The main theme in Diopahntine approximation is to approximate a real number by a rational number with a certain denominator bound. The course covers the case of one real number, that is classical and well understood, and proceeds to simultaneous Diophantin ...
L'étudiant acquiert une initiation théorique à la méthode des éléments finis qui constitue la technique la plus courante pour la résolution de problèmes elliptiques en mécanique. Il apprend à appliquer cette méthode à des cas simples et à l'exploiter pour ...
P-adic numbers are a number theoretic analogue of the real numbers, which interpolate between arithmetics, analysis and geometry. In this course we study their basic properties and give various applications, notably we will prove rationality of the Weil Ze ...
The student will learn state-of-the-art algorithms for solving differential equations. The analysis and implementation of these algorithms will be discussed in some detail. ...
This course aims to provide graduate students a thorough grounding in the methods, theory, mathematics and algorithms needed to do research and applications in machine learning. The course covers topics from machine learning, classical statistics, and data ...
Given a quadratic equation, e.g. x^2 + 2*y^2 = 81, how can we decide whether there is a rational solution (x,y)? This basic question is what the theory of Rational Quadratic Forms is all about. The course gives an introduction and highlights fundamental te ...
This course is a modern exposition of "Duke's Theorems" which describe the distribution of representations of large integers by a fixed ternary quadratic form. It will be the occasion to introduce the students to the adelic language, the theory of automorp ...