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:...

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' STEM av...

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.

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...

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...

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...

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

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...

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...

"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 ...

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...

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

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.

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.