# Mathematical Physics (Master)

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## Infos

**Degree: ** Master of Science (M. Sc.)

**Duration:** 4 semester

**Start: ** each winter semester

**Language:** English B2 level required

**Capacity: ** 25 students

**Credits: ** 120 CP (ECTS)

## M. Sc. Mathematical Physics

Physics and mathematics are indispensable for understanding the world and are strong driving forces for technical innovations in modern society. Their importance in research and development both in the academic sector as well as in industry is bound to increase over the next decades.

Leipzig University has a long-standing tradition in Mathematics and Physics with a line-up of famous former professors such as e.g.

- Werner Heisenberg, who received the Nobel Prize and the Max Planck medal during his time in Leipzig,
- Felix Klein, founding father of the “Mathematics Seminar”, with his fundamental contributions to the theory of algebraic equations and function theory,
- Felix Bloch, Nobel Prize awardee, assistant of Heisenberg with fundamental work on quantum mechanics,
- Sophus Lie, with major contributions to continuous groups of transformations,
- Peter Debye, Nobel Prize awardee and Max Planck medalist,
- Bartel Leendert van der Waerden, with his work on the group-theoretical formalism for quantum mechanics.

These days, we not only have strong Mathematics and Physics Departments, but also benefit strongly from the presence of the local Max Planck Institute for Mathematics in the Sciences (MPI MiS) Leipzig with world leading groups, e.g. in partial differential equations, non-linear algebra (algebraic geometry), information theory or mathematical machine learning.

We invite you to come to Leipzig and prepare for your carrier in this fascinating subject by signing up for our new international master program “Mathematical Physics”.

**We offer a wide range of courses on:**

- dynamical systems
- general relativity and differential geometry
- stochastic processes and statistical physics
- gravity and cosmology
- condensed and soft matter
- partial differential equations
- representation and operator theory
- particles and quantum fields
- advanced quantum mechanics

**In the master program, you:**

- learn general principles of mathematical physics and in-depth knowledge on selected topics
- apply this knowledge to describe, analyze and solve complex problems
- transfer concepts to related questions in other or interdisciplinary fields
- train to read and understand current international specialist literature
- perform independent research in one year research phase under the guidance of a professor or senior scientist
- prepare for a job in academia or industry and economy

**Key benefits:**

- study in a vibrant place with long-standing tradition in mathematical physics
- enjoy small courses led by dedicated lecturers
- contribute to current projects in research groups at Leipzig University or MPI MiS
- profit from a high flexibility and chose the courses according to your own preferences
- option to continue your carrier in the prestigious graduate school IMPRS MiS

**Fee:**

No tuition fees; semester fee of 220 € (includes MDV ticket for public transportation).

## Studieninhalte und Struktur

The master course consists of two one year periods, a first phase in which the basic knowledge in mathematical physics is deepened and widened, followed by a research phase.

The corner stone in the first phase are the two courses on mathematical physics. They will base on your fundamental knowledge on mathematics and theoretical physics and set the background for the advanced specialized modules you take later on.

In the research phase, you will learn to do independent research on a specific topic under the supervision of a professor or senior scientist, become a part of a research group and contribute to research problems of current interest.

The course structure allows individual choices and thus a wide range of specialization options. It consists of compulsory modules (rectangular boxes), elective modules (boxes with rounded corners) and compulsory elective modules (octagonal boxes).

In addition to the wide variety of topics in mathematics and theoretical physics mentioned above you could also make use of the extended selection of elective modules, e.g. from meteorology (data assimilation or numerical weather prediction and climate modelling) or informatics (neuro-inspired information processing, artificial neural networks and machine learning, visualization, graphs and biological nets). The full list of courses can be found in the study documents .

In the following, some of methodologically complementary courses are grouped into "tracks” as examples and guide for you – but they will not appear as sub-title or specialization on your Master certificate. Actually, there are many more options – please feel free to "design" the master program along your individual preferences!

In contrast to the regular plan, some compulsory or elective modules can also shifted into the 2nd semester and elective modules of 10 LP may be replaced by two modules of 5 LP (see track 3).

## Zulassungsvoraussetzungen

**Prerequisite to the admission is:**

- a Bachelor degree in mathematics, physics or informatics at university level
- alternatively, Bachelor degrees of related subjects might be accepted, subject to approval by the aptitude commission, provided the following criteria are met: 30 ECTS of basic mathematics with at least 20 ECTS covering algebra and analysis; 20 ECTS of knowledge in theoretical physics or equivalent subsects as regards to content;
- a B2 level certificate of English language or equivalent proof

## Bewerbungs- und Zulassungsverfahren

Depending on your nationality and country where you obtained your university degree, different procedures and deadlines apply:

**A – Procedure with a German university degree**

**B – Procedure with a foreign university degree**

For details, please refer to:

- central information pages by Leipzig University for applicants with German citizenship
- or for international applicants

## Berufsaussichten

Due to the importance of mathematics and physics in modern society, graduates can follow many avenues for employment in academia and industry. Many graduates do a PhD after receiving their master degree, with excellent local opportunities at our institutes of mathematics and theoretical physics and at the MPI for Mathematics in the Sciences, e.g. as member of our graduate school IMPRS MiS.

Due to the skills shortage in the field of mathematicians, IT specialists, natural scientists and technicians in Germany, graduates of this master program have excellent opportunities to pursue a wide range of careers in industry and business (e.g. in mechanical engineering, electrical engineering, medical technology, software development, finance and insurance, communication systems, energy, transport or logistics). Other job opportunities exist in the service sector (e.g. business consulting, technology consulting) or in scientific research institutions and in administration (e.g. material testing offices, quality assurance, validation, IT security).