Fundamental Mathematics
Source: https://english.spbu.ru/admission/programms/undergraduate/fundamental-mathematics Parent: https://english.spbu.ru/admission/programms/undergraduate
01.05.01 In English and Russian
Level of education Specialist
Type of instruction Full-time
Duration 5 years
Programme description
The programme provides development of the following competences: graduates are capable of using basic and special methods of mathematical research in the analysis and solution of problems of advanced mathematics using in-depth knowledge of physical and mathematical disciplines and information technology; they are also capable of conducting independent research and working in a research team. Students acquire the ability to: set objectives and find the best methods of their solution in the light of modern scientific achievements; use cutting-edge methods and algorithms of computer mathematics; use them for modelling, approximate solutions and presentation of results; and present research findings to different audiences.
Main courses
- Algebra and Number Theory
- Mathematical Analysis
- Geometry and Topology
- Discrete Mathematics
- Mathematical Logic and Set Theory
- Differential Equations
- Dynamical Systems
- Equations of Mathematical Physics
- Functional Analysis
- Probability Theory
- Extremal Problems
- Smooth Manifolds
- Computer Science
- Combinatorics
- Computer Technologies in Mathematical Investigation
- Concepts of Modern Natural Science
- Culture of Mathematical Reasoning
- Mathematical Statistics
- Mathematics Teaching Methods
- Methods of Computation
- Theoretical Cybernetics
- Theoretical Mechanics
- Physics
- Calculus of Variations
Teaching staff
- Nikolai Shirokov, Doctor of Physics and Mathematics, Professor, Head of the Department of Mathematical Analysis. His research focuses on the geometric theory of functions, approximation theory, factorisation, and the boundary behaviour of analytic functions in various spaces. He is the author of over 110 publications, including the monograph Analytic Functions Smooth up to the Boundary. Under his supervision, 12 candidates of science and one doctor of science have defended their dissertations
- Oleg Vinogradov, Doctor of Physics and Mathematics, Professor of St Petersburg University. His research focuses on the theory of approximation of real-variable functions. He is the author of over 90 publications, including a series of textbooks on mathematical analysis
- Evgeny Korotyaev, Doctor of Physics and Mathematics, Professor of St Petersburg University. His research focuses on the spectral theory of differential operators. He is the author of more than 130 publications. He has served as principal investigator on projects supported by grants from the Russian Science Foundation and the Russian Foundation for Basic Research
- Vladimir Nezhinskij, Doctor of Physics and Mathematics, Professor, Head of the Department of Higher Mathematics at St Petersburg University, expert in algebraic topology and knot theory, author of more than 40 publications
- Yuri Bibikov, Doctor of Physics and Mathematics, Professor, a recognised expert in the theory of stability of motion, the qualitative theory of differential equations, and bifurcation theory
- Nina Uraltseva, Doctor of Physics and Mathematics, Professor, Head of the Department of Mathematical Physics, Honorary Professor of St Petersburg University, Professor Emeritus at KTH Royal Institute of Technology (Sweden), laureate of the USSR State Prize, and recipient of the Prize of the Government of St Petersburg and the Saint Petersburg Scientific Centre of the Russian Academy of Sciences for outstanding scientific achievements in science and technology; Honoured Worker of Science of the Russian Federation; and Honoured Worker of Higher Professional Education. She is a world-renowned expert in partial differential equations and the calculus of variations, particularly in the area of free boundary value problems. She is the author of over 150 scientific publications, including four monographs
- Alexander Nazarov, Doctor of Physics and Mathematics, Professor, Honoured Worker of Higher Professional Education. His research focuses on boundary value problems for linear and nonlinear non-divergent equations; symmetries and asymmetries of solutions to extremal problems; applications of the calculus of variations and spectral theory in the theory of random processes and mathematical statistics; non-local operators of the fractional Laplacian type and their properties. He is the author of more than 90 publications
- Arina Arkhipova, Doctor of Physics and Mathematics, Professor, Honoured Worker of Higher Professional Education. Her research focuses on boundary value problems for linear and nonlinear equations and systems of elliptic and parabolic types; problems of solvability and regularity of solutions, including those with constraints within the domain and on its boundary. She is the author of more than 90 publications
- Ildar Ibragimov, Doctor of Physics and Mathematics, Professor, laureate of the Lenin Prize and Member of the Russian Academy of Sciences, Honorary Professor of St Petersburg University. His research focuses on stationary, Markov, and Gaussian random processes, as well as asymptotic estimation theory. He is the author of over 210 publications, including four monographs
- Nikolai Shirokov, Doctor of Physics and Mathematics, Professor, Head of the Department of Mathematical Analysis. His research focuses on the geometric theory of functions, approximation theory, factorisation, and the boundary behaviour of analytic functions in various spaces. He is the author of over 110 publications, including the monograph Analytic Functions Smooth up to the Boundary. Under his supervision, 12 candidates of science and one doctor of science have defended their dissertations
- Oleg Vinogradov, Doctor of Physics and Mathematics, Professor of St Petersburg University. His research focuses on the theory of approximation of real-variable functions. He is the author of over 90 publications, including a series of textbooks on mathematical analysis
- Evgeny Korotyaev, Doctor of Physics and Mathematics, Professor of St Petersburg University. His research focuses on the spectral theory of differential operators. He is the author of more than 130 publications. He has served as principal investigator on projects supported by grants from the Russian Science Foundation and the Russian Foundation for Basic Research
- Vladimir Nezhinskij, Doctor of Physics and Mathematics, Professor, Head of the Department of Higher Mathematics at St Petersburg University, expert in algebraic topology and knot theory, author of more than 40 publications
- Yuri Bibikov, Doctor of Physics and Mathematics, Professor, a recognised expert in the theory of stability of motion, the qualitative theory of differential equations, and bifurcation theory
- Nina Uraltseva, Doctor of Physics and Mathematics, Professor, Head of the Department of Mathematical Physics, Honorary Professor of St Petersburg University, Professor Emeritus at KTH Royal Institute of Technology (Sweden), laureate of the USSR State Prize, and recipient of the Prize of the Government of St Petersburg and the Saint Petersburg Scientific Centre of the Russian Academy of Sciences for outstanding scientific achievements in science and technology; Honoured Worker of Science of the Russian Federation; and Honoured Worker of Higher Professional Education. She is a world-renowned expert in partial differential equations and the calculus of variations, particularly in the area of free boundary value problems. She is the author of over 150 scientific publications, including four monographs
- Alexander Nazarov, Doctor of Physics and Mathematics, Professor, Honoured Worker of Higher Professional Education. His research focuses on boundary value problems for linear and nonlinear non-divergent equations; symmetries and asymmetries of solutions to extremal problems; applications of the calculus of variations and spectral theory in the theory of random processes and mathematical statistics; non-local operators of the fractional Laplacian type and their properties. He is the author of more than 90 publications
- Arina Arkhipova, Doctor of Physics and Mathematics, Professor, Honoured Worker of Higher Professional Education. Her research focuses on boundary value problems for linear and nonlinear equations and systems of elliptic and parabolic types; problems of solvability and regularity of solutions, including those with constraints within the domain and on its boundary. He is the author of more than 90 publications
- Ildar Ibragimov, Doctor of Physics and Mathematics, Professor, laureate of the Lenin Prize and Member of the Russian Academy of Sciences, Honorary Professor of St Petersburg University. His research focuses on stationary, Markov, and Gaussian random processes, as well as asymptotic estimation theory. He is the author of over 210 publications, including four monographs.
Our advantages
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High calibre teaching staff
\ Students attend lectures, including in English, delivered by top scientists in various fields of mathematics and have access to international electronic resources - ##### Traditions of the St Petersburg school of mathematic
\ The modern research team carries on the traditions of one of the leading schools of mathematics in the world - ##### Advanced teaching standards
\ The offered courses make it possible for students to get acquainted with the current state of mathematical research and cutting-edge research methods - ##### Interesting and relevant research topics
\ Students can be engaged in solving challenging scientific problems: they can conduct their own research as part of their term papers and graduation projects; do internships in Russian and foreign universities; and present their reports at Russian and international conferences - ##### Research using state-of-the-art technologies
\ Much attention is paid to theoretical knowledge; and the development of algorithmic design skills and skills for solving problems from various applied fields of science based on the application of cutting-edge achievements of fundamental and applied mathematics - ##### Acquisition of much-in-demand applied skills
\ Working with advanced computer equipment opens up the opportunity to be fully engaged in the development of the national system of the digital economy - ##### Interdisciplinarity of the problems to be solved
\ Fundamental training makes it possible for graduates to reasonably apply mathematical methods while building, analysing and implementing new theoretical and computer models in modern natural science, industry, economics and management
Career opportunities
The graduates acquire the following skills and competences
- Practical application of basic and special methods of mathematical research in the analysis and solution of problems of present-day mathematics. At the same time, they acquire profound knowledge at lecture courses and practical classes in different fields of physics and mathematics. The graduates are also competent in information technologies
- Ability to carry out independent scientific work and work in a research team. The students acquire the skill to set tasks and find optimal methods for their solution by applying the modern achievements of science. Their graduation papers are often published in prestigious mathematical journals
- Ability to freely navigate in modern methods and algorithms of computer mathematics, use them for modelling, approximate solution and presentation of results
- Ability to present their scientific findings in various ways, taking into account the level of the audience. The graduates are capable to teach physical and mathematical disciplines and informatics at higher education institutions, as well as at secondary schools