This English-language, interdisciplinary, research-oriented Master's degree programme is aimed at (international) students of theoretical physics with a strong mathematical inclination as well as (international) students of mathematics with a strong interest in physical applications. They are introduced to modern issues and methods in mathematics and in mathematical and theoretical physics by attending courses offered by both Faculties. The courses offered are jointly organised by the Faculties of Physics and Mathematics.

This degree programme is designed to enable students to understand the mathematically precise formulation and physical relevance of scientific papers, including those of an interdisciplinary nature, to classify them critically and to present their essential content in an understandable way. The degree obtained should qualify students for doctorate/Phd studies in Theoretical Physics or Mathematics. Furthermore, this Master's degree enables entry into one of the many appointments open to these two disciplines.

In the following focus of research in mathematics and theoretical physics we support a fruitful exchange between topics such as

- Dynamical and integrable systems
- Lattice gauge theory and numerical analysis
- Nonlinear differential equations and the early universe
- Probability theory and random matrices
- Quantum field theory and representation theory
- Stochastic analysis and statistical mechanics

Other topics or combinations are of course possible in consultation with our lecturers. For further questions, please contact Prof Gernot Akemann (Physics) or Prof Lubomir Banas (Mathematics).

A distinction is made between two profiles for approval to the degree programme and different admission tracks are prescribed for the Master's degree programme: A. Approval with a specialisation in mathematics and B. Approval with a specialisation in physics.

**Approval requirements for all students:**

- Proof-oriented competences in analysis and linear algebra (in terms of content to the extent of the first academic year of a subject-specific bachelor course with mathematics as the main subject).
- Fundamental, content-based understanding of the physical relationships in four of the following areas of physics: mechanics, electrodynamics, optics, thermodynamics and quantum physics. In addition, a basic understanding of the theoretical concepts in at least one of these areas must be demonstrated. They are able to solve problems from these areas independently and present their solutions in an understandable way.

**A. Further approval requirements for students specialising in mathematics in the Bachelor's degree:**

- Proof-oriented competences in measure and integration theory as well as in three other of the following areas of mathematics: Geometry/topology, function theory, functional analysis, differential equations, numerics, stochastics or algebra..

**B. Further approval requirements for students specialising in physics in the Bachelor's degree:**

- Basic, substantive understanding of the theoretical concepts of quantum mechanics and statistical physics. You will be able to apply these to problems in modern physics and solve problems independently. In these areas in particular, they learn to analyse axioms and their consequences. They also have in-depth competences in the areas mentioned under 2.) and another mathematics module from the areas mentioned under A. (recommended is measure and integration theory)

The content of the individual competences is based on the Bachelor's degree programmes in Mathematics and Physics at Bielefeld University

If no degree certificate from a previous degree programme is available, a provisional degree certificate can be accepted in its place.

For approval via **Profile A**, the following study programme is defined for the Admission Track (20 LP): If theoretical concepts in quantum mechanics are not demonstrated upon approval, they must be acquired in the Admission Track. If theoretical concepts in statistical physics are not demonstrated upon approval, they must be acquired in the Admission Track. Overall, the Admission Track comprises theoretical concepts in quantum mechanics (introduction and specialisation), static physics as well as elementary particle physics, nuclear physics, astronomy & astrophysics and specialisation in classical mechanics and electrodynamics.

For approval via **Profile B**, the following study programme is defined for the Admission Track (20 CP): The Admission Track includes two mathematics modules from the above-mentioned areas of the Bachelor's degree or advanced Master's mathematics modules not considered for approval. If proof-oriented competences in measure and integration theory are not demonstrated upon approval, these must be acquired in the Admission Track.

General: If competences from modules that are to be studied as part of an admission track have already been demonstrated upon approval, the credit points must be acquired in other mathematics or physics modules.