Kharkiv National University

What you'll study

This research-oriented master's emphasises rigorous mathematical theory alongside practical computational skills. Core areas include advanced analysis, numerical methods for differential and integral equations, mathematical modelling of physical and engineering systems, optimisation and control theory, stochastic processes and probability, and scientific computing. Students normally follow a combination of taught modules and supervised research, culminating in an independent master's thesis or research project.

• Core modules: Functional analysis, partial differential equations, numerical linear algebra, and scientific programming.
• Specialist modules: Computational methods for PDEs, inverse problems and parameter identification, numerical methods in fluid dynamics, stochastic modelling, and optimisation techniques.
• Research training: Advanced seminars, research methodology, and preparation for thesis work including literature review, problem formulation and presentation skills.
• Computational practice: Use of mathematical software and programming languages common in research (for example MATLAB, Python, or Fortran), high-performance computing where relevant, and implementation of numerical schemes for large-scale problems.

Programme structure balances taught coursework to build depth in methods with a supervised research component in which students develop an original contribution. Students collaborate with academic staff on theoretical work or applied projects with partners in engineering, physics, computer science and industry.

Entry requirements

Applicants are expected to hold a bachelor's degree (or equivalent) in mathematics, applied mathematics, physics, computer science, engineering or a closely related quantitative discipline, with a strong record in core mathematical subjects. Selection typically considers academic transcripts, references, and a statement of research interests outlining intended thesis topics or areas of investigation.

• Evidence of solid preparation in undergraduate real and complex analysis, linear algebra, differential equations and numerical methods.
• One or more academic references from tutors or supervisors who can comment on research potential.
• For applicants whose previous instruction was not in the language of teaching, proof of language ability or completion of prescribed language courses may be required; the department can advise on available language support.
• International applicants may be asked to provide additional documentation such as certified transcripts and a CV; interviews or brief research proposals can form part of the assessment for research supervision matching.

Career prospects

Graduates are prepared for doctoral study and for research or technical roles across academia, industry and the public sector. The programme's emphasis on modelling and computation opens career paths in scientific research institutes, engineering firms, energy and environmental modelling, aerospace and mechanical engineering, quantitative finance and risk management, data science and machine learning, software development for scientific applications, and government research laboratories.

• Research and teaching in universities and research institutes.
• Numerical modelling and simulation roles in engineering and physical sciences.
• Quantitative analyst roles in finance and insurance, including algorithmic trading and risk modelling.
• Data science, machine learning and analytics positions that require strong mathematical foundations.
• R&D positions in IT and technology companies developing scientific software and computational tools.

Why study at Kharkiv National University

Kharkiv National University has a long tradition in mathematical sciences and a strong community of researchers in applied and pure mathematics. The Department of Mathematics and Mechanics provides close supervision by experienced academics working on contemporary problems in analysis, numerical methods and mathematical modelling. Students benefit from access to departmental seminars, collaborative projects across physics and engineering faculties, and established links with regional research institutions.

The research master's environment supports development of both theoretical rigour and hands-on computational experience, making it suitable for students aiming to continue to PhD-level research or to move into demanding technical careers where advanced mathematical competence is essential.