MATH-418: Heat kernel and analysis on manifoldsThis course develops the theory of the heat equation on Riemannian manifolds. We introduce the Laplace-Beltrami operator, the heat semigroup, and the heat kernel, study its fundamental properties, and explore how it "sees" the geometry of the underlying space.
MATH-467: Probabilistic methods in combinatoricsThe 'probabilistic method' is a fundamental tool in combinatorics. The basic idea is as follows: to prove that an object (for example, graph) with certain properties exists, it suffices to prove that if the object is chosen at random, then it has the desir ...
MATH-328: Algebraic geometry I - CurvesAlgebraic geometry is the common language for many branches of modern research in mathematics. This course gives an introduction to this field by studying algebraic curves and their intersection theory. ...
MATH-476: Optimal transportThe first part is devoted to Monge and Kantorovitch problems, discussing the existence and the properties of the optimal plan. The second part introduces the Wasserstein distance on measures and develops applications of optimal transport to PDEs, functiona ...
DH-405: Foundations of digital humanitiesThis course introduces the core concepts and methodologies of Digital Humanities, integrating both theoretical and practical perspectives. Students learn to work with large-scale cultural datasets, acquiring the tools and techniques required for their proc ...
MATH-106(f): Analyse IIÉtudier les concepts fondamentaux d'analyse et le calcul différentiel et intégral des fonctions réelles de plusieurs
variables. ...
CS-401: Applied data analysisThis course teaches the basic techniques, methodologies, and practical skills required to draw meaningful insights from a variety of data, with the help of the most acclaimed software tools in the data science world (pandas, scikit-learn, Spark, etc.) ...
PHYS-460: Nonlinear dynamics, chaos and complex systemsThe course provides students with the tools to approach the study of nonlinear systems and chaotic dynamics. Emphasis is given to concrete examples and numerical applications are carried out during the exercise sessions. ...
MATH-502: Distribution and interpolation spacesThe goal of this course is to give an introduction to the theory of distributions and cover the fundamental results of Sobolev spaces including fractional spaces that appear in the interpolation theory. Those notions are central to the study of partial dif ...
MATH-323: Topology III - HomologyHomology 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 ...
MSE-466: Wood structures, properties and usesThe presentation of tree growth and formation of wood anatomical structures, linked to the description of specific physical and mechanical properties, makes it possible to understand the different forms of utilisation of this material, including aspects of ...
MATH-101(f): Analyse IÉtudier les concepts fondamentaux d'analyse et le calcul différentiel et intégral des fonctions réelles d'une variable. ...
MATH-101(g): Analyse IÉtudier les concepts fondamentaux d'analyse et le calcul différentiel et intégral des fonctions réelles d'une variable. ...
MATH-203(b): Analysis IIILe cours étudie les concepts fondamentaux de l'analyse vectorielle et l'analyse de Fourier en vue de leur utilisation pour
résoudre des problèmes pluridisciplinaires d'ingénierie scientifique. ...
MATH-124: Géométrie pour architectes ICe cours entend exposer les fondements de la géométrie à un triple titre :
1/ de technique mathématique essentielle au processus de conception du projet,
2/ d'objet privilégié des logiciels de conception paramétrique
3/ de composante à part entière de l'h ...
DH-406: Machine learning for DHThis course aims to introduce the basic principles of machine learning in the context of the digital humanities. We will cover both supervised and unsupervised learning techniques, and study and implement methods to analyze diverse data types, such as imag ...
MATH-203(c): Analysis IIILe cours étudie les concepts fondamentaux de l'analyse vectorielle et l'analyse de Fourier en vue de leur utilisation pour
résoudre des problèmes pluridisciplinaires d'ingénierie scientifique. ...
MATH-494: Topics in arithmetic geometryP-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 ...
