Elite Program TopMath

Are you studying in a mathematics Bachelor program, or have you just completed it? Are you interested in doing at PhD in Mathematics? And would you like to get started right away? Then the TopMath program fits perfect for you.

TopMath - Mathematics with Integrated Doctorate Program

TopMath is a doctoral program in mathematics with a research-oriented Elite Master within the Elite Network of Bavaria and offers outstanding Bachelor’s graduates the opportunity to pursue their doctorate directly after completing their Bachelor’s degree.

TopMath supports students in the field of pure and applied mathematics, as well as related areas of informatics. The broad spectrum of internationally renowned professors at the Technical University of Munich and University of Augsburg give TopMath students many opportunities to pursue their interests in research. 

Watch the facts about our TopMath program in brief in our video:

What do we offer?

News and events

Structure of the TopMath Program

The structure of the TopMath Program consists of:

  • Elite Master Study Program in Mathematics (PreDoc- and Masterphase)


  • Doctoral Program in Mathematics (Doctoralphase)

TopMath begins with enrollment on a research-oriented elite Master’s course. The first two semesters (PreDoc phase) are usually devoted to finding and becoming involved in challenging research-oriented work in mathematics and preparing participants for the transition to the doctoral program. In this phase, students follow a tailor-made curriculum comprising of lectures, seminars and individual research. From the beginning, they are integrated into the scientific community by their mentoring professor.

From the second year of study onwards, the elite Master’s program and the doctoral program are completed simultaneously.

After these two years, TopMath students are expected to complete their Master’s thesis and concentrate on their doctoral project, which usually takes another four semesters.

Documents on TopMath

Information on the design of the program can be found in the program documentation (in German).

New study regulations dated February 23.02.2018:


Old examination regulation:

Bachelor in Elite part-time studies (München)


PhD studies with parallel Masters Hons. (1st July 2014/7th April 2016)

Who can be your TopMath mentor?

Applications for TopMath

Application deadline

is December 1st each year (for a start of studies in the winter semester and in the summer semester)

Program start 

  • winter semester (lecture period: mid-October until mid-February) or
  • summer semester (lecture period: mid-April until the end of July)

Criteria for acceptance into an Elite Master Program (TopMath)

  • Excellent grades in a mathematics Bachelor program or equivalent, lasting a minimum of 6 semesters
  • Ability to carry out basic research, and to work in a scientific and methodic way
  • Keen interest in independent and creative work
  • Exceptional motivation and potential for achievement within the Elite Master Program in Mathematics

Application procedure

Please note there are different requirements for bachelor graduates from the TUM and for external graduates.


Transcript of Records (TOR)

  • for external candidates: TOR with courses equivalent to a minimum of 120 credits or, in case of non-european higher education system, at least two thirds of the overall necessary examinations in a Bachelor programm, which lasts a minimum of 6 semesters. The Transcript of Records must be issued and certified accordingly by the appropriate examination authority or by the appropriate Admissions Office. Please read the information on certified copies and certificates of our Admission Office.
  • for TUM Bachelor graduates: The same conditions apply as for external candidates.


Curriculum of the underlying university degree:

  • for external applicants: Please submit 1) a course catalogue (summary of the content of your mathematical courses and, if applicable, the bibliographical references of the textbooks used in your courses) and use 2) the Excel file below as a template:
  • for TUM bachelor graduates: Please upload 1) the course catalogue or a document with the link to the course catalogue and 2) the empty Analysis of the Curriculum.


Curriculum Vitae

  • for external and internal graduates:  Please submit as a personal data sheet.


Letter of motivation

  • for external and internal graduates: A written statement (letter of motivation) describing the reasons for wishing to be admitted to the Elite Master Program TopMath. This letter of motivation should be written in English or German and be maximum of two A4-pages. It should explain why your specific abilities and interests (please see the criteria above) make you a good candidate for the Elite Master Program TopMath.



  • for external and internal graduates: A scientific mathematical essay, written in English or German language, approximately 10.000 characters in length. (For your orientation: In usual formatting this length will often correspond to roughly four pages.) Please choose one of the following essay topics:

TopMath Essay Topics 2021



Proof of English Language skills

  • for external graduates: If you have not completed your education officially in English nor German, you must provide proof of sufficient language skills in English OR German. Please send us a certified copy of your language certificate. Here you can find out which English or German language certificates are acceptable. If you submit English as a language certificate, you must also have a basic knowledge of German (level A1). If you have no proven German language skills, you will be required to take at least one module during the first two semesters of your studies, in which you acquire basic German language skills. The TUM offers free courses.
  • for TUM Bachelor Graduates: The same conditions apply as for external candidates.


Preliminary Documentation (VPD)

  • for external graduates: Applicants with a qualification for graduate studies (e.g. a bachelor's degree) obtained in a country outside of the EU/EEA who are not already enrolled at TUM or have not successfully completed preparatory studies at a Studienkolleg in Germany are required to have their application documents verified before submission by the University Application Service for International Students(uni-assist e.V.). Uni-assist will issue a VPD certificate.
  • for TUM bachelor graduates: not required

You can apply from 01.10. to 01.12. of each year via TUMonline.

Please take time to read the instructions thoroughly and to complete the application carefully. Please choose from the drop-down menus as follows:

  • "Start of course": next summer semester or next winter semester (depending on when you want to start your studies)
  • in "Study Type": "Elite Master" and
  • for "Degree course": "Mathematics with additional PhD program Mathematics".

After completing the form, you can use this system to print an "application for approval". Please sign it and then upload it back to TUMonline.

For applications for summer semester 2020 or later, you no longer have to submit any hardcopies at this point. 

When assessing your documents, the TopMath-Committee decides whether you will receive

  • a direct study admission, or
  • a direct rejection, or
  • an invitation to an interview.   

If you are admitted or rejected directly, you will be notified in January.

The period for interviews is from 01.01. to 31.03. of each year. We will let you know one week in advance, when exactly your interview will take place. Usually the interview takes place at the Department of Mathematics in Garching. We can also permit foreign applicants to conduct the interview via Adobe Connect. Either way, your interview will take 20 to 30 minutes and will include an evaluation of the following criteria:

  • your ability to work scientifically and in a fundamental and methodical manner (does the applicant show interest in the subject areas of the degree course, as well as in a scientific discussion of the topics involved?)
  • proof of existing knowledge from your first degree course (e.g. by outlining a solution for an exemplary problem set in the interview)

  • the particular ability and willingness to work independently and creatively (e.g. by giving  a short independent presentation of an exemplary problem area),

  • strong motivation and desire to achieve (is the applicant prepared to further their knowledge, beyond the compulsory attendance times of the course).

The result of your interview will be sent to you two weeks later.

  • You have to pay semester fees.
  • You must submit the following documents in order to enroll at TUM:

Bachelor’s Degree or Comparable Qualification for Admission

  • for external graduates: An officially certified copy of the undergraduate degree must be submitted by the beginning of the Elite Master Program TopMath, via post to the address printed on the "Application for Admission".
  • for TUM bachelor graduates: If you proceed directly after your TUM Bachelor to the Elite Master Program TopMath, your diploma will be submitted to the Student Registration Office automatically.


Proof of sufficient health insurance cover

  • for external graduates: In Germany, all students must have health insurance, i.e. you must have proof of sufficient insurance cover in order to be able to enroll at a German university.
  • for TUM bachelor graduates: already confirmed


We recommend that you submit all required documents before the semester begins, as enrollment is not possible until all documents have been received. If you are not officially enrolled at TUM, you cannot register for courses or examinations, nor can you be issued a student ID card or semester ticket.


If you have any questions please do not hesitate to contact us via e- mail: topmath (at) ma.tum.de.

PreDoc Program: Scholarships for international students

If you are an international candidate and not yet a TUM student, you can apply for a PreDoc scholarship parallel to TopMath. Up to two scholarships/year for a period of max. two years are available.

The TopMath program and the PreDoc program complement each other perfectly, but are separate programs. A separate application process is necessary. The deadline 2021 for the PreDoc program is December 1st, 2021, for a start in winter semester 2022/23.

For more information on prerequisites and application, visit the PreDoc website: https://www.ma.tum.de/en/research/predoc-program.html.


TopMath Board

The TopMath-Board is responsible for the professional supervision of the programm. This executive committee specifically ensures the expertise of all persons who are involved in this project, and their compliance with the requirements of the curriculum. It is also in charge of the further development of TopMath.

Members of the TopMath-Board:

Coordination and Advisory Service

For the coordination of the program, quality control measures, organization of workshops, and seminars during vacation within the network of the participating universities and research institutions, as well as the coordination of activities aimed to provide interdisciplinary basic knowledge, the following persons are responsible:

Integration within the TUM Graduate School

Since May 2010 the TopMath doctorate program (Graduate Center, TGZ TopMath) has been integrated into the TUM Graduate School (TUM-GS).

The following members of the TopMath Board supervise the Graduate Center: 

TopMath Students

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