Functional Methods in Differential Equations and Interdisciplinary Research

Profession

The differential equation is one of the basic concepts of mathematics, widely used to solve practical problems in different branches of sciences. The Master’s degree program was created under consistent demand for young professionals working in industry who possess knowledge in fundamental mathematics with an emphasis on differential equations.
The Master’s degree program meets modern trends in mathematical science and aims to train highly qualified specialists who are able to adapt to modern realities thanks to the skills and qualifications they have acquired.
Upon completion of the master’s degree, graduates can engage 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 while teaching. Their professional success is based on the universality of mathematical models, knowledge of modern programming languages, which are the basis for solving applied problems, and the effectiveness of the latest information technologies.
Graduates who have mastered this program can pursue to their postgraduate studies or work in academic environment as research mathematicians, as well as seek employment being comprehensively trained applied specialists.

Educational Process

The purpose of the course is to train specialists in analysis, differential equations and applications. The Master’s degree program seeks to build up-to-date knowledge in solving theoretical and applied problems among future specialists, and educating students to be inclined to do research activities in interdisciplinary studies.
Mastering the course has several important advantages:
1. Highly-qualified teaching staff, including invited scientists from foreign (Germany, France) and Russian (corresponding member of the Russian Academy of Sciences G.G. Lazareva) universities .
2. Under the supervision of a visiting scientist, Ph.D., Professor Volpert V.A. (Lyon, France) the scientific center “Mathematical Modeling in Biomedicine” was established. It hosts researchers who actively investigate mathematical modeling of the cardiovascular system and diseases, oncology, immunology, including studies in cooperation with foreign universities.
3. In addition to the curriculum subjects, the Mathematical Institute organizes regular scientific seminars in fundamental and applied mathematics, within the framework of which Russian and foreign world-class scientists report on the current state of specific mathematical fields and present the results of their own scientific research.
4. The course includes the subject “Foreign Language for a Master Student’s Professional Purposes”, which meets the needs of modern globalization processes. Students interested in learning languages can additionally obtain the qualification of a certified translator from one, two or even three languages. 12 foreign languages are available for the student to study: traditional European and many others (including Chinese, Arabic, Persian).
5. Much time is devoted to the student's research activities and the preparation of their graduation thesis.
It is assumed that graduates will have the skills to solve modern problems in differential equations and functional differential equations with applications to natural sciences and industry, as well as learn how to work in a research team.
The mandatory part of the program includes fundamental training in mathematics, the study of modern mathematical methods and active research work. The availability of several blocks of electives in the course content allows you to determine the most attractive areas of professional activity.
While mastering the curriculum, students study the following disciplines:
First academic year: “Foreign language for a Master Student’s Professional Purposes”; “Computer technologies in science and education”; “History and methodology of mathematics”; “Topological methods in elliptic theory”; “Modern problems of mathematics and applied mathematics”; “Functional differential equations and non-local boundary value problems”; “Functional spaces”.
Block 1 (electives): “Mathematical models in Economics”; “Introduction to low-dimensional topology”; “Nonlinear evolutionary equations”; “Non-Euclidean geometries and their applications”.
Block 2 (Electives): “Mathematical models in biology and medicine”; “Operators in functional spaces”; “Additional chapters of partial differential equations”; “Numerical study of mathematical models”.
Second academic year: “Foreign language for a Master Student’s Professional Purposes”; “Applied problems of mathematical modeling”; “Nonlinear analysis and optimization”; “Additional chapters of mathematical modeling”.
Module 1 (electives): “Mathematical models and databases”.
Module 2 (electives): “Elements of perturbation theory”.
All educational activities and research are conducted in multimedia classrooms and scientific and educational laboratories and centers of the S.M. Nikol’sky Mathematical Institute, as well as in computer classrooms equipped with modern facilities and software for conducting computational experiments.

Practice

The research work and internships provided by the curriculum are carried out on the basis of the Scientific Center for Nonlinear Problems of Mathematical Physics of the S.M. Nikol’sky Mathematical Institute.
Our Institute participates in activities of the German-Russian Interdisciplinary Science Center (German-Russian Interdisciplinary Science Center, G-RISC, https://www.g-risc.org /), within the framework of which students and postgraduates of the Mathematical Institute are sent for internships to leading universities in Germany.
There are cooperation agreements with the Ruprecht and Karl Heidelberg University (Germany), with the Holon Institute of Technology (Israel), which proposes internships.
Master classes of leading experts and representatives of employers of real sectors of economy, Russian and foreign scientists from leading universities and research centers are held for students during the academic year. World-class Russian and foreign scientists are regularly invited to conduct a series of lectures and master classes on topical issues of pure and applied mathematics and mathematical modeling.

Career

The acquired knowledge and practical skills allow graduates to work in 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 research institute;
— information system specialist;
— 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 teacher at a higher educational institution.
There is an opportunity to continue postgraduate studies in “Mathematics and Mechanics” (01.06.01).