Related papers: Popularizing mathematics: from eight to infinity
The objective of this paper is to describe a development of an innovative approach to enable students studying science, technology, engineering, and mathematics (STEM) to apply the concepts learned in physics and mathematics to engineering…
A primary goal of physics is to create mathematical models that allow both predictions and explanations of physical phenomena. We weave maths extensively into our physics instruction beginning in high school, and the level and complexity of…
The constantly growing body of scholarly knowledge of science, technology, and humanities is an asset of the mankind. While new discoveries expand the existing knowledge, they may simultaneously render some of it obsolete. It is crucial for…
We encounter mathematical problems in various forms in our lives, thus making mathematical thinking an important human ability. In this paper, we present Bublz!, a simple, click-driven game for children to engage in and develop mathematical…
Decisions about how the population of the United States should be divided into legislative districts have powerful and not fully understood effects on the outcomes of elections. The problem of understanding what we might mean by "fair…
The distinction between sciences is becoming increasingly more artificial -- an approach from one area can be easily applied to the other. More exciting research nowadays is happening perhaps at the interfaces of disciplines like Physics,…
Math word problems form a natural abstraction to a range of quantitative reasoning problems, such as understanding financial news, sports results, and casualties of war. Solving such problems requires the understanding of several…
Over the past few decades the notion of symmetry has played a major role in physics and in the philosophy of physics. Philosophers have used symmetry to discuss the ontology and seeming objectivity of the laws of physics. We introduce…
What would you do if you were asked to "add" knowledge? Would you say that "one plus one knowledge" is two "knowledges"? Less than that? More? Or something in between? Adding knowledge sounds strange, but it brings to the forefront…
Formal logic has often been seen as uniquely placed to analyze mathematical argumentation. While formal logic is certainly necessary for a complete understanding of mathematical practice, it is not sufficient. Important aspects of…
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…
[Taken from the "README" in the book] My goal with this book is to provide some kind of bridge for mathematics between the high-school-level and college-level for physics students. From my perspective, our job as physicists is to observe…
A few remarks on how mathematics quests for freedom.
We will outline our ideas for teaching in the core mathematics disciplines. They are based on our own experience in teaching at a number of universities in the USA, as well as in Europe. While some of the core ideas stay and have stayed…
The theme of the PME-48 conference, Making sure that mathematics education research reaches the classroom, highlights a key concern: not all mathematics education research informs classroom practice. This raises several fundamental…
New understandings of the functioning of human brains engaged in mathematics raise interesting questions for mathematics educators. Novel lines of research are suggested by neuroscientific findings, and new light is shed on some…
Recent developments show that AI can prove research-level theorems in mathematics, both formally and informally. This essay urges mathematicians to stay up-to-date with the technology, to consider the ways it will disrupt mathematical…
This book provides a comprehensive and accessible introduction to the emerging field of AI for mathematics. It covers the core principles and diverse applications of using artificial intelligence to advance mathematical research. Through…
Computing is an indispensable component of nearly all technologies and is ubiquitous for vast segments of society. It is also essential to discoveries and innovations in most disciplines. However, while past grand challenges in science have…
An introduction to total positivity (TP), with the emphasis on efficient TP criteria and parametrizations of TP matrices. Intended for general mathematical audience.