Master of Science in Mathematics

Overview

This two-year (four-semester) program leads to a Master of Science degree and is designed for students who already hold a first academic qualification in mathematics (for example, a Bachelor's degree). It lets you deepen your mathematical knowledge by specialising in major areas across both pure and applied mathematics, while developing the skills needed for independent scientific work and research.

Independent research and thesis work are carried out within the university’s mathematics institutes, which are active in contemporary, high-level research. These institutes cover a broad spectrum of topics, giving you the opportunity to align your master’s project with specialists in the field and to prepare either for doctoral studies or for analytically demanding careers in industry, finance, or data-driven roles.

Research areas (selected institutes and main topics)

• Institute of Algebra, Number Theory, and Discrete Mathematics: representation theory, arithmetic number theory, reflection groups, arrangements of hyperplanes
• Institute of Algebraic Geometry: algebraic surfaces, Calabi–Yau manifolds and their moduli, mirror symmetry, modular forms, singularity theory
• Institute of Analysis: partial differential equations on manifolds with geometric singularities, spectral geometry, geometric and deformation quantisation, noncommutative geometry and operator algebras, sub-Riemannian geometry, mathematical statistics
• Institute of Applied Mathematics: applied analysis, mathematical modelling, optimisation, numerical analysis, scientific computing
• Institute of Differential Geometry: geometric flow equations, symplectic geometry, Kaehler and hyperkaehler geometry, gauge theory
• Institute of Actuarial and Financial Mathematics: stochastic analysis, actuarial and financial mathematics, probability theory

Entry requirements

• A first academic degree in mathematics (e.g., a Bachelor's degree)
• Language of instruction: English

Curriculum overview

The Master's curriculum is organised into two main stages: a specialisation phase lasting about three semesters, followed by a one-semester research phase. During the specialisation phase you build the core mathematical knowledge and technical skills required for independent research and deepen your understanding in the faculty’s principal research areas. The programme also includes an elective from another scientific discipline (for example physics, chemistry, philosophy, computer science, or economics) to broaden your perspective and foster interdisciplinary competence.

The research phase centres on the Master's thesis, which is carried out as an independent research project addressing a current problem in mathematics. The programme is structured in modules: each module focuses on a thematic area, is assigned credit points according to the expected workload, and is completed through a combination of coursework (e.g., homework, seminars) and formal examinations. Coursework can be repeated several times without affecting the final grade. Full details about required modules, assessment formats, and available electives are specified in the official examination regulations.

Key modules and learning outcomes

• Core modules that establish foundational knowledge for advanced mathematical work and research.
• Advanced modules targeting the faculty’s main research fields to develop specialised expertise.
• An interdisciplinary elective from another scientific field to expand analytical horizons.
• A research-oriented Master’s thesis demonstrating the ability to plan and complete an independent investigation of a contemporary mathematical question.

Requirements (concise)

• Complete the specialisation phase (≈ three semesters) and the research phase (one semester).
• Finish all required modules; each module awards credit points based on workload.
• Earn credits by completing coursework (homework, seminars) and passing examinations.
• Select and complete one elective course from another scientific discipline.
• Complete a Master’s thesis as an independent research project on a current mathematical issue.
• Coursework may be repeated multiple times; repeated coursework does not change the final grade.
• Consult the official examination regulations for the exact list of required modules, coursework details, examination types, and elective options.

Graduates acquire advanced theoretical and practical skills that prepare them for academic research (including doctoral studies) and for analytically demanding roles in industry. Typical career paths include PhD programmes, research positions at universities and institutes, roles in finance and actuarial science, data science and analytics, optimisation and modelling in engineering or technology firms, and consulting.

The programme’s strong emphasis on independent research, modelling and computational techniques also develops transferable skills valued by employers across sectors, such as problem solving, rigorous quantitative reasoning and scientific communication.