The students learn the theory and practice of basic concepts and techniques in algorithms. The course covers mathematical induction, techniques for analyzing algorithms, elementary data structures, major algorithmic paradigms such as dynamic programming, s ...
Concepts de base de l'analyse fonctionnelle linéaire: opérateurs bornés, opérateurs compacts, théorie spectrale pour les opérateurs symétriques et compacts, le théorème de Hahn-Banach, les théorèmes de l'application ouverte et du graphe fermé. ...
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 ...
This course provides students with a working knowledge of macroeconomic models that explicitly incorporate financial markets. The goal is to develop a broad and analytical framework for analyzing the interaction of financial decisions, macroeconomic events ...
The '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 ...
The classical distinction between polynomial time solvable and NP-hard problems is often too coarse. This course covers techniques for proving more fine-grained lower and upper bounds on complexity of computational problems. ...