Related papers: D\'e usted una buena pl\'atica de matem\'aticas
The mathematical picture language project that we began in 2016 has already yielded interesting results. We also point out areas of mathematics and physics where we hope that it will prove useful in the future.
This is an attempt to present axioms for Euclidean geometry, aiming at the following goals: to work with geometric notions (thus not merely identify points with pairs of numbers, giving a special status to a particular coordinate system);…
This PhD thesis deals with a number of different problems in mathematical physics with the common thread that they have probabilistic aspects. The problems all stem from mathematical studies of lattice systems in statistical and quantum…
Discourse parsing is an integral part of understanding information flow and argumentative structure in documents. Most previous research has focused on inducing and evaluating models from the English RST Discourse Treebank. However,…
Mathematical text is written using a combination of words and mathematical expressions. This combination, along with a specific way of structuring sentences makes it challenging for state-of-art NLP tools to understand and reason on top of…
Group Theory has become an invaluable tool in the physics community. Despite numerous introductory books, the subject remains challenging for beginners. Mathematica has emerged as a popular tool for research and education, offering various…
This article discusses epistemological problems in the philosophy of mathematics and issues concerning the reliability of the mathematical literature.
The purpose of this informal article is to introduce the reader to some of the objects and methods of the theory of p-adic representations. My hope is that students and mathematicians who are new to the subject will find it useful as a…
This paper is an attempt to bring together two approaches to language analysis. The possible use of probabilistic information in principle-based grammars and parsers is considered, including discussion on some theoretical and computational…
This material is a rewriting and expansion of notes for beginning graduate students in seminars in combinatorics (Department of Mathematics, University of California San Diego). Solid skills in linear and multilinear algebra were required…
A popular scientific contribution should not contradict any established facts and ought to be understandable. I complied with both these requirements and am offering a sufficiently full introduction to probability theory. Furthermore, I…
This article of mathematical education reflects author's experience with job applications and teaching methods and procedures to employ in the American Higher Education. It is organized as a standard questionnaire.
The Mizar language aims to capture mathematical vernacular by providing a rich language for mathematics. From the perspective of a user, the richness of the language is welcome because it makes writing texts more "natural". But for the…
In this work we present a state of the art in the area of Computational Creativity (CC). In particular, we address the automatic generation of literary sentences in Spanish. We propose three models of text generation based mainly on…
My purpose is to examine some concepts of mathematical logic, which have been studied by Carlo Cellucci. Today the aim of classical mathematical logic is not to guarantee the certainty of mathematics, but I will argue that logic can help us…
This is an explanation and defense of "mathematical conceptualism" for a general mathematical and philosophical audience. I make a case that it is cogent, rigorous, attractive, and better suited to ordinary mathematical practice than all…
Mathematics is an essential element of physics problem solving, but experts often fail to appreciate exactly how they use it. Math may be the language of science, but math-in-physics is a distinct dialect of that language. Physicists tend…
The paper provides a survey of semantic methods for solution of fundamental tasks in mathematical knowledge management. Ontological models and formalisms are discussed. We propose an ontology of mathematical knowledge, covering a wide range…
This text is aimed at undergraduates, or anyone else who enjoys thinking about shapes and numbers. The goal is to encourage the student to think deeply about seemingly simple things. The main objects of study are lines, squares, and the…
We give an overview of our philosophy of pictures in mathematics. We emphasize a bi-directional process between picture language and mathematical concepts: abstraction and simulation. This motivates a program to understand different…