Non-classical Problems of Analysis and Differential Equations, Mathematical Modeling and Machine Learning

Profession

The key professional activity of a master graduate specialized in Mathematics is education and science, including research and mathematical modeling in communications, information and communication technologies, software development and testing, creation and support of information and communication systems and databases. The success of professional activity in these areas is based on the elegance and versatility of mathematical models, the power of modern computer systems and the efficiency of the latest information technologies.
Graduates can be involved in research activities, are able to solve relevant and significant problems of fundamental and applied mathematics, improve and implement new mathematical methods for solving applied problems, build and analyze mathematical models in modern natural science, technology, economics and management, use knowledge in mathematics in pedagogical practice.

Educational Process

The Master’s course is designed to prepare specialists in mathematics, applied mathematics and mathematical modeling, mathematical economics. The program aims to form modern knowledge in solving theoretical and applied problems, to cultivate students' aptitude for research activities. The mandatory part of the program includes fundamental training in mathematics, the study of modern mathematical methods and active research work. There are several blocks of electives, which allows students to the most attractive areas of professional activities.
The Master’s course includes:
— several review compulsory subjects that broaden student’s mathematical horizons (“Modern problems of mathematics and applied mathematics”, “History of mathematics methodology “, “Elements of algebraic topology”)
— several mandatory subjects within the main areas of graduate departments’ research (“Optimal control”, “Theory of extreme problems”, “Nonlinear problems and optimization”);
— a number of electives, including “Nonlinear evolutionary equations”, “Partial differential equations”, “Mathematical models in economics and ecology”, “Numerical study of mathematical models”. These disciplines cover a wide range of modern branches of mathematics and applied mathematics and allow students to choose an individual learning trajectory that meets their interests and needs.
The three-semester course “Computer Technologies in Science and Education” provides serious and in-depth knowledge in computer science and programming. Much time is devoted to students’ research activities and the preparation of their graduation paper: in fact, the whole second year is aimed at research and writing a master’s thesis.

Practice

Pedagogical and research internships provide real opportunities for students to try teaching mathematics and computer science and conduct mathematical research. The internships included into the curriculum are conducted on the basis of the Scientific Center for Nonlinear Problems of Mathematical Physics of the S.M. Nikol’sky Mathematical Institute. The Mathematical Institute closely cooperates with Lomonosov Moscow State University, Steklov Mathematical Institute of the Russian Academy of Sciences, the Dorodnitsyn Computing Center of the Russian Academy of Sciences, and Microsoft. Master classes are held annually for students by leading experts and representatives of employers of real sectors of economy, Russian and foreign scientists from leading universities and research centers. There is a Moscow-wide scientific seminar on differential and functional differential equations, which is attended by major Russian and foreign mathematicians, teachers, students, postgraduates and doctoral students.

Career

The acquired knowledge and practical skills allow graduates to work in large scientific and research centers. Graduates are in demand in aviation and space industries, and thanks to pedagogical training also in education. In addition, many of them work in the financial sector: in banks, major insurance companies, investment and pension funds.
Possible jobs:
— researcher at the science and research organization;
— programmer, system administrator in IT enterprises and divisions of commercial organizations;
— financial analyst and applied programmer in financial departments of government and commercial organizations;
— a lecturer at a higher educational institution.
There is an opportunity to pursue to postgraduate studies in the following areas:
— 01.06.01 “Mathematics and Mechanics”;
— 09.06.01 “Computer Science and Computer Engineering”.