Master of Science in Mathematics

The Master's programme has a prescribed length of four semesters (two years) and ends with the Master of Science degree. It builds on a first academic degree in mathematics (e.g. a Bachelor's degree) and it offers the opportunity to deepen the academic knowledge in one of the several major areas of mathematics, both pure and applied. The training in independent scientific work can be undertaken at one of the seven institutes that engage in cutting edge research in a wide variety of contemporary areas of the mathematical sciences. The main research topics at each institute include the following: Institute of Algebra, Number Theory, and Discrete Mathematics: representation theory, arithmetic number theory, reflection groups and 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, formation of mathematical models, optimisation, numerical analysis and scientific computing Institute of Differential Geometry: geometric flow equations, symplectic geometry, Kaehler and hyperkaehler geometry, gauge theory Institute of Actuarial and Financial Mathematics: stochastical analysis, actuarial and financial mathematics, probability theory The Master's programme is divided into a specialisation phase, which takes about three semesters, and a research phase, which takes one more semester. In the first phase, students acquire the basic knowledge and skills necessary for independent research work in mathematics as well as advanced knowledge in the major research fields of our faculty. The study programme is rounded off by an elective course from another scientific field (e.g. physics, chemistry, philosophy, computer science, economic sciences, etc.) The central element of the research phase is the Master's thesis. It is based on an independent research project on a current issue of mathematics. The study programme is divided into modules. To earn the Master's degree, students must complete all required modules. Each module covers a thematic subject area. To each module, credit points are assigned, according to the expected workload. To earn credits for a module, students must complete various forms of coursework (homework, seminars) and pass an examination. Coursework may be repeated several times and does not have an impact on the final grade. The official examination regulations list the required modules, the coursework, the forms of examinations, and the possible elective courses. PDF Download