Mathematics

The master's programme in Mathematics is taught in English and offers the opportunity to obtain two diplomas: one from HSE University and another from the University of Passau (Germany) following a year-long stay in Germany.

Because application of deep mathematical training is becoming more and more extensive given the significant changes taking place in the labour market and the digitalization of the economy, the master’s programme aims to train highly qualified specialists in the field of fundamental mathematics who are able to design, research, interpret and optimize mathematical models for solving scientific and engineering problems. Graduates are positioned to pursue further education in PhD programmes at top-tier universities around the world or to work in industries requiring significant understanding of mathematics, such as IT, insurance, and analytics.

The curriculum assumes that students have previously mastered the primary mathematical subjects, including mathematical analysis, number theory, logic, differential equations, differential geometry, probability and statistics.

The first year of the master's programme in Nizhny Novgorod includes courses covering the following subjects:

• Mathematical methods of natural science
• Differential equations on manifolds
• One-parameter semigroups and evolution equations
• Ergodic theory
• An elective from the MAGOLEGO university-wide pool
• First steps in Linear algebra for machine learning

Students learn the basics of scientific work by participating in research seminars, including Elements of the Theory of Solitons, Modern Theory of Dynamical Systems, and Theory of Bifurcations of Multidimensional Systems. In addition, they work under a research supervisor to write a term paper.

In the second year, students have the opportunity to study in Passau, Germany, where they can choose from approximately 40 pure and applied mathematical subjects. Other students choose to continue their studies in Nizhny Novgorod by taking courses such as Programming Languages, Quantum Mechanics for Mathematicians, and History and Methodology of Mathematics. They also take part in research seminars like Dynamics of Endomorphisms and Modern Theory of Dynamic Chaos. In the final stage of studies, master’s students write a final qualifying work and defend it.

Courses and final qualification papers cover a diverse range of topics, including the theory of dynamical systems, hyperbolic dynamics, topology, geometry of foliations, elements of the theory of solitons, algebraic geometry, and other fields.

Students can include subjects from any HSE faculty in their individual curriculum, as well as attend the Yandex School of Data Analysis where the basics of neural networks are studied. They are also able to select a minor.

The Department of Fundamental Mathematics at HSE University - Nizhny Novgorod is a young but serious centre of mathematical education in Russia and globally. The department has two international scientific laboratories that employ foreign specialists from top-tier global universities.

The main research area is related to dynamical systems, which have been the hallmark of Nizhny Novgorod mathematics since the foundation of the Academician A.A. Andronov School of Nonlinear Oscillations. Dynamical systems are used in almost all areas of human activity: mathematics, physics, mechanics, biology, neurodynamics, mechanical engineering, robotics, computer science, economic modelling, among others. The modern theory of dynamical systems is a collective name for research where methods from various branches of pure and applied mathematics are widely used and effectively combined. For example, these sections include topology, algebra, algebraic geometry, measure theory, theory of differential forms, theory of singularities and catastrophes, theory of Lie groups and Lie algebras, scientific computing, and theory of complex systems.

The master’s programme offers the opportunity to obtain two diplomas in two years: a diploma in Mathematics from the Higher School of Economics and, if desired, a diploma in Computational Mathematics from the University of Passau following a year-long stay in Germany.

• High level of training – Both Russian and foreign scientists with unquestionable authority in their fields of research are involved in teaching in the master's programme; this ensures that students are immersed as much as possible in research work.
• Instruction in English – Teaching in English and constantly use of a foreign language helps graduates increase their competitiveness on the global labour market.
• Focus on solving new and complex problems – While stress and confusion can come when encountering a problem for which the solution algorithm is unknown, the experience of scientific research creates a normal working environment for mathematicians in situations of intellectual uncertainty; this allows for independent formulation of a worthwhile problem and the invention of ways to solve it.

Master's degree students are primarily focused on pursuing careers in science and are therefore expected to be widely involved in basic research undertaken at HSE laboratories and in joint research projects with leading Russian and foreign scholars.

Most applications are either already dependent on mathematical methods (e.g., economics, finance, computer science and IT) or are rapidly becoming so (e.g., linguistics, medicine, and sociology). A hundred years ago, for example, economics was obviously a humanitarian science, but now almost half the Nobel laureates in economics hold a bachelor's degree in physics and mathematics. This process of mathematization is affecting new areas and is resulting in increased demand for specialists with academic mathematical qualifications in Russia and abroad.

It goes without saying that the labour market that graduates are entering is a global market for intellectual labour.

While the master's programme in Mathematics at the Higher School of Economics in Nizhny Novgorod was only recently opened in 2019 and therefore does not yet have a graduating cohort, a significant proportion of mathematicians who graduate from the Higher School of Economics in Moscow continue their studies at graduate schools in the top mathematics faculties around the world, including Harvard, Caltech, Columbia, MIT, Princeton, and ETH Zurich. Many graduates also enter related fields with high-tech applications, pursuing careers as auditors, analysts, business analysts, Yandex developers, software engineers, and software engineers, for example. A strong mathematics background allows graduates to achieve considerable success in these fields.

Admission to the programme is based on the results of an entrance test that consists of a portfolio and an interview. View the portfolio composition and the evaluation criteria on our website.

The interview consists of two parts. The first part covers applicants’ motives for admission to the master's programme and the scope of professional interests. The second part includes a variety of tasks that test mastery of basic knowledge in the subject area.