Advanced combinatorics

In September 2015, the Moscow Institute of Physics and Technology launched a new master’s program. Now we are looking for fresh motivated students who wish to apply for that program in 2018. The classes begin Oct. 1.

This program is focused on the modern aspects of combinatorics — or, a bit more generally, discrete mathematics — and their applications in computer science and in the theory of complex networks. You can find a list of courses below, but first we would like to provide some additional details about the program and stress its competitive advantages.

Advantages of the program
  1. The program lasts two years. All courses are taught in English.
  2. The tuition is free for five strongest applicants selected by the program committee. Moreover, these students will be paid a monthly stipend of 5,000 rubles (about $90). A further supplementary scholarship is available as well.
  3. Additional students selected by the committee are welcome to join the program. The annual tuition fee is 4,000 euros (about $4,900).
  4. MIPT provides all students with accommodation in modern buildings on campus. The monthly apartment rental fee is 1,250 rubles, which is just $22.
  5. The Institute helps international students receive a Russian visa and get a health insurance.
  6. Besides courses by great MIPT professors — including Vladimir Dolnikov, Alexei Kanel-Belov, Roman Karasev, Andrey Raigorodskiy, Dmitry Shabanov, Ilya Shkredov, and others — we also invite top researchers from renowned scientific institutions as visiting lecturers. Among them are David Gamarnik from MIT, Gyula O. H. Katona from the Alfréd Rényi Institute of Mathematics (Hungary), János Pach from the École polytechnique fédérale de Lausanne (France) and the Rényi Institute (Hungary), Benny Sudakov from ETH Zurich (Germany), Prasad Tetali from the Georgia Institute of Technology (USA), and Nelly Litvak from the University of Twente (Netherlands). This team is truly unique!
  7. We partner up with renowned combinatorial research centers worldwide. Among them are MIT, the Alfréd Rényi Institute of Mathematics, the École polytechnique fédérale de Lausanne, Tel-Aviv University, ETH Zurich, the French Institute for Research in Computer Science and Automation (Inria), Cambridge University, University College London, the Free University of Berlin (FU Berlin), the Technical University of Berlin (TU Berlin), Georgia Tech, and many others. Thus, we can help our students who complete the master’s program to not only become PhD students at MIPT, but also apply for graduate studies at the partner institutions mentioned above.
  8. MIPT’s Department of Discrete Mathematics, which is responsible for this master’s program, employs prominent professors and has a well-established partnership with Yandex — the company behind Russia’s top search engine. Professor Andrey Raigorodskiy, the head of the department and the director of the program, leads a research division at Yandex, which applies combinatorial methods to create good models for webgraphs and improve search quality. This means that our students have an opportunity to add an internship at Yandex research labs to their portfolio.
  9. Our program covers advanced modern combinatorics and state-of-the-art applications, but we do spend some time in the first semester to introduce our students to the basics of the subject.

Approximate curriculum

The program starts with a bunch of courses that we call “reintroduction.” These are needed to smooth out the differences between the students’ basic knowledge in algebra, probability theory, and basic discrete mathematics. These subjects underlie the study during the next three semesters, which is aimed at forming a solid picture of modern combinatorics with a slight emphasis on graph (and network) theory and geometry. Every semester features at least one course by a visiting professor. A list of courses follows.

First semester
  • Discrete Structures
  • Probability Theory
  • Linear Algebra
  • Extremal Combinatorics (a course by Miklós Simonovits)
  • Introduction to Discrete Geometry I
Second semester
  • Introduction to Discrete Geometry II
  • Random Graphs I
  • Advanced Graph Theory
  • Extremal Problems on Posets and Beyond (by Gyula O. H. Katona)
  • Modern Discrete Geometry (by János Pach)
Third semester
  • Random Graphs II
  • Game Theory
  • Complex Networks (by Nelly Litvak)
  • New Approaches to Hard Problems of Extremal Combinatorics (by Benny Sudakov)
  • Additive Combinatorics
Fourth semester
  • The fourth semester is solely devoted to research and the work on a master’s thesis.

How to apply

To apply for this program, first write a letter to professor Andrey Raigorodskiy, the program director. His email address is Please attach a CV including places where you have studied or worked, a description of the courses in mathematics and computer science that you have taken, and any other information related to your academic background. At least two letters of recommendation are also required. Basic knowledge of combinatorics, probability theory, calculus, and linear algebra is desirable. Applicants are interviewed via Skype, Hangouts, or other videoconferencing software.