Mathematics Main Site











Qualifying Exam


Course Descriptions










Mathematics BSc




Visiting Program


Summer School


Program Contact:

Ivan Penkov

Professor of Mathematics


Research I, 111

+49 421 200 3219


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Structure of the Program

Graduate education at Jacobs University is governed by the appropriate policies. Additional program specific rules are described below.

Initial Academic Advisor

Every incoming graduate student is assigned an initial academic advisor prior to coming to Jacobs University. The initial advisor guides the graduate students through the program, monitors his or her progress, and helps him or her select a PhD advisor.

Study Plan: Integrated PhD Program

The following study plan is the default variant for students entering with a BSc degree. Faster progress is always possible.

Semester Coursework Research Additional Information
1-2 3 courses, 1 seminar    
3 3 courses, 1 seminar Preliminary work Qualifying exam must be completed at the beginning of the 4th semester
4 1 course, 1 seminar PhD research proposal PhD proposal must be presented by the beginning of the 5th semester
5-9 1 seminar PhD research PhD phase begins
10 1 seminar PhD dissertation PhD thesis must be defended by the end of the 10th semester

An individual course plan is prepared by every graduate student in cooperation with his or her academic advisor and further faculty members as appropriate. Qualified students can enter the program at various advanced stages, depending on their qualifications. For instance, the graduate committee may waive the qualifying examination for students holding an MSc degree.

Students pass to the Ph.D. phase if they have received the prescribed credits, have passed the qualifier, and have the agreement of a faculty member to be their PhD advisor.

Course Requirements

In order to obtain a PhD or MSc degree, a student has to satisfy the following coursework requirements (in addition to the general Jacobs University requirements):

  1. For a PhD degree: graduate courses and seminars worth at least 95 ECTS credits
  2. For a Master's degree: graduate courses and seminars worth at least 95 ECTS credits
  3. For both degrees: the courses Introductory Algebra (100 321) or Algebra (100 421), Real Analysis (100 313), and Introductory Complex Analysis (100 312) or Topics in Complex Analysis (100 412).

Throughout their studies, graduate students are required to take one graduate level seminar each semester. In addition, all graduate students are expected to regularly attend the mathematics colloquium.

Graduate classes are 400 level courses and above; up to three elective 300 level undergraduate courses may be counted towards the course credit for PhD or Master's degrees.

Courses at 300 and 400 level carry 7.5 ECTS credits; advanced graduate seminars carry 5 ETCS credits. A research proposal, including presentation, carries 25 ECTS credits. The Master's thesis carries 25 ECTS credits as well.

Jacobs University Bremen reserves the right to substitute courses by replacements and/or reduce the number of mandatories/mandatory elective courses offered.

Qualifying Examination

Every graduate student working towards a PhD in mathematics must pass a comprehensive examination in mathematics at the beginning of the fourth semester. By the end of the third semester, the student has to request from the coordinator of the graduate program in mathematical sciences time and date for her or his examination.

The purpose of this examination is to manifest solid knowledge of advanced but core material in mathematics and/or applied and computational mathematics, to show the ability to make connections between areas of mathematics usually taught in different courses, and to demonstrate the potential for research in the mathematical sciences.

Students are free to choose between two examination formats, Mathematics or Applied and Computational Mathematics.

Both examination formats are oral, the exam takes at least 90 minutes. The material covered is described below according to format.


  1. Algebra
  2. Real Analysis
  3. Complex Analysis
plus a choice of one among the following topics
Numerical Analysis
Partial Differential Equations
Mathematical Physics
Functional Analysis
Probability Theory

Applied and Computational Mathematics

  1. Concepts from Algebra and Complex Analysis
  2. Real Analysis
  3. Numerical Analysis
plus a choice of one among the following topics
Scientific Computing
Partial Differential Equations
Mathematical Physics
Functional Analysis
Probability Theory

The syllabi for all topics are presented in Section 4. The examination is given by three professors appointed by the graduate committee.

Master's Option

Any graduate student may at any time request to work for a Master's degree, independently of whether or not he or she continues to work for a PhD degree.

The graduation requirements are specified by the Jacobs University's policies; the coursework requirements are described in Section 2.3. There is no separate Master's examination or qualifying examination.

The following table describes a study plan for a graduate student who has entered the program with a Bachelor's degree and wishes to conclude his or her graduate education with a Master's degree after four semesters.

Semester Coursework Research
1-2 3 courses and 1 seminar  
3 3 courses and 1 seminar Preliminary work
4 1 course and 1 seminar Master's thesis


Last updated 2014-08-07, 18:04. © Jacobs University Bremen. All rights reserved.