Contemporary combinatorics and Applications

Online Master’s program in English

Phystech School of Applied Mathematics and Informatics

Remote Open Day 2021

Program Overview

The Phystech School of Applied Mathematics and Informatics of the Moscow Institute of Physics and Technology (MIPT) launches a call for the two-year Online Master’s Program «Contemporary combinatorics and Applications» (in English). The Program will create a solid foundation of knowledge of modern discrete mathematics and its applications in computer science and in the analysis of complex networks.

This program is focused on the modern aspects of combinatorics (discrete mathematics) and its applications in computer science and in the theory of complex networks. Students both study advanced state-of-the-art methods used in discrete mathematics and foster intuition of working with discrete objects and models and do research in various topics of discrete mathematics – either pure or applied.

We invite you

János Pach is a mathematician and computer scientist working in the fields of combinatorics and discrete and computational geometry. Pach received his Candidate degree from the Hungarian Academy of Sciences, in 1983, where his advisor was Miklós Simonovits. Since 1977, he has been affiliated with the Alfréd Rényi Institute of Mathematics of the Hungarian Academy of Sciences. He was Research Professor at the Courant Institute of Mathematical Sciences at NYU (since 1986), Distinguished Professor of Computer Science at City College, CUNY (1992-2011), and Neilson Professor at Smith College (2008-2009). In 2008, he joined École Polytechnique Fédérale de Lausanne as Professor of Mathematics.

Watch video invitation from János Pach

Gyula O.H. Katona is a Hungarian mathematician known for his work in combinatorial set theory, and especially for the Kruskal–Katona theorem and his beautiful and elegant proof of the Erdős–Ko–Rado theorem in which he discovered a new method, now called Katona's cycle method. Since then, this method has become a powerful tool in proving many interesting results in extremal set theory. He is affiliated with the Alfréd Rényi Institute of Mathematics of the Hungarian Academy of Sciences.

Watch video invitation from Gyula O.H. Katona

"MIPT is one of the strongest universities in Europe. Especially in Graph Theory, Combinatorics and their Applications.

This is why I did not hesitate a minute when I was asked in 2015 to join the new Master’s program. I accepted this offer with great pleasure. Since then I give each year a series of lectures on my favorite area: Extremal Set Theory. So, you do not know what it is? I give an example.

There are n people, members of a society. For different tasks they form committees. The democratic rule is that no committee can be a proper subset of another one. At most how many committees can be formed? If you chose this program, I will tell the answer in the first class. Extremal Set Theory has many other similar, but not so easy problems. But Combinatorics has many other, nice, interesting subfields. You can learn all of those from my excellent colleagues.

What is nice about Combinatorics? On the one hand it asks questions that can be explained to a highschool student between two bus-stops, though to answer the question might be very difficult, needing surprising ideas. On the other hand Combinatorics is in "one step" from real life problems, it is really an applicable mathematics, I always enjoyed teaching these classes, since the audience consisted of smart, motivated young people from all around the world. And I had the impression that they liked that I taught them. In one case it was sure. A Chinese lady, after receiving her Master’s degree at MIPT, came to Budapest to continue her studies and she is now writing her PhD thesis under my supervision.

One more thing. From MIPT, within 30 minutes you can reach the center of an exciting, vibrant city: MOSCOW."

Nelly Litvak is professor in Algorithms for Complex Networks and has a background in Applied Probability and Stochastic Operations Research. She works on mathematical methods and algorithms for complex networks, such as social networks and the WWW. Real-life networks are modeled as random graphs, and algorithms are used to extract information from the massive network data.

The overall goal of her research is to extract value from (Big) Data, focusing on network data. Her research revolves around three main topics: Information extraction and predictions based on data, mathematical analysis of network characteristics and randomized algorithms. The first looks at defining and collecting the correct measurements and data for specific purposes and deducing networks from data. The second examines mathematical properties of algorithms in networks, for example, the famous PageRank that Google invented to rank web pages. The third looks at efficient algorithms for computing network characteristics when the complete network data is not available.

Watch video invitation from Nelly V. Litvak

Features of the implementation of the Master’s program

With the help of new educational technologies and the “flipped learning” approach, courses on basic specialties, compulsory general education courses and interaction with a research supervisor on writing research are being transferred to the online form.

The educational program consists of:

  • 1. electronic courses in which the student will be able to vary the pace of study;
  • 2. weekly webinars in the format of “office hours”, in which you can interact interactively with the teacher and ask the questions;
  • 3. personal advice on the conduct of scientific work.

Intermediate exams are taken using remote identity verification technologies with a remote proctor controller.

Career benefits for the graduates

Top 5 skills

The students who enter the program are expected to develop/strengthen the following skills:

  • — The ability to read original research papers on various topics of combinatorial mathematics.
  • — The ability to carry out a supervised research in the area of choice in combinatorics.
  • — The ability to design mathematical models for a real world problems.
  • — The ability to present the results of the research to professional community.
  • — The ability to carry out computational experiments backed by theoretical considerations.

Career tracks

  • — Researcher (mathematics, applied mathematics, computer science).
  • — Software developer / algorithm designer.
  • — Analyst.

Spheres for future employment

  • — Research institutions in mathematics in computer science.
  • — Information technology companies, incl. the Program Partners.


Our students can choose courses from any track and create their own educational profile. This program provides an opportunity to get solid background in fundamental mathematics and highly practical skills in operational research and data science. This broad diversity in educational program allow you to choose your future work trajectory freely.

The Program will create a solid foundation in modern discrete mathematics
and its applications in data science and operation research.

The program offer three tracks:

(academic) Advanced combinatorics

The program was founded in 2015. It is focused on modern aspects of combinatorics (or, a bit more generally, discrete mathematics) and its applications in computer science and in the theory of complex networks. 

The program starts 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.

Where to work after graduation:

  • - Academy (Discrete mathematics, Computer Science, Complex networks, Bioinformatics and e.t.c.)
  • - Telecommunications (Huawei, Cisco e.t.c.)
  • - FAANG and their small brothers
  • - Software development companies (Yandex, ABBYY, 1С e.t.c.)
  • and others

Why choose this program:

  • - Broad range of additional courses in advanced topics from world's leading scientists.
  • - Additional courses in OR/DS can be chosen
Career opportunities

Mathematician (academic career):
One of the most respected profession! We propose one of the best academic track in combinatorics/discrete mathematics.

(applied) Operation Research

This track is designed for the students to concentrate in most applied areas of mathematics: optimization, probability and statistics, modeling and machine learning.

This track allow you to build successful career as research scientist in Finance (Risk / Revenue management), Supply Chain management, Logistics, Business Analytics, Operation management and other areas with non-trivial modeling problems. This track is also the best choice for students with background in Economics, Finance, Transportation, Marketing, Supply Chain management, Logistics who wish to upgrade technical skills and get in touch with most advanced modeling tools and concepts.

Where to work after graduation:

  • - Academy
  • - E-commerce (Amazon, Alibaba, Coupang, Ozon e.t.c.)
  • - Banks and Hedge-funds (Tinkoff, Sberbank, J.P.Morgan Chase, Blackrock, Bridgewater, Two Sigma e.t.c.)
  • - Transportation and Supply Chain (Uber, Nestle, PepsiCo e.t.c.)
  • - Software development companies (Yandex, ABBYY, 1С e.t.c.)
  • and others

Why choose this program:

  • - MIPT is world-known university with one of the best MS and PhD programs in Operation Research (Optimization, Statistics, Discrete Math and Data Scinece)
  • - Additional courses in pure math/DS can be chosen
Career opportunities

Operation Research Researcher:
Profession in the cornerstone of IT and Decision-making are in high demand in many industries: e-commerce and retail, transportation and logistics, telecommunications and finance.

(applied) Data Science

Data Science is one of the most popular research field in latest decade with broad range of applications. This program track dedicated novel research area: Data-driven operation research. It takes machine learning and deep learning, discrete mathematics, statistics, optimization and algorithms as main ingredients to forge new modeling and computational approaches for most complicated real-life problems.

Resent rise of Deep RL and RL for combinatorial problems is just one of examples.

This program allow you to study Data Science, Operation Research and how this two fields can be used together in real life.

Where to work after graduation:

  • - Academy
  • - Telecommunications (Huawei, Apple, Verizon e.t.c.)
  • - Software development companies (Yandex, ABBYY, 1С e.t.c.)
  • - E-commerce (Amazon, Alibaba, Coupang, Ozon e.t.c.)
  • - Banks and Hedge-funds (Tinkoff, Sberbank, J.P.Morgan Chase, Blackrock, Bridgewater, Two Sigma e.t.c.)
  • - Transportation and Supply Chain (Uber, Nestle, PepsiCo e.t.c.)
  • and others

Why choose this program:

  • - Fast but comprehensive dive in novel research field with huge potential and broad range of applications
  • - MIPT is world-known university with one of the best MS and PhD programs in Operation Research and Data Science (Optimization, Statistics, Discrete Math and Data Science)
  • - Additional courses in pure math can be chosen - make your understanding deeper
Career opportunities

Data Scientist/Data Analytics:
One of the hottest professions in IT industry with highest salary and huge demand: Amazon, Google and all other tech giants competing for skilled individuals in this area.


Subject name
Foreign Languages:
History, Philosophy and Methodology of Natural Science
Russian as a Foreign Language
Core science:
Theory of Probability
Introduction to Combinatorics
Linear Algebra
Introduction to Graph Theory
Subject name
Foreign Languages:
Russian as a Foreign Language
Elective Set of Courses 1:
Random Graphs. Part 1
Applied mathematical modeling
ML/Data Mining
Elective Set of Courses 2:
Advanced Graph Theory
Game Theory
Python for Data Analysis
Elective Set of Courses 3:
Computational Complexity
ordsIndustrial programming and DevOps
Machine Learning
Applied Statistics
Personal Research Project
Subject name
Foreign Languages:
Russian as a Foreign Language
Elective Set of Courses 4:
Random Graphs. Part 2
Approximation Algorithms
Elective Set of Courses 5:
Additive Combinatorics
Applied Discrete Optimization
Elective Set of Courses 6:
Extremal Combinatorics
Optimization [under uncertainty]
Generative Models
Elective Set of Courses 7:
Complex Networks
Algorithmic Game Theory
Reinforcement Learning
Neural Networks
Personal Research Project
Subject name
Probabilistic Graphical Models
State Final Certification:
Performance of and Defence of Graduation Thesis
Personal Research Project
- Advanced combinatorics
- Operation Research
- Data Science

How to apply

To apply for our program, please, fill-in the application form or write a letter to our email address interadmission@phystech.edu until mid-September. To your letter, you should attach your documents. The complete list of documents for applying:

Copy of passport which will be used to enter Russian Federation. The passport should be valid for at least 18 month after the presumed date of starting the education program.

Documents of your previous education (bachelor/specialist/master diploma) with the list of subjects studies and grades for them. If you haven’t received it yet – you can attach a certificate that you are still studying and will receive a diploma this year.

Your CV including places where you have studied before or worked before.

Letters of recommendation (at least two) are needed. Recommendation letters should be send by your referees directly to our email address interadmission@phystech.edu.

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 consequences, continuous functions, limits of functions, derivatives, Taylor series.

Probability: classical definition of event probability, geometrical probability model.

Beginning of the program - October 1, 2021.

Costof the program

The program welcomes any additional number of students selected by the committee.
The annual tuition fee is as low as 350 000 RUR.

Program partners

Our students have an opportunity to add an internship at Yandex research labs, Sberbank labs, 1C labs, Tinkoff labs, BioCad labs, ABBYY labs, Huawei labs, to their portfolio.


Our School

School of Applied Mathematics and Computer Science of MIPT in a nutshell

1. Program included mathematics, physics and theoretical physics at the highest level possible in Soviet Union at that time.

2. World-renowned scientists were giving lectures, 8 of them later became Nobel Prize winners.

3. Not only lectures but also seminars were taught by professional researchers (at least of PhD level).

4. Starting from the third year of study students started participating in the cutting edge research at the best labs and research centers in Moscow.

1. MIPT has a nation-wide reputation and the best research labs, design engineering bureaus and businesses are competing to employ MIPT graduates. Specialists consider MIPT as one of the very best Russian Universities.

2. A significant part of the alumni take the scientific path and become fundamental researchers. Their education allow them to become the world leading scientists, like Nobel Prize Winners Andre Gaim and Konstantin Novoselov, the discoverers of graphene.

During the contest the ICPC team has interviewed Prof. Andrei Raigorodskii, the head of the MIPT School of Applied Mathematics and Informatics. The video interview is available on YouTube.

Other programs

Two-year Master's program Phystech School of Applied Mathematics and Informatics (MIPT)

Bachelor program Phystech School of Applied Mathematics and Informatics (MIPT)