = − 0.42). Moreover, in accorda...

The findings propose mobile devices' integration, running developmentally appropriate apps, in kindergarten classrooms, based on the three levels of Realistic Mathematics Education (RME), targeting fundamental mathematical concepts for the kindergarten level.

The purpose of this study was to reveal both the effects of problem-posing interventions on the mathematical creative ability of students and how students’ creative self-efficacy in mathematics was related to their mathematical creative ability. Elementary school students (n = 205) were randomly assigned to one of two groups: problem-posing or control. Results showed the mathematical creativity for the problem-posing group increased (p < 0.05) more than for students in the control group (d = 0.77). Results from the Confirmatory Factor Analysis showed that mathematical creativity was a higher o...

Social cognitive theory posits that teacher self-efficacy beliefs should be related to not only their own well-being outcomes but also classroom processes and student outcomes in the general ecology of the classroom environment. However, little research has directly examined the associations of teachers' self-efficacy beliefs with these teacher and student-level outcomes simultaneously. The present study proposes and tests an integrative model of the relations of teachers' self-efficacy for teaching math with their job satisfaction and student math achievement both directly and indirectly via ...

R.A. Lesh, Foundations for the Future in Engineering and Other Fields That Are Heavy Users of Mathematics, Science, & Technology, and Diversity by Design: The What, Why, and How of Generativity in Next-Generation Classroom Networks.

This textbook strikes a balance between mathematical foundations and statistical practice. Concepts and methods are presented as clear and relevant through careful explanations and a range of applications involving real data and accessible situations.

When mathematician Hermann Weyl decided to write a book on philosophy, he faced what he referred to as conflicts of conscience--the objective nature of science, he felt, did not mesh easily with the incredulous, uncertain nature of philosophy. Yet the two disciplines were already intertwined. In Philosophy of Mathematics and Natural Science, Weyl examines how advances in philosophy were led by scientific discoveries--the more humankind understood about the physical world, the more curious we became. The book is divided into two parts, one on mathematics and the other on the physical sciences. ...

This survey paper describes how the internet is transforming the mathematics classroom and mathematics teacher education, and identifies trends for future research regarding theoretical and methodological aspects, and recognise new opportunities requiring further engagement.

Representation is an important element for teaching and learning mathematics since utilization of multiple modes of representation would enhance teaching and learning mathematics. Representation is a sign or combination of signs, characters, diagram, objects, pictures, or graphs, which can be utilized in teaching and learning mathematics. Normally, there are four modes of representations in the domain of mathematics: (1) verbal, (2) graphic (3) algebraic, and (4) numeric. Certain type of representations can be dominant in teaching and learning mathematics; however, representation needs to be t...

This book takes stock of the state of affairs of the teaching and learning of mathematical modelling with regard to research, development and practice. It provides a conceptual framework for mathematical modelling in mathematics education at all education levels, as well as the background and resources for teachers to acquire the knowledge and competencies that will allow them to successfully include modelling in their teaching, with an emphasis on the secondary school level. Mathematics teachers, mathematics education researchers and developers will benefit from this book. Expertly written an...

This Research Note presents several contributions and mathematical studies in fluid mechanics, namely in non-Newtonian and viscoelastic fluids and on the Navier-Stokes equations in unbounded domains. It includes review of the mathematical analysis of incompressible and compressible flows and results in magnetohydrodynamic and electrohydrodynamic stability and thermoconvective flow of Boussinesq-Stefan type. These studies, along with brief communications on a variety of related topics comprise the proceedings of a summer course held in Lisbon, Portugal in 1991. Together they provide a set of co...

This textbook presents, in a mathematically precise manner, a unified introduction to deterministic control theory. With the exception of a few more advanced concepts required for the final part of the book, the presentation requires only a knowledge of basic facts from linear algebra, differential equations, and calculus. In addition to classical concepts and ideas, the author covers the stabilization of nonlinear systems using topological methods, realization theory for nonlinear systems, impulsive control and positive systems, the control of rigid bodies, the stabilization of infinite dimen...

The book gives a streamlined introduction to quantum mechanics while describing the basic mathematical structures underpinning this discipline. Starting with an overview of key physical experiments illustrating the origin of the physical foundations, the book proceeds with a description of the basic notions of quantum mechanics and their mathematical content. It then makes its way to topics of current interest, specifically those in which mathematics plays an important role. The more advanced topics presented include: many-body systems, modern perturbation theory, path integrals, the theory of...

Information science has long been a complex and interdisciplinary field. Recent developments in applied mathematics have been employed to construct proper solutions in related fields. In this Special Issue, we deal with research developments in various areas of applied mathematics and/or the application of artificial intelligence, statistical models, etc., to improve the state-of-the-art problems in the field of information science.

Contents: Preface. J.T. Sowder, Making Sense of Numbers in School Mathematics. K.C. Fuson, Research on Learning and Teaching Addition and Subtraction of Whole Numbers. P. Nesher, Solving Multiplication Word Problems. M. Lampert, Teaching and Learning Long Division for Understanding in School. J. Hiebert, Mathematical, Cognitive, and Instructional Analyses of Decimal Fractions. T.E. Kieren, Rational and Fractional Numbers as Mathematical and Personal Knowledge: Implications for Curriculum and Instruction. L.B. Resnick, From Protoquantities to Operators: Building Mathematical Competence on a Fou...

This book includes the seven papers that contributed to the Special Issue of Mathematics entitled “Mathematical Methods in Applied Sciences”. The papers are authored by eminent specialists and aim at presenting to a broad audience some mathematical models which appear in different aspects of modern life. New results in Computational Mathematics are given as well. Emphasis is on Medicine and Public Health, in relation also with Social Sciences. The models in this collection apply in particular to the study of brain cells during a stroke, training management efficiency for elite athletes, and op...