Université de Montréal - Département de mathématiques et de statistique - Dimitris Koukoulopoulos
- MAT2050 - analyse 2 (intégrales et suites de fonctions), Université de Montréal, hiver 2016
- MAT2611 - algèbre 2 (anneaux et modules), Université de Montréal, hiver 2016
- MAT3632 - théorie des nombres, Université de Montréal, automne 2017
- MAT6111 - mesure et intégration, cours gradué, Université de Montréal, automne 2017
- MAT6627 - la distribution des nombres premiers, cours gradué, Université de Montréal, automne 2016
- MAT6684W - méthodes de crible, cours gradué, Université de Montréal, automne 2012
Sieve methods: these notes were written for a graduate course on sieve methods at Université de Montréal in the Fall of 2012. While writing them I consulted various sources, primarily Kevin Ford's online notes and the book Opera de cribro by Friedlander and Iwaniec.
UPDATE (March 2015): the notes have been updated to incorporate the recent developements on small and large between primes, as well as a pretentious proof of the Siegel-Walfisz theorem.
The distribution of prime numbers: these notes were written for an introductory course to Analytic Number Theory. The contents include basic summation techniques, elementary prime number theory, a brief introduction to sieve methods, the Prime Number Theorem for arithmetic progressions, Linnik's theorem, the Bombieri-Vinogradov theorem, results on bounded gaps between primes, and the analytic theory of L-functions.
Analyse 2 (in French): these notes were written for the second part of an undergraduate course in Real Analysis. The contents include the theory of Riemann integration, asymptotic techniques for the estimation of sums and integrals, series and sequences of functions, and an introduction to Fourier series.
Théorie des nombres (in French): these notes were written for an advanced undergraduate course in Number Theory. The contents include basic elementary number theory, a brief introduction to group theory and its applications to the study of modular arithmetic, an introduction to diophantine equations, and an introduction to Analytic Number Theory.
Algèbre 2 (in French): these notes, which are in progress, are being written up for the second part of an undergraduate course in Abstract Algebra covering basic ring and module theory.