MSc in Mathematical Physics

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 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.

Elective Areas

Elective Area 1 (Physics)

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 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

Elective Area 2 (Mathematics)

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

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

Elective Area 3 (Advanced Seminar)

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.

Free Elective Area 1

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
1/2/3	12-PHY-MWPCQM2	Physics of Driven and Open Quantum Systems	5
1/2/3	12-PHY-MWPCQM3	Geometry and Topology in Quantum Matter	5
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.

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

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

Focus on Dynamical Systems and Stochastics

For the focus on dynamical systems and stochastics, we recommend the following modules for the elective and free elective areas:

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

Focus on Stochastics and Condensed Matter

For the focus on stochastics and condensed matter, we recommend the following modules for the elective and free elective areas:

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

Focus on Quantum Field Theory and Functional Analysis

For the focus on quantum field theory and functional analysis, we recommend the following modules for the elective and free elective areas:

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

Focus on Field Theory and Dynamical Systems

For the focus on field theory and dynamical systems, we recommend the following modules for the elective and free elective areas:

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