Guidelines for Master's theses

Prerequisites

The Master's thesis is a specialization in the field of stochastics and requires solid knowledge in the scope of the lecture (measure-theoretical) probability theory. Furthermore, you should have completed at least one of the following 4+2 hour modules

  • Financial mathematics in continuous time
  • Mathematical statistics
  • Spatial stochastics
  • Statistical Learning

and at least one of the following advanced modules:

  • Brownian motion
  • Extreme value theory
  • Generalized regression models
  • Lévy processes
  • Markovian decision processes
  • Nonparametric statistics
  • Percolation
  • Poisson processes
  • Risk theory
  • Control of stochastic processes
  • Stochastic geometry
  • Time series analysis

The content of this module should match that of the first module. Please ask the lecturer whether there are any connections.

It is also recommended that you attend a seminar at the Institute of Stochastics. This can serve as a transition to the Master's thesis.

Topic

As a rule, a current journal article is processed, supplemented and, if possible, extended in a Master's thesis. Sometimes specific tasks also have to be completed. Possible topics range from practical applications to theoretical problems. We are also happy to receive specific suggestions for topics. If you are planning a Master's thesis in cooperation with industry, please discuss the topic and research question with us in advance.

Language

The Master's thesis can be written in German or English.

Scope

The length is relative and can vary between 50 and 120 pages. As a rule, the more theoretical the thesis, the smaller the number of pages. For practical theses, the 120 pages may include programs, data, etc.

Structure

A possible structure of the thesis is

  1. Introduction
  2. Basics
  3. Modeling and problem definition
  4. Mathematical analysis of the model/problem
  5. Summary/Outlook Appendix (optional, may contain important mathematical tools)
  6. Literature
  7. Declaration of independence

What is important?

The further you detach yourself from the model, the better (depending on the quality of the model and the result!). You should keep the following key questions in mind:

  • Can you add further results or extend the existing model or comprehensively solve the task set?
  • Is the structure coherent and logical?
  • Is the paper written in such a way that someone who has listened to a relevant core lecture in the field of stochastics can understand it?
  • If possible, use terms that you know from the lecture.

Latex

You can find a possible latex template for your paper at

http://www.math.kit.edu/lehre/seite/bachmastarbeiten/de

download.

Declaration

The Master's thesis must contain a declaration with the following wording: I hereby declare that I have written the thesis independently and have not used any sources and aids other than those specified, that I have marked the passages taken verbatim or in terms of content as such and that I have observed the statutes of the Karlsruhe Institute of Technology for safeguarding good scientific practice in the valid version.

Karlsruhe, the