Contemporary combinatorics
The Department of Discrete Mathematics of the Moscow Institute of Physics and Technology (MIPT) launches a call for the two-year Master’s Program «Contemporary combinatorics». 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.
The program is 2 years long. All courses in our program are taught in English by highly qualified professors and renown mathematicians: A.M. Raigorodskii, G.O.H. Katona, A.B. Dainiak, V.L. Dolnikov, A.Ya. Kanel-Belov, R.N. Karasev, A.A. Polyanskii, I.D. Shkredov, , J. Pach, N. Litvak M.E. Zhukovskii.
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:
Electronic courses in which the student will be able to vary the pace of study;
Weekly webinars in the format of “office hours”, in which you can interact interactively with the teacher and ask the questions;
personal advice on the conduct of scientific work.
Intermediate exams are taken using remote identity verification technologies with a remote proctor controller.
Main courses
Random graphs
In the course, we will consider certain models of random graph, but the main focus will be on the binomial model. We will study the main methods and tools of the random graphs theory and see how they are used to estimate distributions of the main graph characteristics (such as independence number and chromatic number). We will also speak about the most known applicable models.
Advanced graph theory
During more than a century of active development graph theory went a long way fr om an offspring of topology and miscellanea of recreational-type questions to one of the mainstream disciplines within modern combinatorics, employing highly sophisticated techniques in the proofs and having many applications in other branches of mathematics. This course of advanced graph theory illustrates some of the important advanced proof techniques in graph theory (algebraic and probabilistic methods), as well as introducing the learners to some research topics beyond standard introductory courses on graph theory.
Additive Combinatorics
Additive Combinatorics is a new explosively growing field of the modern combinatorics. Roughly speaking, additive combinatorics is an area studying any combinatorial questions regarding the group operation. This area of mathematics uses a variety of tools from different areas such as (in addition to Number Theory and Combinatorics) Dynamical Systems, Computer science, Probability Theory, Functional Analysis, Geometry and so on. In our course we are planning to introduce some fundamental results of the area and describe some connections of Additive Combinatorics with Number Theory, Combinatorics, Ergodic Theory, Graph Theory, Fourier analysis, Geometry and other branches of mathematics.
Computability and complexity
This is an introductory course on theory of algorithms and computational complexity. The main goal of the course is to provide an intuition on what is an algorithmic problem, what is its intrinsic complexity and how the complexity of various problems may be characterized.
Introduction to Artificial Intelligence
This is an introductory course on Artificial Intelligence. We will present the basic AI concepts, such as knowledge representation models, state space search strategies, machine learning techniques, AI-planning methods etc. Programming skills are welcome, but not required. It’s up to the learner whether to do a programming project (either in Python or C++) or not.
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.
Cost of the program
The program welcomes any additional number of students selected by the committee. The annual tuition fee is as low as 435 000 RUR (or $7000 / 6000 €).
How to apply
To apply for our program, firstly please write a letter to our email address contcombi@phystech.edu until September 1. 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 wh ere 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 contcombi@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.
Starting date is October 1 of each year. If you wish to join us or if you have any questions feel free to contact us: contcombi@phystech.edu.
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