Related papers: The AMC -- What It Is and Why It Matters
The world of mathematics is often considered abstract, with its symbols, concepts, and topics appearing unrelated to physical objects. However, it is important to recognize that the development of mathematics is fundamentally influenced by…
Mathematics has become inescapable in modern, digitized societies: there is hardly any area of life left that isn't affected by it, and we as mathematicians play a central role in this. Our actions affect what others, in particular our…
A sketch of some of the fundamental notions related to the nature of knowledge is offered, with special focus on the role of mathematics and my own opinions. No single idea exposed here is entirely original; indeed, this topic has been…
This article gives a brief survey of the theory and applications of anomalies.
This article provides a historical overview of Geometry of Numbers. 1. Figures, 2. The circuit problem and its relatives, 3. Minkowski lattice point set, 4. The young Hermann Minkowski, 5. The geometry of numbers develops, 6. Minkowski…
One of the variants for systematizing the activities of the historian of mathematics is proposed, as well as a scheme for organizing research and search work in the preparation of scientific articles and reports on the history of science.
We claim that human mathematics is only a limited part of the consequences of the chosen basic axioms. Properly human mathematics varies with time but appears to have universal features which we try to analyze. In particular the functioning…
An informal guide to the history of Heisenberg's matrix mechanics. It is designed for mathematicians with only a minimal background in either physics or geometry, and it is based upon Heisenberg's original arguments.
An expository hitchhikers guide to some theorems in mathematics.
We try to clarify the relationship between computation and concurrency. Base on the so-called pomsetc automata and step automata, we introduce communication and more operators, and establish the algebras modulo language equivalence and…
In the past two decades, teaching and outreach have come to hold an expected place in more missions of mathematics departments and organizations. Still, there is more to do as a mathematical sciences community for mathematics education and…
The paper describes methodology of math education for students interested in chemistry. Suppose we have mathematical circle 2 hours per week. What can be done? We can not provide any systematic study, but we can choose one subject and show…
In recent years, random matrices have come to play a major role in computational mathematics, but most of the classical areas of random matrix theory remain the province of experts. Over the last decade, with the advent of matrix…
This overview article highlights the critical role of mathematics in artificial intelligence (AI), emphasizing that mathematics provides tools to better understand and enhance AI systems. Conversely, AI raises new problems and drives the…
Over the past thirty years or so the authors have been teaching various programming for mathematics courses at our respective Universities, as well as incorporating computer algebra and numerical computation into traditional mathematics…
In this survey I should like to introduce some concepts of algebraic geometry and try to demonstrate the fruitful interaction between algebraic geometry and computer algebra and, more generally, between mathematics and computer science. One…
This lecture addresses some general ideas behind numerical computations ranging from representation of numbers in computers to stability and accuracy of standard algorithms for some simple mathematical problems.
Everything has already been said about the Monty Hall problem, to the point of attracting attention of the high school mathematics program. The purpose of this text is therefore not to add more, but rather to to sort it out while clarifying…
This article presents a source list to support departments in creating more equitable, diverse, and inclusive mathematics classrooms. Included are relevant general-interest books, as well as articles and books presenting research results…
We provide an introduction to the old-standing problem of isometric immersions. We combine a historical account of its multifaceted advances, which have fascinated geometers and analysts alike, with some of the applications in the…