相关论文: The Role of History in Learning and Teaching Mathe…
Most if not all of today's revolutionary technologies have a common foundation, namely the intelligent use of information. It is clear that computers play a central role: but the contribution of mathematics, though less visible, is no less…
These are lectures notes for a 4h30 mini-course held in Ulaanbaatar, National University of Mongolia, August 5-7th 2015, at the summer school "Stochastic Processes and Applications". It aims at presenting an introduction to basic results of…
These lecture notes are based on lectures given in 2019 Saint-Flour Probability School.
The purpose of this paper is to emphasize the role of language in the process of teaching and learning mathematics. We will begin with the definition of mathematics given by Cassiodorus (in its essential features repeated in Kolmogorov's…
In this paper, our aim is to discuss the outcome of a ten-year experimental workshop activity carried out by the Center `matematita' (http://www.matematita.it/) with classes of pre-university students of any age. We analyse the potential…
Based on a variety of philosophical approaches and my own work for decades in pure and applied mathematics teaching and research, I explain my view upon the basic difficulties of acquiring the Mathematical Experience (in the sense of P.J.…
The paper deals with popular mathematics and mathematical education of talented students. The paper is devoted to high school students mathematical conferences, problem contest for them, academical policy. The paper was supported by grant…
A didactical survey of the foundations of Algorithmic Information Theory. These notes are short on motivation, history and background but introduce some of the main techniques and concepts of the field. The "manuscript" has been evolving…
Here I share a few notes I used in various course lectures, talks, etc. Some may be just calculations that in the textbooks are more complicated, scattered, or less specific; others may be simple observations I found useful or curious.
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…
Lectures presented at the 1st CERN Asia-Europe-Pacific School of High-Energy Physics, Fukuoka, Japan, 14-27 October 2012. A pedagogical selection of topics in probability and statistics is presented. Choice and emphasis are driven by the…
This text is based on an invited talk at the Dedekind Symposium at Braunschweig in October 2016. It summarizes views from my recent commented edition of Dedekinds two books on the foundations of mathematics.
The aim of this chapter is to identify and characterise the pedagogical model prescribed for this particular mathematics teaching delivered in post-primary vocational training. More specifically, the contribution investigates two major…
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…
Politics is everywhere. In this paper, I propose a simple model to demonstrate political behavior in human society.
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.
Invitation to the statistical study of language: The topic of this presentation is the interdisciplinary nexus between linguistics and statistics. It targets linguists, for whom it may have a theoretical interest, or professionals that work…
We describe and explain the desire, common among mathematicians, both for unity and independence in its major themes. In the dialogue that follows, we express our spontaneous and considered judgment and reservations by contrasting the…
Mathematics is one of the most powerful conceptual systems developed and used by the human species. Dreams of automated mathematicians have a storied history in artificial intelligence (AI). Rapid progress in AI, particularly propelled by…
People sometimes change their opinions when they discuss things with other people. Researchers can use mathematics to study opinion changes in simplifications of real-life situations. These simplified settings, which are examples of…