MATH-220: Topology I - point set topologyA topological space is a space endowed with a notion of nearness. A metric space is an example of a topological space, where a distance function measures the concept of nearness. Within this abstract
MATH-410: Riemann surfacesThis course is an introduction to the theory of Riemann surfaces. Riemann surfaces naturally appear is mathematics in many different ways: as a result of analytic continuation, as quotients of complex
ME-427: Networked control systemsThis course offers an introduction to control systems using communication networks for interfacing sensors, actuators, controllers, and processes. Challenges due to network non-idealities and opportun
CS-448: Sublinear algorithms for big data analysisIn this course we will define rigorous mathematical models for computing on large datasets, cover main algorithmic techniques that have been developed for sublinear (e.g. faster than linear time) data
PHYS-431: Quantum field theory IThe goal of the course is to introduce relativistic quantum field theory as the conceptual and mathematical framework describing fundamental interactions.
MATH-225: Topology II - fundamental groupsOn étudie des notions de topologie générale: unions et quotients d'espaces topologiques; on approfondit les notions de revêtements et de groupe fondamental,et d'attachements de cellules et on démontre
CS-450: Algorithms IIA first graduate course in algorithms, this course assumes minimal background, but moves rapidly. The objective is to learn the main techniques of algorithm analysis and design, while building a reper
MATH-203(a): Analysis III (for SV, MT)The course studies the fundamental concepts of vector analysis and Fourier-Laplace analysis with a view to their use in solving multidisciplinary problems in scientific engineering.
MATH-301: Ordinary differential equationsCe 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 équ
PHYS-432: Quantum field theory IIThe goal of the course is to introduce relativistic quantum field theory as the conceptual and mathematical framework describing fundamental interactions such as Quantum Electrodynamics.
MATH-497: Topology IV.b - homotopy theoryWe propose an introduction to homotopy theory for topological spaces. We define higher homotopy groups and relate them to homology groups. We introduce (co)fibration sequences, loop spaces, and suspen
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
COM-502: Dynamical system theory for engineersLinear and nonlinear dynamical systems are found in all fields of science and engineering. After a short review of linear system theory, the class will explain and develop the main tools for the quali
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 devel
MGT-416: Causal inferenceStudents will learn the core concepts and techniques of network analysis with emphasis on causal inference. Theory and
application will be balanced, with students working directly with network data th
MATH-506: Topology IV.b - cohomology ringsSingular cohomology is defined by dualizing the singular chain complex for spaces. We will study its basic properties, see how it acquires a multiplicative structure and becomes a graded commutative a
