Specialization "Stochastics and Dynamical Systems" (SDS)

This page collects the most important information from the specialization "Stochastics and Dynamical Systems", sorted by study programme.

Teacher training programme

Students of the teacher training programme encounter contents belonging to the area of SDS in the  compulsory stochastics module. This module introduces the mathematical foundations of probability theory and statistics, and also addresses paedagogical aspects. There is a large variety of  topics suitable for bachelor and master's theses in SDS for students of the teacher training programme.

Bachelor programme

In the bachelor programme, the compulsory module on probability theory and statistics offers an introduction to the mathematical foundations of stochastics. Optional modules based on this include financial mathematics, stochastics, and applied statistics. Basic aspects of dynamical systems are introduced in courses on differential equations.

Information on the contents of individual courses can be found in the curriculum for the bachelor programme in mathematics. The concluding bachelor seminar offers various topics from the field of SDS for bachelor theses.

Master programme

Within the master programme, "Stochastics and Dynamical Systems" is one of 7 main areas of specialization. You have to choose one of these 7 areas and the chosen main area of specialization results from the completion of the compulsory module group "Basic courses in the area of specialization ...". The further modules of the master programme can be divided into courses from the chosen area of specialization and courses from other areas of specialization.

The standard curriculum in this area of specialization contains 4 compulsory modules:

  • The module on stochastic processes introduces the most important types of random processes, in particular Markov chains in discrete and continuous time, like random walks and branching processes, and some of their applications. This course should be taken at the very start of the master programme.
  • The module on measure theory and integration provides the analytical basis for most of the other courses here. It should also be taken at the very start of the master programme.
  • The module on advanced probability theory covers the core material of probability in a measure-theoretic setup. Topics include laws of large numbers, distributional convergence, central limit theorems, existence of stochastic processes, Brownian motion, and invariance principles.
  • Seminars on SDS.

Further lecture courses on advanced topics often reflect the research interests of faculty members. We regularly offer courses on stochastic analysis, financial mathematics, ergodic theory, and further aspects of dynamical systems.

It is advisable to think about a possible topic and a supervisor of a master's thesis at an early stage of the master programme, and to contact potential supervisors in time. There is a broad range of topics suitable for Master's theses.  Theses closely related to current research, however, usually study topics from some faculty member's field or research. Information on those can be found on the webpages.

Doctoral programme

As usual at the faculty of mathematics, there is no real difference between advanced courses for the master programme and courses for the doctoral programme in the area of specialization "Stochastics and dynamical systems" but their recognition will be specified individually in an agreement ("Dissertationsvereinbarung").

The research interests of the individual faculty members play a much larger role in the choice of a topic and supervisor for a doctoral thesis than for a master's thesis. The topics are usually related to the (more or less) immediate research area of the supervisor, to be found on the personal homepages.