Program focus

It focuses on deep, research-oriented teaching of Combinatorial Geometry, Game Theory, Discrete Analysis, Random Graphs, Analysis of Complex Networks and other relevant fields.

The program stars with a bunch of courses that we call “re-indroductional”. These are needed to equate students’ basic knowledge in algebra, probability and basic discrete mathematics. We will rely on that basic tools during the next three semesters to build a solid picture of modern combinatorics, with a slight emphasis on graph (and network) theory and geometry. Every semester we will also have at least one course by an invited lecturer.

Prof. Andrey Raigorodskiy, Phystech School director, about Master's program 'Advanced Combinatorics'

Curriculum

• Random graphs
• Advanced graph theory
• Analysis of Complex Networks
• Additive Combinatorics
• Discrete Geometry
• Game Theory

Full program curriculum

Program highlights

Besides courses by strong lectors from MIPT the program also features visiting lectures and mini-courses by top-tier experts in the field from the renowned scientific institutions: D. Gamarnik (MIT), G.O.H. Katona (Rényi Institute), J. Pach (EPFL), B. Sudakov (ETH Zurich), P. Tetali (Georgia Tech), N. Litvak (Twente), and others. This is a really unique combination!

We have strong partnership with many renowned combinatorial research centers all around the world. Among them are: MIT Boston, Renyi Institute Budapest, EPFL Lausanne, Tel-Aviv University, ETH Zurich, INRIA France, Cambridge University UK, UCL UK, Technische and Freie Universities Berlin, Georgia Tech Atlanta, and many others. Thus, we can help our students who successfully finish our Master’s program not only to become PhD students at MIPT, but also to apply for graduate studies at the above-listed partner institutions.

Specific entry requirements

Applicants should have a basic knowledge of: 

• Algebra: groups, rings, fields, finite fields, matrices, polynomials. 
• Linear Algebra: vector spaces, bases, dimension, vector spaces over finite fields, examples. 
• Basics of Combinatorics: rules of addition and multiplication, permutations, combinations with repetition and without, binomial coefficients and binomial theorem. 
• Calculus: limits of sequences, continuous functions, limits of functions, derivatives, Taylor series. 
• Probability: classical definition of event probability, geometrical probability model.