Mathematics

Type of Study: Full-time

Standard Duration of Studies: 4 semesters

Credits: 120 ECTS

Main Locations: Garching 

Start of Degree Program: summer or winter semester

Language of Instruction: English

Costs: Semester fees, tuition fees for international students

Professional Profile: Mathematics

The master’s degree program in mathematics allows students a considerable degree of freedom when putting together their individual academic profile. They can obtain credits from various areas of mathematics, but you can also choose supplementary modules from computer science, physics, chemistry, economics or a number of other disciplines.

For their area of specialization, students can choose from numerous options, such as analysis and PDE, algebra and geometry, probability theory, numerical analysis and scientific computing, optimization or biomathematics and biostatistics. They can also add modules from one or several minors to their competency profile.

In interdisciplinary courses, students will acquire soft skills in areas like public speaking and presentation, which are indispensable for their future careers. And the flexible structure of the program allows students to study abroad for one or two semesters at one of TUM's partner universities.

The master's thesis in the fourth semester concludes the program.

As a graduate, you will have gained a deep understanding of core mathematical areas and profound knowledge from several subareas of modern mathematics. In addition, you will have acquired unique expertise and skills depending on your choice of majors and specializations.

Your professional competencies will be complemented by interdisciplinary soft skills, such as rhetoric, presentation techniques or management skills.

Graduates of the master’s degree program in mathematics have excellent career prospects in a wide range of industries. They can gain employment, for example, at higher education institutions, research institutes, research and development departments at large companies, government authorities, consulting firms, and numerous medium-sized businesses. Mathematicians often work in basic research, software development, business consulting, finance and insurance, data security, communications or IT.

The application can be submitted via our portal TUMonline. After creating your account please enter your personal data and educational information and upload the required documents. Applications must be submitted electronically. 

Only if you have been accepted, you will have to submit some additional documents as certified copies in paper form for enrollment. Applicants with an international higher education entrance qualification ("Bildungsausländer:innen") usually must have their documents reviewed in advance via uni-assist.

How to apply for a Master's Degree Program – Step by Step

Prospective students who have earned their qualification to pursue a master’s degree (e.g. bachelor’s degree) outside the EU / EEA will need to have their graduation certificates and transcript checked in advance by uni-assist before submitting their online application. Since this can take up to four weeks, it is strongly recommended to initiate this process at an early stage.

On the TUM website you will find detailed information for international applicants.

For your application please upload the following documents in TUMonline:

• Copy of your degree certificate or a copy of your subjects and grades (transcript) with at least 140 Credits
• Proof of English language proficiency
• Form for grade calculation
• Comprehensive and up-to-date CV
• Letter of motivation (in English)
• Scan of Identity card or passport
• Course catalogue / curriculum
• Preliminary Documentation (VPD) if applying with an undergraduate degree/qualification from outside the EU/EEA
• APS certificate for applicants with a degree from a Chinese, Vietnamese or Indian university

For more information on all required documents, see the Document Glossary of the Technical University of Munich. Depending on your previous education and origin, we may require additional application documents. You will be informed which documents these are via TUMonline during the online application process.

In the first stage, we evaluate the final grade and written documents using a point system. Depending on the score, applicants are either immediately admitted, rejected, or invited to an aptitude assessment interview.

Discipline-specific requirements

To be accepted to the TUM master’s program in mathematics, applicants must have a qualified university degree in 

• mathematics,
• physics or
• a comparable course of study that does not differ significantly in terms of the competencies acquired in the aforementioned bachelor's degree programs at TUM.

The equivalency and comparability of programs that are not listed will only be decided during the application process. Unfortunately, it is not possible to make any statements on this in advance.

Additionally, proof of suitable competencies is required, as listed on the checklist to the extent indicated. If applicants fail to meet these requirements by only a narrow margin, they will receive a point deduction in the application procedure. If too much is missing, this will lead to the application being rejected.

Detailed information on the selection process can be found in Appendix 2 of the FPSO.

Language requirements

Another requirement is adequate proficiency in the English language. If your official language of education was not English, you will need a recognized language certificate. If you have previously written your graded thesis in English or can prove that you have completed at least 10 credits in English-language examination modules, you are considered to have demonstrated adequate proficiency in English.

The aptitude interview is conducted in English either in an in-person meeting in Garching or as a web conference. It lasts 20 to 30 minutes. The interview focuses on the applicant's knowledge of the subject from their first degree, their motivation, and their ability to work scientifically or in a fundamentally and methodologically oriented manner.

When does it take place?

Aptitude interviews for applications for the summer semester take place between January and March, for the winter semester between June and September. Invitations are sent out at least one week in advance. The exact time of the aptitude interview depends on the time the application is being processed. The earlier an application is received in full, the earlier we can process it.

Once you have received an acceptance letter and have accepted the place in your TUMonline account, you will be required to pay the tuition fees and submit the documents necessary for enrollment. Among other things, this includes the signed application for enrollment on paper, the certified degree diploma, and the certified degree certificate. You will find the list of required documents in your TUMonline account. Please be aware that your matriculation will only be effected after you have successfully submitted these documents.

Recognition of previously earned credits

Please check which modules, if any, you can have recognized from your Bachelor's program and where you have to submit the request for recognition of examination credits.

Upon request, you can focus on a specific area of specialization while studying for your master’s degree. You will then choose your modules primarily from this area, which will also be indicated on your final transcript of records. Alternatively, a broadly based course of study without a designated area of focus is also possible.

You can choose from the following areas of specialization:

Analysis and PDE

Here you will take modules in the areas of analysis, dynamical systems, functional analysis, partial differential equations or Fourier analysis.

Algebra and Geometry

This specialization covers projective geometry, differential geometry, algebra 2 or algebraic surfaces, as well as algebraic number theory, topology or algebraic geometry.

Probability Theory

Focus on probability theory, stochastic analysis, Markov processes, or probability methods and algorithms in data analysis.

Numerical Analysis and Scientific Computing

This area covers modules such as numerics, partial differential equations, finite elements methods, optimal control of general differential equations, or compressed sensing.

Optimization

In this area of specialization you will take modules from non-linear, integer or combinatorial optimization, such as polyhedral combinatorics or modern methods of non-linear optimization.

Biomathematics and Biostatistics

This area includes modules on mathematical models in biology, statistical learning, population genetics or mathematical ecology.

Students can attend selected lectures from minor subjects like informatics, physics, chemistry or economics, as well as other academic disciplines upon request. However, they can also earn all required ECTS credits in mathematics.

If you decide on a minor subject, will independently select modules from the respective minor subject catalog in TUMonline. It is possible to combine modules from different areas. You will find more detailed information in the respective Academic and Examination Regulations for the mathematics program.

The Advanced Seminar (Hauptseminar) is one of the obligatory courses. When choosing a seminar, please note that some departments link the awarding of the thesis to a seminar that you have taken and passed. Therefore, you will usually take a suitable main seminar in the third semester.

A four week professional internship is part of the degree program. In the accompanying internship seminar, you will have the opportunity to find out about suitable tasks and to exchange experiences during the professional internship.

You will round off your individual skills and competency profile with modules from the area of Support Electives. You can choose from a wide range of soft skills courses or language courses depending on your interests.

Detailed information can be found under Examinations. The General Academic and Examination Regulations (APSO) of the TUM and the respective program-specific Academic and Examination Regulations (FPSO) apply to all students:

Current regulations (valid for courses starting from winter semester 2023/24).

• Program-specific Academic and Examination Regulations, as of August 17, 2023

Expiring regulations (valid for start of studies from winter semester 2019/20 but before the winter semester 2023/24).

• Unofficial accessible version of the current regulations, as of August 20, 2021
• Program-specific Academic and Examination Regulations, as of July 18, 2019

Expiring regulations (valid for start of studies up to and including summer semester 2019)

• Program-specific Academic and Examination Regulations, as of August 4, 2010
• 1. Amending Statute, March 27, 2012
• 2. Amending Statute,  April 25, 2013 (with Annex 2 as amended)
• 3. Amending Statute from September 16, 2013
• 4. Amending Statute, April 11, 2014 (with Annex 3 as amended)
• Collective Amending Statutes, May 03, 2016 (new application deadlines)
• 6. Amending Statute, April 27, 2018 (double degree, verification of language skills)

To complete a master's degree, students will be required to write a scientific paper: the master's thesis. They are given six months to complete it. It is possible to register for the master's thesis on the 1st and 15th of each month. The topic of the thesis depends on the area in which a student chose to deepen their knowledge during their course of studies.

Please find everything you need to know from planning to submitting your thesis under Final Thesis.