Academic Articles & Research Papers

Mathematics in Population Biology

"The formulation, analysis, and re-evaluation of mathematical models in population biology has become a valuable source of insight to mathematicians and biologists alike. This book presents an overview and selected sample of these results a...

DAF-UNet: Deformable U-Net with Atrous-Convolution Feature Pyramid for Retinal Vessel Segmentation

Segmentation of retinal vessels from fundus images is critical for diagnosing diseases such as diabetes and hypertension. However, the inherent challenges posed by the complex geometries of vessels and the highly imbalanced distribution of ...

A Truncated-Kernel Mollification Method for the Cauchy Problem of the Modified Helmholtz Equation

This paper addresses the Cauchy problem for the multi-dimensional modified Helmholtz equation, a classical and severely ill-posed problem. A truncated-kernel mollification method is proposed as an effective regularization approach. Both the...

System 2 Thinking in OpenAI’s o1-Preview Model: Near-Perfect Performance on a Mathematics Exam

The processes underlying human cognition are often divided into System 1, which involves fast, intuitive thinking, and System 2, which involves slow, deliberate reasoning. Previously, large language models were criticized for lacking the de...

Graded weakly 1-absorbing prime ideals

In this paper, we introduce and study graded weakly 1-absorbing prime ideals in graded commutative rings. Let $G$ be a group and $R$ be a $G$-graded commutative ring with a nonzero identity $1\neq0$. A proper graded ideal $P$ of $R$ is call...

Mathematics and Computation

Mathematical Statistics

Traditional texts in mathematical statistics can seem - to some readers-heavily weighted with optimality theory of the various flavors developed in the 1940s and50s, and not particularly relevant to statistical practice. Mathematical Statis...

Mathematical Capabilities of ChatGPT

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...

Mathematics without Numbers

Abstract Develops a structuralist understanding of mathematics, as an alternative to set‐ or type‐theoretic foundations, that respects classical mathematical truth while minimizing Platonist commitments to abstract entities. Modal logic is ...

Advanced Engineering Mathematics

A long-standing, best-selling, comprehensive textbook covering all the mathematics required on upper level engineering mathematics undergraduate courses. Its unique programmed approach takes students...

Mathematics and the Body

This book explores alternative ways to consider the relationship between mathematics and the material world. Drawing on the philosophy of Gilles Châtelet and the post-humanist materialism of Karen Barad, the authors present an 'inclusive ma...

On Mathematical Problem Posing.

In mathematics classes at all levels of schooling in all countries of the world, students can be observed solving problems. The quality and authenticity of these mathematics problems has been the subject of many discussions and debates in r...

Mathematics for Economists

An abundance of applications to current economic analysis, illustrative diagrams, thought-provoking exercises, careful proofs, and a flexible organization-these are the advantages that Mathematics for Economists brings to today's classroom....

The Mathematics of Financial Derivatives

Finance is one of the fastest growing areas in the modern banking and corporate world. This, together with the sophistication of modern financial products, provides a rapidly growing impetus for new mathematical models and modern mathematic...

The Nature of Mathematical Knowledge

Abstract The Nature of Mathematical Knowledge develops and defends an empiricist approach to mathematical knowledge. After offering an account of a priori knowledge, it argues that none of the available accounts of a priori mathematical kno...

The Ethics of Mathematics: Is Mathematics Harmful?

The Handbook of Mathematical Cognition

Part 1: Cognitive Representations for Number and Mathematics. M. Fayol, X. Seron, About Numerical Representations: Insights from Neuropsychological, Experimental and Developmental Studies. M. Brysbaert, Number Recognition in Different Forma...

Introduction to Mathematical Logic.

is sometimes called the foundation of mathematics: the logician studies the kinds of reasoning used in the individual steps of a proof. Alonzo Church was a pioneer in the field of mathematical logic, whose contributions to number theory and...

A Mathematical Theory of Evidence

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 probabilit...

Mathematics and Learning Disabilities

Between 5% and 8% of school-age children have some form of memory or cognitive deficit that interferes with their ability to learn concepts or procedures in one or more mathematical domains. A review of the arithmetical competencies of thes...