Related papers: D\'e usted una buena pl\'atica de matem\'aticas
Our interdisciplinary team Mathematics for Applications in Cultural Heritage (MACH) aims to use mathematical research for the benefit of the arts and humanities. Our ultimate goal is to create user-friendly software toolkits for artists,…
With the introduction of large language models (LLMs), automatic math reasoning has seen tremendous success. However, current methods primarily focus on providing solutions or using techniques like Chain-of-Thought to enhance…
A significant amount of research has considered mathematical proofs, the students who learn them, and the instructors that teach them, from a variety of perspectives. This paper considers this topic from four main perspectives: students'…
This is the first Internet course on elementary quantum mechanics written in Spanish ("castellano") for the benefit of Spanish speaking students. I thank my eight Mexican students at the Institute of Physics, University of Guanajuato, Leon,…
We present a version of arithmetic in all finite types which allows for a definition of equality at higher types for which all congruence are derivable, for which the soundness of the Dialectica interpretation is provable inside the system…
This talk presents foundations of mathematics as a historically variable set of principles appealing to various modes of human intuition and devoid of any prescriptive/prohibitive power. At each turn of history, foundations crystallize the…
Since its existence, the computer tool has often supported mathematicians, whether it is to implement an approximation method (numerical calculation of a root, of an integral, ...) or to simulate a phenomenon (geometric in nature,…
A general introduction to lattice QCD suitable for graduate students in experimental and theoretical particle physics. Aimed at those who want to know how lattice calculations are done, and what the pitfalls are, without having to do the…
The present study proposes an annotation scheme for classifying the content and discourse contribution of question-answer pairs. We propose detailed guidelines for using the scheme and apply them to dialogues in English, Spanish, and Dutch.…
Mathematical maturity is a key concept for the professional life of a mathematician. This paper is not only a brief discussion of the importance of mathematical maturity but also presents some unusual ways we can use the concept to help our…
"Math is not a spectator sport." "Lecturing is educational malpractice." Slogans like these rally some mathematicians to teach classes that feature "active learning", where lecturing is eschewed for student participation. Yet as much as I…
This text contains over three hundred specific open questions on various topics in additive combinatorics, each placed in context by reviewing all relevant results. While the primary purpose is to provide an ample supply of problems for…
This paper examines various methods and ideas for humanizing mathematics. The term 'humanizing mathematics' which includes elements of 'aesthetic mathematics' refers to approaches that emphasize the aesthetic, philosophical, and subjective…
The present article introduces ptarithmetic (short for "polynomial time arithmetic") -- a formal number theory similar to the well known Peano arithmetic, but based on the recently born computability logic (see…
Can AI solve all math? What do we actually mean by doing mathematics? How do we communicate mathematics? What is mathematics beyond problem solving? This essay is my attempt to answer these questions.
Scientific documents rely on both mathematics and text to communicate ideas. Inspired by the topical correspondence between mathematical equations and word contexts observed in scientific texts, we propose a novel topic model that jointly…
Latent Semantic Analysis (LSA) was initially conceived by the cognitive psychology at the 90s decade. Since its emergence, the LSA has been used to model cognitive processes, pointing out academic texts, compare literature works and analyse…
This is a tract on the art and practice of mathematical writing. Not only does the book cover basic principles of grammar, syntax, and usage, but it takes into account developments of the last twenty years that have been inspired by the…
This is a former PhD student's take on his teacher's scientific philosophy. I describe a set of 'principles' that I believe are conducive to good applied mathematics, and that I have learnt myself from observing Hans van Duijn in action.
These lecture notes provide a self-contained introduction to the mathematical methods required in a Bachelor degree programme in Business, Economics, or Management. In particular, the topics covered comprise real-valued vector and matrix…