In the English-language master’s course of study Mathematical Physics you will learn general principles of mathematical physics and acquire in-depth knowledge of selected topics. You apply the knowledge to describe, analyse and solve complex problems. You transfer concepts to related questions in other or interdisciplinary areas. You will train to read and understand current specialist literature. Under supervision, you will learn to perform independent research and complete your studies with an independent research work, the 23-week master's thesis.
In our commitment to diversity, we welcome people of all backgrounds and cultures. We are particularly proud of the fact that more than 1500 students from 38 countries are currently studying in our German and international courses. For an international faculty like ours, diversity and inclusion are important resources for incorporating multifaceted approaches and ways of thinking into innovative teaching and research. We are therefore committed to cosmopolitan coexistence, where everyone is welcome regardless of origin, gender and religion.
Additional Information on the Application
You obtained your first university degree in Germany and would like to apply for the master’s course of study in Mathematical Physics? Then please apply via AlmaWeb and submit the following documents in addition by e-mail or by mail to the dean of our faculty:
-
Application for evaluation of admission requirements (informal letter or email)
-
Transcript of records/certificate of a first degree qualifying for a profession which includes:
- 30 credit points of algebra and analysis; up to ten credit points can be accepted from other areas of mathematics,
- 20 credit points of theoretical physics or in areas that are related to theoretical physics in terms of content (e.g. quantum mechanics, experimental physics, complex and meteorological systems, dynamic systems, differential equations).
-
Short curriculum vitae in tabular form
-
Proof of knowledge of the English language at the level B2 of the Common European Framework of Reference (or equivalent)
Please submit these documents by 1 September for a start in the winter semester of the same year.
The master's admissions committee uses these documents to check whether you meet the requirements for the admission to the master's course of study. You will receive a written notification about this, which you should submit to the Studierendensekretariat with the other documents for your enrolment.
Please apply via AlmaWeb by 15 September for a start in the winter semester of the same year.
You obtained your first university degree abroad? In this case, please apply directly via uni-assist e.V. by 31 May for a start in the winter semester of the same year.
Structure of the Course of Study
You will learn the general principles of mathematics and theoretical physics in two fundamental courses on mathematical physics. Basing on your knowledge in analysis, algebra and theoretical physics obtained during your bachelor's courses, you will deepen your expertise on topics like symmetries, geometry, field theory and quantum mechanics. You will gain in-depth knowledge on selected fields by taking elective courses. The course structure allows for multiple individual choices – you can shape the programme along your own preferences.
The master’s course of study Mathematical Physics consists of two one-year phases: a first phase in which the physics knowledge is deepened and widened, followed by a research phase.
| Modules | ||||
|---|---|---|---|---|
| 1st Sem. | Mathematical Physics 1 | Mathematical Physics 2 | Elective Area 1 (Physics) or Free Elective Area 1 or 2 | |
| 2nd Sem. | Free Elective Area 1 or Elective Area 1 (Physics) | Elective Area 2 (Mathematics) | Free Elective Area 1 or 2 or Elective Area 3 (Advanced Seminar | |
| 3rd Sem. | Free Elective Area 1 or 2 | Elective Area 3 (Advanced Seminar) | Research Practice | |
| 4th Sem. | Master's Thesis | |||
The information on the module numbers and credit points can be found in the detailed overview.
The foundations in the first phase are the two modules on mathematical physics. These build on your basic knowledge of mathematics and theoretical physics. They form the basis for the special modules that you will take later.
In the research phase, you will be guided in a selected specialised field to work on issues relating to current national and international research. In the fourth semester, the focus is on the master's thesis. You can also do this in cooperation with domestic or foreign companies, universities or research institutions.
The master's course of study Mathematical Physics is offered jointly by the Faculty of Mathematics and Computer Science and the Faculty of Physics and Earth Sciences. Modules starting with numbers 10-MAT- are administered by the study office of the Faculty of Mathematics and Computer Science, modules with numbers 12-PHY- by our study office. Semester schedules can be found in the course catalogue from mathematics (click path: Nach Studiengängen – Math.MP) and the course catalogue from physics.
Elective Areas
For the elective area 1 (physics), you choose a module from the following compulsory elective modules:
| Sem. | Module No. | Module Title | CP |
|---|---|---|---|
| 1 | 12-PHY-MWPT1 | Advanced Quantum Mechanics | 10 |
| 2 | 12-PHY-MWPT2 | Advanced Statistical Physics | 10 |
| 1/3 | 12-PHY-MWPQFG1 | General Relativity | 10 |
| 1/2/3 | 12-PHY-MWPQFG2 | Cosmology | 10 |
| 1/2/3 | 12-PHY-MWPTET4 | Relativistic Quantum Field Theory | 10 |
For the elective area 2 (mathematics), you choose a module from the following compulsory elective modules:
| Sem. | Module No. | Module Title | CP |
|---|---|---|---|
| 2 | 10-MAT-MPDG1 | Advanced Differential Geometry I | 10 |
| 2 | 10-MAT-MPSP1 | Stochastic Processes I | 10 |
| 1/3 | 10-MAT-MPAN1 | Advanced Analysis – PDE | 10 |
| 1/2/3 | 10-MAT-MPFOP1 | Functional Analysis/Operator Theory | 10 |
In the elective area 3 (advanced seminar), the focus is not only on imparting specialist knowledge, but also on developing and improving methodological skills. These are literature research, presentation skills and academic writing. In each semester, aspects of current topics from the research areas of both institutes are studied in the advanced seminars. Possible topics in the field of theoretical and mathematical physics are, for example: quantum field theory, gravity, condensed matter theory, quantum theory of condensed matter, quantum statistical physics, complex systems and complex quantum systems. You choose a module from the following compulsory elective modules:
| Sem. | Module No. | Module Title | CP |
|---|---|---|---|
| 2/3 | 12-PHY-MWPSTP | Specialised Topics of Theoretical Physics | 5 |
| 2/3 | 12-PHY-MWPSMP | Specialised Topics of Theoretical and Mathematical Physics | 5 |
| 2/3 | 10-MAT-MPHSAL | New Developments in Algebra | 5 |
| 2/3 | 10-MAT-MPHSAN | New Developments in Analysis | 5 |
| 2/3 | 10-MAT-MPHSG | New Developments in Geometry | 5 |
| 2/3 | 10-MAT-MPHSS | New Developments in Stochastics | 5 |
Free Elective Areas
The free elective area comprises elective modules totalling 30 CP, at least 20 CP from free elective area 1 and up to ten CP from free elective area 2. Alternatively, you can choose additional modules from the elective areas 1 (physics) and 2 (mathematics) as well as another advanced seminar from elective area 3.
For the free elective area 1, you choose modules with a total of at least 20 CP from the following elective modules:
| Sem. | Module No. | Module Title | CP |
|---|---|---|---|
| 2/3 | 12-PHY-MWPQFG3 | Quantum Field Theory on Curved Space Times | 10 |
| 2/3 | 12-PHY-MWPSTP1 | Quantum Field Theory of Many-Particle Systems | 10 |
| 1/3 | 12-PHY-MWPSTP2 | Statistical Mechanics of Deep Learning | 10 |
| 2 | 12-PHY-MWPMMP1 | Black Holes | 10 |
| 1/2/3 | 12-PHY-MWPTKM3 | Theory of Soft and Bio Matter | 10 |
| 1/2/3 | 12-PHY-MWPTKS1 | Stochastic Processes in Physics, Biology and Earth Science | 10 |
| 1/2/3 | 12-PHY-MWPTKS2 | Non-linear Dynamics and Pattern Formation | 10 |
| 1/2/3 | 12-PHY-MWPXT1 | Group Theory and Its Applications in Physics | 10 |
| 2 | 10-MAT-MPDS1 | Dynamical Systems | 10 |
| 3 | 10-MAT-MPDS2 | Advanced Theory of Dynamical Systems | 10 |
| 2/3 | 10-MAT-MPSTAN | Selected Topics in Analysis | 10 |
| 2/3 | 10-MAT-MPDST | Discrete Stochastic Models in Physics | 10 |
| 2/3 | 10-MAT-MPSTAG | Selected Topics in Algebra and Geometry | 10 |
| 3 | 10-MAT-MPAN2 | Advanced Analysis II | 10 |
| 3 | 10-MAT-MPDG2 | Advanced Differential Geometry II | 10 |
| 3 | 10-MAT-MPFOP2 | Advanced Operator Theory | 10 |
| 3 | 10-MAT-MPSP2 | Stochastic Processes II | 10 |
You can also choose up to two modules from the following practical courses:
| Sem. | Module No. | Module Title | CP |
|---|---|---|---|
| 2/3 | 12-PHY-MWPTKM4 | Practical Course: Condensed Matter Theory | 5 |
| 2/3 | 12-PHY-MWPCQM1 | Practical Course: Quantum Theory of Condensed Matter | 5 |
| 2/3 | 12-PHY-MWPQFG6 | Practical Course: Quantum Field Theory and Gravity | 5 |
| 2/3 | 12-PHY-MWPTKM5 | Practical Course: Quantum Statistical Physics | 5 |
| 2/3 | 12-PHY-MWPTKS3 | Practical Course: Complex Systems | 5 |
For the free elective area 2, you choose modules with a total of up to ten CP. You can choose further modules from the free elective area 1. You can also take modules from other courses of study from the Fächerkooperationsvereinbarungen. The Fächerkooperationsvereinbarungen exist for the following modules:
| Sem. | Module No. | Module Title | CP |
|---|---|---|---|
| 1/3 | 12-111-1026 | A3 – Numerical Weather Prediction and Climate Modelling (MSc Meteorology) | 5 |
| 2 | 12-111-1034 | T6 – Data Assimilation (MSc Meteorology) | 5 |
| 2 | 10-202-2104 | Neuro-Inspired Information Processing (MSc Computer Science) | 10 |
| 1/3 | 10-202-2133 | Artifical Neural Networks, Deep Learning, Machine Learning and Signal Processing (MSc Computer Science) | 10 |
| 1/3 | 10-202-2201 | Visualisation (MSc Computer Science) | 10 |
| 1/3 | 10-202-2205 | Graphs and Biological Nets (MSc Bioinformatics) | 10 |
Model Curricula
Here you will find curricula for taking modules if you want to specialise in a certain topic. These are to be understood as examples. You can also combine other compulsory elective and elective modules. The chosen focus will not be mentioned on your master's certificate.
For the focus on gravitation and differential geometry, we recommend the following modules for the elective and free elective areas:
| Modules | ||||
|---|---|---|---|---|
| 1st Sem. | Mathematical Physics 1 | Mathematical Physics 2 | General Relativity | |
| 2nd Sem. | Cosmology or Quantum Field Theory on Curved Space Times | Advanced Differential Geometry I | Dynamical Systems or Advanced Analysis – PDE | |
| 3rd Sem. | Advanced Differential Geometry II | New Developments in Geometry or Quantum Field Theory and Gravity | Research Practice | |
| 4th Sem. | Master's Thesis | |||
The information on the module numbers and credit points can be found in the detailed overview.
For the focus on dynamical systems and stochastics, we recommend the following modules for the elective and free elective areas:
| Modules | ||||
|---|---|---|---|---|
| 1st Sem. | Mathematical Physics 1 | Mathematical Physics 2 | General Relativity or Selected Topics in Algebra and Geometry or Theory of Soft and Bio Matter | |
| 2nd Sem. | Advanced Statistical Physics | Stochastic Processes I | Dynamical Systems | |
| 3rd Sem. | Advanced Differential Geometry II or Stochastic Processes II | New Developments in Stochastics | Research Practice | |
| 4th Sem. | Master's Thesis | |||
The information on the module numbers and credit points can be found in the detailed overview.
For the focus on stochastics and condensed matter, we recommend the following modules for the elective and free elective areas:
| Modules | |||||
|---|---|---|---|---|---|
| 1st Sem. | Mathematical Physics 1 | Mathematical Physics 2 | Advanced Quantum Mechanics or Theory of Soft and Bio Matter or Computational Physics I | ||
| 2nd Sem. | Advanced Statistical Physics | Stochastic Processes I | Condensed Matter Theory and Computer Simulations II | ||
| 3rd Sem. | Computational Physics II or Stochastic Processes II | Practical Course: Condensed Matter Theory | Research Practice | ||
| 4th Sem. | Master's Thesis | ||||
The information on the module numbers and credit points can be found in the detailed overview.
For the focus on quantum field theory and functional analysis, we recommend the following modules for the elective and free elective areas:
| Modules | ||||
|---|---|---|---|---|
| 1st Sem. | Mathematical Physics 1 | Mathematical Physics 2 | Advanced Quantum Mechanics | |
| 2nd Sem. | Relativistic Quantum Field Theory or Cosmology | Functional Analysis/ Operator Theory | Stochastic Processes I or Advanced Analysis – PDE | |
| 3rd Sem. | Quantum Field Theory on Curved Space Times or Selected Topics in Algebra and Geometry or Quantum Field Theory of Many-Particle Systems | Quantum Field Theory and Gravity or Quantum Field Theory | Research Practice | |
| 4th Sem. | Master's Thesis | |||
The information on the module numbers and credit points can be found in the detailed overview.
For the focus on field theory and dynamical systems, we recommend the following modules for the elective and free elective areas:
| Modules | ||||
|---|---|---|---|---|
| 1st Sem. | Mathematical Physics 1 | Mathematical Physics 2 | General Relativity | |
| 2nd Sem. | Selected Topics in Analysis or Cosmology | Advanced Analysis – PDE | Dynamical Systems | |
| 3rd Sem. | Advanced Theory of Dynamical Systems or Selected Topics in Analysis | Quantum Field Theory and Gravity | Research Practice | |
| 4th Sem. | Master's Thesis | |||
The information on the module numbers and credit points can be found in the detailed overview.