Related papers: Mathematical Encounters
These are the notes of the three lectures I delivered at the mini-workshop "Knot Theory and Number Theory around the A-Polynomial" at the Instituto Superior Tecnico (IST) in Lisbon in January 2014. The goal of the lectures was to…
These lecture notes highlight the mathematical and computational structure relating to the formulation of, and development of algorithms for, the Bayesian approach to inverse problems in differential equations. This approach is fundamental…
We illustrate the use of the notion of derived recurrences introduced earlier to evaluate the algebraic entropy of self-maps of projective spaces. We in particular give an example, where a complete proof is still awaited, but where…
Since the introduction of strong anticipation by D.~Dubois the numerous investigations of concrete systems have been proposed. In proposed paper the new examples of discrete dynamical systems with anticipation are considered. The…
In this note, we present few examples of Piecewise Deterministic Markov Processes and their long time behavior. They share two important features: they are related to concrete models (in biology, networks, chemistry,. . .) and they are…
In this paper, we present a series of mathematical problems which throw interesting lights on flamenco music. More specifically, these are problems in discrete and computational mathematics suggested by an analytical (not compositional)…
The author describes some of his experiences as a mathematician cooperating with diabetes specialists.
This book was intended to serve as supporting material for a mini-course on web geometry delivered at the 27th Brazilian Mathematical Colloquium which took place at IMPA in the last week of July 2009.
Recently delivered lectures on Self-Referential Mathematics, [2], at the Department of Mathematics and Applied Mathematics, University of Pretoria, are briefly presented. Comments follow on the subject, as well as on Inconsistent…
The present paper presents some reflections of the author on divergent series and their role and place in mathematics over the centuries. The point of view presented here is limited to differential equations and dynamical systems.
Since its introduction by P.L. Lions in his lectures and seminars at the College de France, see [9], and also the very helpful notes of Cardialaguet [4] on Lions' lectures, the Master Equation has attracted a lot of interest, and various…
This paper collects and extends the lectures I gave at the "XXIV International Fall Workshop on Geometry and Physics" held in Zaragoza (Spain) August 31 - September 4, 2015. Within these lectures I review the formulation of Quantum…
We overview a series of recent works addressing numerical simulations of partial differential equations in the presence of some elements of randomness. The specific equations manipulated are linear elliptic, and arise in the context of…
Following the processing of individual topics of elementary school mathematics as content of empirical theories the question is adressed wether the associated conception of mathematics finds itself under established concepts, and how it can…
This is the first paper of a series aiming to present a new teaching sequence for Particle Physics in high school. We propose a systematic discussion of the subject, covering not only the understanding of its key concepts, but also of the…
This is the first of a series of papers in which we study deep computations (ultracomputations) and deep iterates, formalizing the ideas of "asymptotic limit" of computations and compositional iterates, respectively. In this first paper of…
In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…
Thirty original and collected problems, puzzles, and paradoxes in mathematics and physics are explained in this paper, taught by the author to the elementary and high school teachers at the University of New Mexico - Gallup in 1997-8 and…
We describe our adventures in creating a new first-year course in Experimental Mathematics that uses active learning. We used a state-of-the-art facility, called The Western Active Learning Space, and got the students to "drive the…
Development of conceptual multiple-choice tests related to a particular physics topic is important for designing research-based learning tools to reduce the difficulties. We explore the difficulties that the advanced undergraduate and…