The student who follows this course will get acquainted with computational tools used to analyze systems with uncertainty arising in engineering, physics, chemistry, and economics. Focus will be on sampling methods as Monte Carlo, quasi Monte Carlo, Mark ...
Homology is one of the most important tools to study topological spaces and it plays an important role in many fields of mathematics. The aim of this course is to introduce this notion, understand its properties and learn how to compute it. There will be m ...
The goal of the course is to introduce relativistic quantum field theory as the conceptual and mathematical framework describing fundamental interactions. ...
This course serves as an introduction to classical differential geometry, which studies the geometric properties of curves and surfaces in the Euclidean space. ...
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. ...
We develop, analyze and implement numerical algorithms to solve optimization problems of the form min f(x) where x is a point on a smooth manifold. To this end, we first study differential and Riemannian geometry (with a focus dictated by computational con ...
Ce cours donne une introduction rigoureuse au principaux thèmes de la théorie des équations différentielles ordinaires (EDO). Les EDO sont fondamentales pour l'étude des systèmes dynamiques et des équations aux dérivées partielles. Des applications dans ce ...
This course will provide an introduction to model category theory, which is an abstract framework for generalizing homotopy theory beyond topological spaces and continuous maps. We will study numerous examples of model categories and their applications in ...