# Specialization "Biomathematics"

## Master's program

In the Master's program, "Biomathematics" is one of 7 main areas of specialization. The basic courses in the specialization "Biomathematics" consists of the following 5 compulsory modules:

- The theory of discrete- and continuous-time Markov chains is the center of the module Stochastic Processes, in particular the classification of states and long-time behavior. Furthermore, special Markov chains (for example, random walks and branching processes) and various applications are covered. This course should be taken in the first semester of the Master's program since only prior knowledge of probability is necessary but not measure theory. Moreover, knowledge about stochastic processes is needed in mathematical population genetics and in advanced courses.
- The module Mathematical Population Genetics deals with the basic models describing the evolution of the genetic composition of a population under processes like selection, mutation, recombination, or random drift. These models, which describe the change of gene frequencies in the course of many generations, are formulated with the aid of differential equations, difference equations, or Markov chains.
- The module Mathematical Ecology is devoted to models of population growth, models of the interaction of different species (for instance, predator-prey or host-parasite interaction, and competition for resources) but also models of pattern formation (for example, the Turing mechanism, morphogenesis, chemotaxis). Likewise the analysis of (systems of) differential equations plays a central role.
- In the module Seminar: Biomathematics, you have to complete two seminars (for example, Seminar (Biomathematics) or Seminar (Mathematical Population Genetics)), and an introductory seminar on one of the compulsory modules. Further seminars and introductory seminars can be taken as advanced courses.

The module Stochastic Processes is offered every winter semester, whereas the modules Mathematical Population Genetics, Mathematical Ecology, and Game Theory are offered in a three semester cycle (for example, ecology in WS2015, game theory in SS2016, population genetics in WS2016, etc.).

The offering of advanced courses for the Master's program is closely linked to the research interests of the faculty members working in this area. Usually advanced courses are offered following one of the compulsory basic courses, but there are also sometimes other topics from biomathematics, such as systems biology or pattern formation offered.

The Master's thesis should be connected to one of the advanced courses but other topics can be assigned as a Master's theses as well. Students should get in touch with possible supervisors as soon as possible, preferably by the end of the first semester.

## Doctoral program

In principle, all advanced courses for the Master's program can be chosen as courses for the doctoral program provided that they have not been credited for the Master's program. The recognition of courses for the doctoral program will be specified individually in the "dissertation agreement" (Dissertationsvereinbarung).

Topics for a doctoral thesis are usually assigned from the areas of research of the supervisors. It is extremely important that you contact a potential supervisor before starting the doctoral program and talk about a possible supervision. It does not make sense to enroll for the doctoral program first and then look for a supervisor.