Do you want to unravel the mathematical theory behind the laws of nature and do research at the interface of mathematics and physics? In the two-year English-language master’s programme “Mathematical Physics M.Sc.” at Leipzig University, you will learn about modern topics in theoretical physics and the mathematical theory that underpins them. You have the freedom of choosing your own direction via a large variety of courses offered at both the mathematics and physics departments. You will learn how to describe, analyze and solve complex problems and apply your knowledge in an interdisciplinary setting. You will also learn how to perform independent research, understand specialist literature and write a master thesis under the supervision of world-leading experts.

Highlights of the Mathematical Physics M.Sc. programme.

• International and taught entirely in English
• Interdisciplinary
• Design your master’s programme according to your interests.
• Develop your analytical skills.
• Participate in cutting-edge international research as part of a research group at Leipzig University or the Max Planck Institute Mathematics in the Sciences.

Why study in Leipzig?

• We offer small-group courses with personal attention by dedicated lecturers.
• Leipzig University has a rich and long tradition in mathematical physics.
• Leipzig is a vibrant city with a buzzing cultural scene, affordable housing, lots of green space and many lakes.

In the 1st semester of the programme (Year 1) you will start with the compulsory modules Mathematical Physics 1 and Mathematical Physics 2, which form the basis of the courses and seminars offered in the rest of the programme. You will learn tools from mathematics and physics that are needed for the later, more advanced and specialized modules.

The structure of the programme allows for a high degree of flexibility and accommodates to individual preferences in the choice of elective modules. In addition to the wide range of modules offered in mathematics and theoretical physics, you can take advantage of an extended range of elective modules from meteorology (data assimilation or numerical weather prediction and climate modelling) to computer science (neuro-inspired information processing, artificial neural networks and machine learning, visualization, graphs and biological networks).

In the 3rd semester (Year 2), you will do the module Research Practice, where you will learn how to do research and presentations. The 4th semester (Year 2) is devoted to your master thesis.

• 1^st semester: 20 ECTS in the compulsory courses Mathematical Physics 1 and 2.
• 1^st and 2^nd semester: 10 ECTS in elective courses in mathematics

  List modules mathematics

  Semester	Module number	Module title	ECTS
  2nd	10-MAT-MPDG1	Advanced Differential Geometry I	10
  2nd	10-MAT-MPSP1	Stochastic Processes I	10
  1st /3rd	10-MAT-MPAN1	Advanced Analysis I – Partial Differential Equations	10
  1st /2nd /3rd	10-MAT-MPFOP1	Functional Analysis / Operator Theory	10

  and 10 ECTS in elective courses in theoretical physics

  List modules theoretical physics

  Semester	Module number	Module title	ECTS
  1st	12-PHY-MWPT1	Advanced Quantum Mechanics	10
  2nd	12-PHY-MWPT2	Advanced Statistical Physics	10
  1st /3rd	12-PHY-MWPQFG1	General Relativity	10
  1st /2nd /3rd	12-PHY-MWPQFG2	Cosmology	10
  1st /2nd /3rd	12-PHY-MWPTET4	Relativistic Quantum Field Theory	10

• 1^st - 3^rd semester: A total of 30 ECTS in elective modules of which at least 20 ECTS in courses in physics and mathematics

  List free electives physics and mathematics

  Semester	Module number	Module title	ECTS
  1st	12-PHY-MWPTKM4	Practical Course: Theory of Condensed Matter	5
  2nd /3rd	12-PHY-MWPQFG6	Theoretikum Quantum Field Theory and Gravity	5
  2nd /3rd	12-PHY-MWPQFG3	Quantum Field Theory in Curved Spacetimes	10
  2nd /3rd	12-PHY-MWPSTP1	Quantum Field Theory of Many-Particle Systems	10
  2nd	12-PHY-MWPMDC2	Computer Simulation II	5
  1st /2nd /3rd	12-PHY-MWPTKM3	Theory of Soft and Bio Matter	10
  1st	12-PHY-MWPCQT1	Computational Physics I	10
  3rd	12-PHY-MWPCQT2	Computational Physics II	10
  1st /2nd /3rd	12-PHY-MWPXT1	Group Theory and Its Applications in Physics	10
  2nd	10-MAT-MPDS1	Dynamical Systems	10
  3rd	10-MAT-MPDS2	Advanced Theory of Dynamical Systems	10
  2nd /3rd	10-MAT-MPSTAN	Selected Problems in Analysis	10
  2nd /3rd	10-MAT-MPDST	Discrete Stochastic Models in Physics	10
  2nd /3rd	10-MAT-MPSTAG	Selected Problems in Algebra and Geometry	10
  3rd	10-MAT-MPAN2	Advanced Analysis II	10
  3rd	10-MAT-MPDG2	Advanced Differential Geometry II	10
  3rd	10-MAT-MPFOP2	Advanced Operator Theory	10
  3rd	10-MAT-MPSP2	Stochastic Processes II	10

  and up to 10 ECTS may be in courses from other subject areas

  List free electives other

  Semester	Module number	Module title	ECTS
  1st /3rd	12-111-1026	A3 – Numerical Weather Prediction and Climate Modelling (M.Sc. Meteorology)	5
  2nd	12-111-1034	T6 – Data Assimilation (M.Sc. Meteorology)	5
  2nd	10-202-2104	Neuro-inspired Information Processing (M.Sc. Computer Science)	10
  1st /3rd	10-202-2128	Artificial Neural Networks and Machine Learning (M.Sc. Computer Science)	5
  1st /3rd	10-202-2201	Visualization (M.Sc. Computer Science)	10
  1st /3rd	10-202-2205	Graphs and Biological Networks (M.Sc. Bioinformatics)	10

• 3^rd semester: 5 ECTS in an elective advanced seminar

  List adavanced seminars

  Semester	Module number	Module title	ECTS
  2nd /3rd	12-PHY-MWPHS4	Quantum Field Theory and Gravitation	5
  2nd /3rd	12-PHY-MWPHS5	Quantum Field Theory	5
  2nd /3rd	12-PHY-MWPHS7	Theory of Condensed Matter	5
  2nd /3rd	12-PHY-MWPHS8	Computational Quantum Field Theory	5
  2nd /3rd	12-PHY-MWPHS9	Quantum Statistical Physics	5
  3rd	10-MAT-MPHSAL	New Developments in Algebra	5
  3rd	10-MAT-MPHSAN	New Developments in Analysis	5
  3rd	10-MAT-MPHSG	New Developments in Geometry	5
  3rd	10-MAT-MPHSS	New Developments in Probability Theory	5

  and 5 ECTS in the compulsory Research Practice course.
• 4^rd semester: 23-week Master Thesis

In view of the large variety of courses, you can find below the following example "tracks" to take during your master’s programme (click to open a PDF with the track overview).

1. Gravitation / Differential Geometry
2. Dynamical Systems / Stochastics
3. Stochastics / Condensed matter
4. Quantum Field Theory / Functional Analysis
5. Field Theory / Dynamical Systems

You can find detailed descriptions of the modules (in German).

The following prerequisites are required:

• a B.Sc. (or equivalent) university degree in mathematics, physics or computer science, or
  
  
• a B.Sc. (or equivalent university degree) in a different area, with proof of the following passed in mathematics or theoretical physics:
  1. At least 30 ECTS in mathematics courses, of which at least 20 ECTS in algebra and analysis courses.
  or
  2. At least 20 ECTS in theoretical physics courses, or related courses. For example, quantum mechanics, experimental physics, complex and meteorological systems, dynamical systems, differential equations.
  
  
• Proof of knowledge of English at level B2 of the Common European Framework of Reference for Languages (or equivalent)

In our commitment to diversity, we welcome people of all backgrounds and cultures. For an international faculty like ours, diversity and inclusion are important resources for developing and innovating how we think, teach and perform research. We are proud of the fact that more than 1400 students from 38 countries are currently studying in our German and international courses.

First degree obtained in Germany

If you obtained your first university degree in Germany, please apply via AlmaWeb. You should also submit the following documents independently of your AlmaWeb application to the Dean of the Faculty of Physics and Geosciences.

• An informal letter or email with your application for evaluation of admission requirements.
• A transcript of records/certificate of a first university degree satisfying the prerequisites above.
• A short CV in tabular form.
• Proof of knowledge of the English language at the level B2 of the Common European Framework of Reference (or equivalent)