Advanced combinatorics

The programme is focused on modern aspects of combinatorics (discrete mathematics) and its applications in computer science and in the theory of complex networks.

KEY ADVANTAGES:
  • We admit students with solid knowledge of basic math (algebra, analysis, probability, discrete mathematics), who wish to study advanced combinatorial techniques and applications.
  • We teach advanced state-of-the-art methods used in discrete mathematics and foster intuition of working with discrete objects and models.
  • We employ leading MIPT professors and invite visiting professors from renowned research groups in the field of combinatorial mathematics.
  • We provide our students with an opportunity to do research in various topics of discrete mathematics – both pure and applied.

TEACHING METHODS:
Only in the first semester, we have four elective courses re-introducing our students into calculus, algebra, combinatorics, and probability. In all the semesters, we have:
  • 3-4 main courses with weekly lectures and seminars;
  • 1-2 intensive courses by prominent visiting professors including Benjamin Sudakov, David Gamarnik, Janos Pach, Gyula O.H. Katona, Prasad Tetali;
  • Research meetings with scientific advisors (office hours);
  • Interdepartmental seminar on Discrete Mathematics (every week);
  • Seminar on Discrete Mathematics and its Applications in Network Analysis (every week at Yandex, the top Russian internet search engine).

STUDIED COURSES INCLUDE:
    “Introductory” courses with emphasis on combinatorial viewpoint:
  • Combinatorics;
  • Graph Theory;
  • Probability;
  • Calculus and algebra;
Common methods:
  • Discrete Analysis;
  • Extremal combinatorics;

    Specialized topics:
  • Random graphs;
  • Advanced graph theory;
  • Combinatorial  geometry;
  • Additive combinatorics;
Courses with applied flavour:
  • Game theory;
  • Discrete Optimization;
  • Computational  complexity;
  • Complex networks.

PROGRAM CURRICULUM 2016/17
1st YEAR

1st SEMESTR
ECTS credits2nd SEMESTR
ECTS credits
3030
Russian as foreign language2Russian as foreign language2
Re-introduction to Linear and Common Algebra2Random Graph Part I2
Re-introduction to Probability2Advanced Graph Theory3
Re-introduction to Combinatorics and Graph Theory2Combinatorial Geometry: Advanced Topics2
Combinatorical Geometry3Extremal Problems on Posets and Beyond 
(course by invited professor G.O.H. Katona)
3
Topics in Combinatorics (course by invited professor
M. Simonovits
3Modern Discrete Geometry (course by invited
professor J. Pach
2
Re-introduction to Linear and Common Algebra2

Personal research project14Personal research project14

2nd YEAR

1st SEMESTR ECTS credits2nd SEMESTR ECTS credits
3030
Russian as foreign language2Personal research project20
Random Graph Part II2 Master thesis 10
Game Theory3

Additive Combinatorics3
New Approaches to Hard Problems of External
Combinatorics (course by invited professor B. Sudakov)
2
Random Graph Part II2
Personal research project13
Qualification exam3

VISITING PROFESSORS:

Benny Sudakov

Department of Mathematics, ETH (Switzerland)

Algebraic and Probabilistic Methods in Combinatorics, Extremal Graph and Hypergraph Theory, Ramsey Theory, Random Structures, Application of Combinatorics to Theoretical Computer Science

Fellow of AMS, Humboldt Research Award (2014)


David Gamarnik

Operations Research MIT Sloan School of Management

Applied Probability, Stochastic Processes and Queueing Theory Random Structures and Random Graphs, Combinatorial Optimization Statisticallearning Theory.

INFORMS Applied Probability Society Best Publication Award (2011), IBM Faculty Award(2006), Erlang Prize (2004)


Janos Pach

EPFL (Switzerland), Renyi, Institute Budapest (Hungary)

Combinatorics, Graph Theoryand Computational Geometry

Grünwald Medal (1982), Ford Award (1990), Rényi Prize (1992)


Gyula O.H. Katona

Renyi Institute Budapest (Hungary)

Extremal Set Theory, Databases

Rényi Prize (1975), Ernst Moritz Arndt Medal (1997), Széchenyi Prize (2005)


Miklosh Simonovits

Renyi Institute Budapest(Hungary)

Extremal Graph Theory, Theoretical Computer Science, Random Graphs

Széchenyi Price (2014)


PROGRAMME PARTNERS:
  • Steklov Mathematics Institute (Russia);
  • Yandex (Russia);
  • Alfréd Rényi Institute of Mathematics (Hungary);
  • École Polytechnique Fédérale de Lausanne (Swiss).
Programme Coordinator
Prof. Andrei Raigorodskii
mraigor@yandex.ru