Master of Science in Mathematics

The Master in Mathematics in Bonn is a research-oriented degree which requires a Bachelor degree in Mathematics (or an equivalent degree). For further information on the application process we refer to this page. The language of instruction is English. You may also attend courses in German but this is not obligatory.

Program
To complete the Master's program you have to earn 120 credit points ("CP"). Credit points measure the so-called workload of a module. One credit point roughly translates to about 30 hours of actual work. Each module has a certain number of credit points. You can earn these credit points by passing the module exam. There are several types of modules which can be attended in this program. These include lecture courses (some of them with exercise sessions), seminars, a master thesis with associated seminar and practical training courses. For further information on the different modules offered here, you may have a look into the module handbook.
Beyond that it is possible to choose a secondary subject (up to 24 CP). If you plan on taking a secondary subject other than physics, economics and computer science (the so-called canonical secondary subjects), you should consult with the Bachelor-Master office of the Department of Mathematic. Regarding the canonical secondary subjects, you can take any module from their respective Master's programs unless the board of examinations states otherwise.
In any case, it is advisable to make yourself familiar with the Examination rules. For international students the Bachelor-Master office has also provided a non-binding translation. If you have any difficulties or questions regarding these regulations, you can always ask.
We try to give an overview on the most important regulations here but we advise you to consider the official webpage of the Department of Mathematics.

Lectures (48 CP):
Overall you have to cover at least three of the following six areas with respectively 23 CP, 16 CP and 9 CP earned by lecture courses.
These areas are:

  • A) Algebra, Number Theory, and Logic
  • B) Analysis and Differential Equations
  • C) Discrete Mathematics
  • D) Geometry and Topology
  • E) Numerical Mathematics and Scientific Computing
  • F) Probability and Stochastic Analysis

A special kind of lecture courses are the so-called foundation modules, which can be chosen both during the Master's and the Bachelor's program. Students in the Bachelor's program usually take foundations courses at the end of their program, whereas students enrolled in the Master's program attend these at the beginning of their studies as an introductory course to an area they are interested in. You may attend several foundation courses (even within one area), but you can only obtain 9 credit points per area using foundation modules for your Master's degree. Further lecture courses offered may be used to deepen your knowledge attained in your previous studies.
There are lecture courses with exercise sessions (9 credit points), advanced topics lecture courses (no exercise sessions) and selected topics courses (only one lecture each week). The topics covered in the advanced topics are diverse and varies each semester.
The module handbook provides you with a rough overview on the topics discussed in the lecture courses and which prerequisites are advisable to be met. If you are unsure about your qualification for certain courses, you can consult your mentor, a professor who is assigned to you at the beginning of your first semester.
If you are interested in a specific lecture course, you may also contact the lecturer himself or see if the lecturer has a webpage for his or her course.

Free Electives (24 CP):
Here you can choose further mathematics modules (lecture courses, seminars) or modules from a secondary subject, usually economics, physics and computer science.
Furthermore you can take practical training courses (Practical Teaching Course, External Internship, Programming Project). These are not necessarily offered every semester. It is important to inform yourself about these modules in advance, preferably during the semester before you want to take them, as you need to have a job as a tutor for a practical teaching course or an external internship at a company (which needs to eligible for this program) depending on the respective module.
If you want to be a tutor you should consult with Dr. Beate Doerffel and/or Dr. Michael Welter.
If you are interested in a external internship, you may consult with Carsten Rezny and Hildegard Gebertz.
Regarding the programming projects it is advisable to inform yourself via basis or to look for postings in the mathematics department.
A secondary subject as mentioned above would be part of the free electives.

seminars (12 CP):
It is obligatory to pass at least two graduate seminars during your studies.
Here are some rough information on how a seminar is usually held: At the end of the semester previous to the seminar or at the very beginning of the new semester, seminars are announced via basis and (but not necessarily) by postings in the mathematics department. Additionally, lecturers may announce their seminar in a lecture course. Usually, the lecturers provide a rough overview on the content of the seminar on their own webpages, on the postings or during a pre-seminar talk.
During a pre-seminar talk the seminar's instructor roughly presents the material covered during the seminar and divides the overall topic into several talks. If you are interested in one of the talks presented, you can register for the seminar and the specific talk there. This is already a binding registration. Additionally, you have to register for the seminar via basis at the beginning of the semester. This is necessary to ensure that you receive the credit points earned in the seminar.
If you miss a pre-seminar talk, do not worry. You can contact the instructor and ask for more information.
Once the semester starts, the actual seminar starts, too. One after another each students gives his or her previously chosen talk, which will be graded by the instructor.
However, depending on the instructor and the number of participants seminars may vary in their form. You may be asked to give more than one talk, you may be asked to write a hand-out or a summary or exercises (or all three of them), your talk may take 30, 60 or 90 minutes, there may be an active discussion afterwards, the session may be weekly or biweekly or completely irregular, you may be asked to prepare your seminar while keeping close contact to an assistant of the instructor or with the instructor himself.

Master Thesis and associated seminar(30+6 CP):
Once you have earned 30 credit points, you can register for your master thesis. To do this, you need an advisor. Your advisor is usually a lecturer, whom you have met in previous courses and who works in an area, which you are interested in. Once you have contacted a lecturer and agreed upon a topic for your thesis, you can register for both the Master thesis and its seminar at the Bachelor-Master-office with this form.
Once registered, you have exactly one year to complete the thesis. Unless you have important issues prohibiting you from meeting the deadline, you are obliged to work within the given timeline. We advise to consult with the Bachelor-Master-office in case of serious issues as early as possible. The final talk of the seminar may be before or after you hand in your thesis depending on your advisor.
The details of the master-thesis seminar also depend on your advisor. You may give a presentation in front of other students also working on their Bachelor or Master thesis or you may be asked to give a talk in front of the research group of your advisor. Overall you have to give three talks about your Thesis in the associated seminar.
As every other module, the Master thesis and the Master Thesis seminar influence your overall grade by the number of credit points earned by it. This means that the Master Thesis makes up 25% of your overall grade (30 of 120 credit points to be earned). The seminar's and the Master Thesis' grade may differ.

You can find more detailed informationhere.

Examinations
Lecture courses are completed by a graded exam at the end of the semester. The grade for the exam will be your overall grade for the lecture course and influences the final grade of your Master's degree by the number of credit points given for it. Depending on the lecture course, it may be completed with an oral or written exam. The exact examination dates or announced during the beginning of the semester here and by postings in the mathematics department. For each lecture course there are two examination dates given. You can only attend the second exam if you have failed the first one or you have been unable to attend the exam due to sickness. In the latter case, seek further information here (as early as possible).
If you fail both exams, you can decide to try again the next time the module is offered. Even though the module codes can be identical, the content of the courses may significantly differ. It is therefore advisable to retake the whole lecture course.
If you fail both exams in your retake, the module is failed entirely and you cannot retake the exam.

Application and Enrollment
You can enroll for the Master's program in both the summer and winter semester but you have to apply beforehand. You can find the important deadlines and required documents here.
If you have trouble with the enrollment, you should contact the Studentensekretariat.

Questions?
Do not hesitate to make contact in case of any questions.
You are always welcome in the Fachschaft, you can ask questions in person, by telephone or write an email.
If you are unsure, whom to turn to with your questions, we may be of help, too.

At the beginning of the your first semester there will be a presentation containing the most important regulations by the Bachelor-Master office. Nevertheless, you can always contact the Bachelor-Master-Office, too.