Master's Mathematics in Science and Engineering
Are you attracted to the way of thinking in the engineering and natural sciences? Do you want to convert problems in the field into mathematical models? Then why not use mathematics to take up the challenge of putting innovative ideas into practice, and drive research and development forward? In the Mathematics in Science and Engineering Master’s program you learn everything in four semesters that you need to work in the interdisciplinary field of software and technology, in development departments at large corporations, as well as at research institutes specializing in the natural and engineering sciences.
Major fields of study
Areas such as mathematical model building, numerical analysis, applied analysis, optimization, stochastics and informatics are all central to the Mathematics in Science and Engineering Master’s program. Having chosen an associated area of application in the engineering or natural sciences, students acquire solid foundational knowledge that prepares them for future work in interdisciplinary teams. Seminars on topics such as rhetoric and presentation techniques are also permanent components of this Master’s program.
Here you will find important dates, deadlines and other relevant information.
Measures due to the corona pandemic
We have created a department corona page for students of mathematics with information about the effects and limitations of the corona pandemic on various study-related matters. We have also added notes on current practice at our department. This page is going to be updated regularly.
Further information can also be found on the TUM page on Corona.
Please continue to check your TUM email and the web pages regularly.
Profile: The essentials for the Master's program
The Mathematics in Science and Engineering Master’s program is full time. The standard duration of study is four semesters.
Commencing the degree program
Students can commence the Master’s program at TUM in either the winter or summer semester.
Language of instruction
The language of instruction in the Master’s program in Mathematics in Science and Engineering is English.
The curriculum should be agreed with Prof. Rainer Callies. For orientation, please see:
Field of application
Having consulted the student academic advisor, you must select a field of application for your Master’s program, such as physics, medical technology and engineering, structural or fluid mechanics.
Be sure to take into consideration that the assignment of the final thesis is conditional in some departments upon successful completion of the Advanced Seminar.
Foundational subjects such as Numerical Analysis and Optimization are important components of the degree course, along with courses from modules in Applied Analysis and Computational Mathematics.
Details of all modules relevant to the degree program, along with associated times and locations, are available in the department’s curriculum at TUMonline. Here you can create your own timetable and save it digitally.
Whether you write on numerical analysis, optimization, stochastics, or applied analysis depends on the area in which you have acquired advanced knowledge. Read everything you need to know about the Master’s thesis here.
A four-week professional internship is integrated into the program. The accompanying Internship Seminar offers you the chance to inform yourself about suitable occupations and to discuss the experience you acquired during the internship.
You can round up your individual personal competence profile through modules out of the field of extradisciplinary competencies. Lead by your own interests you can choose out of a large offer of soft skilsl or language courses.
Academic and examination regulations
All students must note the general information concerning examinations as well as the current program-specific Academic and Examination Regulations (FPSO).
The prerequisite for the TUM Master´s program "Mathematics in Science and Engineering" is an accredited university degree in Mathematics, Engineering Mathematics, Physics, or a comparable course of study. If you are interested in the Master´s program you should refer to the "Basics of the Bachelor´s degree course in Mathematics at the TU Munich" (see Check list) to verify the required competencies in detail. You need to have acquired at least 29 ECTS credits from among the lectures listed in Table A3.1. If these conditions have been missed by only a narrow margin, you´ll have points decucted during the application process. If the commission thinks that there is too much missing content, your application will be rejected.
Your Language of Instruction
In case the language of instruction during your undergraduate study was not English, you will need a language certificate (see Check List) before the end of the application period.
Additional German Language Knowledge
If you already have a German language certificate to at least the A1 level, please submit that with your application. Applicants who provide just an English language certificate with their application will be admitted on the condition that they complete one module providing integrative knowledge of the German language within the first two semesters of their studies. TUM offers free courses for that purpose (see Check List).
Application: How to get a place
Please note: The process described here is partly new and applies from the application for the summer semester 2020!
Language tests are only offered on the appointed days and their evaluation requires some time. In any case the certificate has to be uploaded before the application deadline. Schedule enough time for that!
Preliminary Documentation (VPD)
You can apply for the preliminary documentation from uni-assist throughout the year but you have to apply before the end of TUM application period. If you have applied for a VPD but it is not yet available, you can confirm the timely completion of the application for the VPD by submitting our form instead. As soon as you receive the final VPD upload that instead to your TUMonline account.
for the winter semester: January 1 - May 31
in 2020 because of COVID-19 (coronavirus SARS-CoV-2) for once extended till june 30!
for the summer semester: October 1 - November 30
All necessary documents must be uploaded by the end of the application deadline!
You don't need to have your Bachelor's degree at the moment of your application: some documents, such as your Bachelor's certificate, can be sent up to the so called enrollment deadline. This deadline is normally about 5 weeks after the start of the corresponding semester.
Compile the necessary documents for your application as early as possible. All documents necessary for admission in a Master´s program at the Technical University of Munich must be uploaded on the platform TUMonline. A candidate account is required for this purpose. You can find detailled information on this website.
|Documents, that have to be uploaded before the application deadline||External applicants||TUM Bachelors|
|Application form (printed from TUMonline)||✓||✓|
|Transcript of Records with courses equivalent to a minimum of 140 ECTS||✓|
just upload an unauthenticated transcript from TUMonline
|Form with grade calculation (curricular analysis) from the best 140 ECTS||✓||✓|
|Curriculum of the underlying university degree||✓||✓|
Please upload that
|Actual Curriculum Vitae (CV)||✓||✓|
|Letter of Motivation||✓||✓|
|Proof of language skills (German or English)||✓||✓*|
|uni-assist VPD certificate||✓|
Only applicants outside of the EU/EEA
* For Science amd Engineering English is needed!
|Documents, that have to be uploaded or sent in after admission but within the enrollment deadline||External applicants||TUM Mathematics Bachelors|
|Signed printout of the application for enrollment (from TUMonline)||✓||✓|
|Bachelor’s Degree or comparable qualification for admission||✓||If you proceed directly after your TUM Bachelor to the TUM Master your diploma will be forwarded to the Student Registration Office automatically.|
|Proof of sufficient health insurance||✓|
The electronic applicant wizard guides you through the application step by step. All required documents for admission must be uploaded.
The application for admission will be generated as a PDF document in your applicant account once the online application has been submitted electronically. Download that file, sign it and upload it back again to your TUMonline applicant account. Only then will your application be complete.
Important: choose "consecutive Master degree" as the form of study below the point "study programme selection".
Check your candidate account on TUMonline on a regular basis. You will be notified there about missing documents and receive an offer or refusal of a study place. If you do not receive an offer, you can register one more time for the selection procedure. You will also receive important individual information at the e-mail address provided in your applicant account.
In order to obtain a place in the Master´s program, you must follow the procedure for verification of eligibility. This takes place once every six months and is carried out by the Faculty of Mathematics. After reviewing your application documents, the board of examiners decides whether you will receive an acceptance, a rejection, or an invitation to an aptitude assessment interview.
The aptitude assessment interview, which has to be completed by only a few candidates, takes place personally in Garching or as a webconference in German or English and lasts 20 to 30 minutes. The interview focuses on the candidates' motivation and ability to apply structured working methods. The expertise acquired from undergraduate courses is also assessed.
After you have been admitted for the master's program and after you have accepted the place of study in your TUMonline account, you still have to pay the administrative fees and submit the necessary documents for enrollment. This includes amongst others the signed application for admission on paper as well as the certified diploma. The list of required documents can be found in your TUMonline account. Only then you'll be enrolled.
Recognition of examination and study achievements
Please find out for which modules from your Bachelor´s degree you may be able to receive credits from your Bachelor´s degree and where you have to submit the application request for their recognition.
Master’s thesis: From planning to submission
In order to successfully complete a Master’s program at the TUM Department of Mathematics, students must write a scientific thesis: the Master’s thesis. Everything you need to know about the Master’s thesis, from planning to submission, can be found here in overview.
Until further notice the following applies for the registration, extension and submission of the master's thesis:
Registration documents and applications for renewal of the master's thesis (with the consent of the supervisor in electronic form), as well as the final thesis should be submitted in due time as PDF document to master (at) ma.tum.de. The original documents, printed copies of the thesis, USB's/CD's, should be sent by postal mail to the Infopoint.
For questions relating to the content of your Master’s thesis, please contact your thesis supervisor as defined in the General Academic and Examination Regulations (APSO) or the Student Advisory Office responsible.
ATTENTION: Measures due to the Corona pandemic
Until further notice applies for the registration, extension and submission of the Master's thesis:
- Registration and extension: The completed form must be submitted in due time as a pdf or photo/scan (readable) to master (at) ma.tum.de, either by the student (examiner in CC) or by the examiner (student in CC). The signature of the examiner can be provided digitally on the document, or the consent of the examiner is made clear in the attached e-mail correspondence. It is currently not necessary to send the original forms by post.
- Route Card for the Diploma Supplement: please send the completed form as a pdf or photo/scan (readable) to master (at) ma.tum.de.
- Submission of the Thesis: Please submit the Thesis as a pdf file to master (at) ma.tum.de within the deadline. Please send the two identical and signed printed copies of the Thesis, USB's / CDs, by post to the Infopoint Mathematics.
You have six months to complete your Master’s thesis. This period begins on the date of registration. You normally complete the Master’s thesis in the fourth semester of your Master’s program, after you have fulfilled all other academic and exam requirements.
Examiners and assessment
The Master’s thesis must be approved and evaluated by someone who is authorized to do so (thesis supervisor as defined in the APSO) at the TUM Department of Mathematics. You will find an overview of all such persons in the following list:
Registration: When and where?
It is possible to register your Master’s thesis on the 1st and 15th of each month (though not retrospectively). Please submit the registration form signed by your thesis supervisor at the Infopoint Mathematics.
Registration: Which documents?
In addition to the Registration Form, you must also sign and submit the Route Card for the Diploma Supplement of the TUM Department of Mathematics. Please also submit the route card even if no activities are supposed to be incorporated. Please do not forget to provide a German and an English title for your thesis – both will appear on your transcript of records.
Note: The Diploma Supplement is an English-language supplement to the university diploma and describes the qualifications linked to the study program. Under the heading “Additional Information” in this document, you can request the incorporation of specific details of extracurricular activities completed within the framework of your degree course.
The thesis can be written in the German or English language.
Cover page and page 1
Here you indicate the topic of the work as well as your name and that of the supervisor. In addition, you indicate the date of submission.
Here you make the following declaration:
“I hereby declare that this thesis is my own work and that no other sources have been used except those clearly indicated and referenced.” (Place, date, signature)
Change of title
Please write an e-mail containing the new thesis title to master(at)ma.tum.de and copy in your co-supervisor and your supervisor.
The Master’s thesis is to be submitted in bound form (adhesive binding). On the spine of your Master’s thesis, please indicate your first name and surname and the short title of the thesis.
Number of copies
You must submit two identical, signed copies of your Master’s thesis (including all data files that are relevant for the grading of your thesis) at the Infopoint Mathematics or at Ms. Hoffmann's office. We will forward one copy to the thesis supervisor (for grading) and the second copy stays at Ms. Hoffmann's office (to be archived). You do not receive confirmation of submission.
Should the submission date fall on a weekend or a public holiday, submission on the subsequent workday is also possible. Theses can of course also be submitted prior to the planned submission date.
In the event that you need more time to work on your thesis, you must submit an application at the Infopoint Mathematics for an extension, at least seven days prior to the planned submission date. This application must have been signed by your thesis supervisor. In the event of a second extension, the Chair of the Examination Board must sign the application as well as the thesis supervisor.
The typesetting system LaTeX is the standard program worldwide for the compilation of theses that contain mathematical formulas. It is recommended that you familiarize yourself with LaTeX as early as possible during the course of your studies. It is a good exercise to prepare sheets for seminar presentations using LaTeX.
You can find further information, templates and helpful advice on our LaTeX info page.
LaTeX-Vorlagen für die Abschlussarbeit
The TUM Library does not only offer outstanding access to all manner of books, newspapers, and electronic media, it also offers courses on, by way of example, bibliographical research and how to correctly cite works.
Please also note subject-specific practices when citing works.
Further seminar papers and tools specific to mathematics
For licensing and contractual reasons, some of these databases are only accessible via domains belonging to the TUM Departments of Mathematics and/or Informatics. Please address queries where applicable to your supervisor or the TUM Library:
MathSciNet – Mathematical reviews on the web
The English Writing Center offers all TUM members free one-to-one advice on writing English texts and helps you to enhance your writing skills.
You can print your thesis at the computer room. Contact your supervisor to receive a sufficient print quota.