Related papers: Programme de Langlands en bref
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.
At the 2023 Les Houches Summer School on Theoretical Biological Physics, several students asked for some background on information theory, and so we added a tutorial to the scheduled lectures. This is largely a transcript of that tutorial,…
English: This work is a doctoral thesis in mathematics by compendium of four articles. Here we explain, using a language as simple as possible, the results achieved in those articles. The general objective is the classification of gradings…
We present a general introduction to continued fractions, with special consideration to the function fields case. These notes were prepared for a summer class given this year in Beijing at Beihang university.
In recent years, in France, computer learning (under the term of code) has entered the school curriculum, in primary and high school. This learning is also aimed at developing computer thinking to enable students, girls and boys, to start…
This index covers the lecture notes and the final course project reports for COMP6411 Summer 2010 at Concordia University, Montreal, Canada, Comparative Study of Programming Languages by 4 teams trying compare a set of common criteria and…
These are the notes for two lectures delivered at the Les Houches summer school Mathematical Statistical Mechanics, held in July 2005. I review some basic notions on sparse graph error correcting codes with emphasis on `modern' aspects,…
Large Language Models (LLMs) are increasingly explored for educational tasks such as grading, yet their alignment with human evaluation in real classrooms remains underexamined. In this study, we investigate the feasibility of using an LLM…
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…
Brief lecture notes for a course about random matrices given at the University of Cambridge.
These notes provide a quick introduction to the Coq system and show how it can be used to define logical concepts and functions and reason about them. It is designed as a tutorial, so that readers can quickly start their own experiments,…
Computer Science Circles is a free programming website for beginners that is designed to be fun, easy to use, and accessible to the broadest possible audience. We teach Python since it is simple yet powerful, and the course content is…
This paper investigates how high school students approach computing through an introductory computer science course situated in the Logic Programming (LP) paradigm. This study shows how novice students operate within the LP paradigm while…
These notes contain part of the lectures of an introductory course on orthogonal polynomials and special functions that I gave in the joint PhD Program in Mathematics UC|UP in the academic years 2015-2016 (at University of Porto) and…
The intention of these notes is to give a mathematical account of how I believe students could be taught to think about functional programming languages and to explain how such languages work.
This is a concise foreword to, rather than a review of D-brane physics.
For several years, students visit us on different occasions at the university. But how to bridge from the school curriculum to the contents of the university mathematics? And how to find a focal point at which an active contribute, despite…
Undergraduate programs in science and engineering include at least one course in basic programming, but seldom presented in a contextualized format, where computing is a tool for thinking and learning in the discipline. We have created a…
The rapid growth in natural language processing (NLP) over the last couple years has generated student interest and excitement in learning more about the field. In this paper, we present two types of students that NLP courses might want to…
Juppix is a Linux Live-CD with a comfortable programming environment for the Java, C and O'Caml programming languages that has been distributed to hundreds of undergaduate students at the University of Paris 7 over the last few years. We…