Bachelor Mathematics

Given their wide-ranging abilities, many doors are open to mathematics graduates: in banks and insurance companies for example, they calculate risks or create climate models. In biology, they model molecules, for logistics and airline companies they optimize routes and freight sizes. The foundation for all this is the Bachelor's degree course. Here, students acquire a broad base of knowledge incorporating both methodology and theory, this also being the best possible preparation for one of five Master’s programs at the TUM Department of Mathematics.

Academic content

If you would like to discover the subject’s practical areas of application as well as the foundations of abstract mathematics, the Technical University of Munich (TUM) is the perfect place of study for you. The TUM Department of Mathematics is one of Europe's leading centers for applied and interdisciplinary mathematics. The mathematics degree program not only deals with analysis, algebra, geometry, or probability theory but also confronts the question: where and how is mathematics applied in natural and engineering sciences, in industry, or in other areas? After the fourth semester you can specialize either in abstract mathematics or in any of the main areas of applied mathematics: mathematical finance, mathematical economics, or mathematics in engineering and science, as well as mathematics in data science.


Don't miss

Here you will find important dates, deadlines and other relevant information.

Information event

Information at the beginning of winter semester 2022/2023

At the beginning of the semester there will be information sessions (in German) on topics such as contact persons, study plan, exams, abroad, bachelor thesis and graduation.

  • 1. semester: info session on exams and GOP: 15.12.2022 , 18:00 Uhr in MI HS 3

Slides of the information sessions can be found on the German webpage.



The Department of Mathematics offers preparatory courses for all new students. The pre-course in mathematics will take place from 26th September to 6th October 2022. For Bachelor students with a minor in physics, we also recommend the subsequent additional module. The preliminary courses are voluntary, but they facilitate your entry into your studies and are a good opportunity to get to know your future fellow students. Take advantage of the offer!

calendar: vacation courses

Vacation courses including Introduction to Programming

Following the lecture period, vacation courses will be offered for in-depth study, review and clarification of questions.

The lecture/exercise session toMA0010 Einführung in die Programmierung takes place: 5.10. / 6.10. / 11.10.  / 13.10. (All dates are subject to change).

Study Introduction Days

Study Introduction Days (SET) and L&L

The Student Council Mathematics, Physics, Informatics holds an introductory event at the beginning of each semester for new first-year students, called Study Introduction Days (Studieneinführungstage: SET). On these days, student representatives introduce the campus and give useful tips on studying. We especially recommend that mathematics students who are transferring to TUM from another university take part.

The module Teaching and Learning methods (Lehr- und Lernformen: L&L), which is aimed at all first-year students of mathematics, also takes place in this context.

Registration for examination

Registration for your exam

In order to attend an examination (written or oral exams) you have to register in TUMonline using curricula support. Observe the registration periods:

Repeat examinations: 22.11.2021 - 15.01.2022

Exceptions are possible.

Graduation Ceremony

Graduation Ceremony

The ceremonial farewell of our graduates will take place on 8th July 2022, starting at 16:00. More information, including a possibility to register for the event, is available at Graduation Ceremony. We look forward to your participation!

Consultation hours for Bachelor's Students

Please be aware: From 14.03.2023 until further notice, only the online consultation hour from 13-14:00 takes place with Ms. Kudlich.


On-Campus consultation hours

On-Campus consultation hours: 
Tuesdays, 14:00 - 15:00 at room 00.10.053 (Kathrin Ruf and Heike Kudlich)

Online consultation hours:

Zoom-Video, passcode 882715

  • Tuesdays, 13:00 - 14:00: questions regarding the organization of your studies (Heike Kudlich)
  • Tuesdays, 15:15 - 16:00: other questions regarding your studies (Kathrin Ruf)

Consultation hours on request

If you do not have time for the above listed consultation hours, individual consultation dates can be scheduled (online or on campus) upon request by email to bachelor (at) Please write us some date suggestions to choose from.

Profile: The essentials for the Bachelor’s program


In order to study maths, you first and foremost need enthusiasm for the subject matter and to enjoy diving deeper into the topic. Are you ready for this? A small test: 

  1. Mathematics has always been easy for me at school.
  2. When I look at a mathematical problem, I think about it for as along as it takes to find a solution – even if that means a long time.
  3. I often try out new things, I like thinking laterally and out-of-the-box.
  4. If asked what I particularly enjoyed about mathematics at school, at least two things immediately spring to mind. Tricky tasks in stochastics, for example, or proof of a geometric theorem such as the Pythagorean theorem.
  5. I like working in groups and can integrate well in a learning team.


At least three of the five points apply to you? Then you are well placed for a successful maths degree course. 

Application and admission

All those who are interested are admitted as long as they have

  • an appropriate Higher Education Entrance Qualification (e.g. Abitur) and
  • submit all necessary documents in due form and in good time.

The second item includes the requirement of full participation in the study orientation process.

Study orientation process

Unfortunately, inaccurate perceptions of the requirements and goals of a mathematics degree often cause students to drop out. It is therefore important to us that all those who opt to study at our department have first considered doing so in detail.

Participation means:


Please note the general information on applying for a Bachelor's degree program at TUM.

Any questions?

Then please read the detailed information on the application process and get in touch with us.

Application process: The way to a place on our degree program

Application period

For the winter semester: 15 May to 15 July.

For the summer semester (only for lateral entry from the 2nd semester of enrollment in a current degree program): 15 November to 15 January

Application deadline and extended deadline

The online application must without exception be submitted to the TUM no later than the application deadline and it must be complete. That is, wherever you have been asked to upload a document, you must have uploaded a suitable document.

In general, all further documents that are relevant to the admission process (school-leaving certificate, curriculum vitae, essay, and letter of motivation for the orientation process, as well as verification of language skills etc.) must have reached the TUM no later than the application deadline. An extended deadline of usually two weeks after the application deadline can be granted for these documents in the event that there are valid reasons for doing so. For example, if your school-leaving certificate is first made available to you too late. However, even in this case you must have uploaded an explanatory document at the appropriate place.

Please refer to the more detailed information by the Admissions and Enrollment Office.


In the mathematical essay, you should present a specific mathematical topic of your own choice. You should favor a topic that highlights scientific and conceptual aspects (as opposed to predominantly calculative and practical aspects), and which you could potentially revisit during the program. We would like to get an impression of your understanding of “mathematics” and what sort of questions you expect to explore during your studies.

Below, you will find a list of example topics. Please be creative! Of course, we do not expect anything that goes beyond the material you covered at school. There are no limitations within mathematics; you do not need to ask for permission for any specific topic. The essay is to be written in German.

Bachelor’s program: Example topics for the mathematical essay (in German) 

Letter of Motivation

In the letter of motivation (maximum one page), you should cover why you have opted

  1. for the Bachelor’s program in Mathematics and, in particular,
  2. at the TUM.

More specifically, you should convey your understanding of what a degree in mathematics is about. The following questions may help you:

On the grounds of which abilities, interests, or professional ambitions would you like to pursue a degree in mathematics? Why are you confident that you will be able to understand the scientific content of the degree program and independently handle the abstract questions that arise? Is there further information regarding your background that could be of relevance?

The letter of motivation is also to be written in German, as this is the language of instruction in this program.

Please gather the documents required for your application at the earliest possible opportunity. Most parts of the application process for all degree programs of TUM are done via the platform TUMonline. For this purpose, an applicant’s account is required. See here for more information.

Please note that only one account is created; otherwise, it is not possible for the application to be sent. In principle, you can commence your online application as soon as your grades have been confirmed in full.

You should submit all documents in PDF format.

For questions or queries concerning the VPD certificate (Preliminary Documentation by uni-assist), or the verification of language skills, or the health insurance, please use only the contact details provided on the pages linked below.

ZULASSUNGS­RELEVANTE UNTERLAGEN (Frist: 15. Juli, vgl. Schritt 0)Einreichungsform
Valid higher education entrance qualification (e.g. Abitur certificate)Upload
Curriculum vitae (tabular, current, no gaps up to and including the point in time of your application)Upload
Mathematical essay (see step 1)Upload
Letter of motivation (see step 1)Upload
Uni-assist VPD certificate (where the secondary school certificate was issued abroad)Upload of the VPD certificate (or, if not yet available, of the confirmation form)
Recognized verification of language skills (unless you graduated from a German-language secondary school certificate)Upload
Scan of your passport or German ID cardUpload
Where applicable, further documents (see Glossary of Documents) 

The online application process is explained on the web pages of the TUM Central Administration, with reference to both the German Abitur and international higher education entrance qualifications.

Your application will only be considered if it is complete. It is complete if and only if allnecessary documents (if impossible: a suitable replacement, see step 0) has been uploaded prior to the application deadline.

Since late 2019, any postal submission of documents (hard-copies) is no longer necessary at this stage, but also no longer possible.

Please regularly check your applicant's account at TUMonline. There you will be notified of any missing or irregular documents. All messages will be sent to the e-mail address that you provided when creating your account. This applies to notifications of the completion of the orientation process or the invitation to an orientation interview. If you do not receive a message, please check your spam folder.

Why an orientation interview?

The orientation interview is intended to give both you and ourselves an impression of whether you can be expected to independently and responsibly achieve the aim of the degree program, which is geared towards the fundamentals of science, a focus that is typical of TUM in that it is theoretical and application-oriented in equal measure. 

When and how will I be invited? When does it take place? 

In the event that you are not invited to an interview, you are normally informed by e-mail a few days after we receive your application documents by mail. Close to the deadline, it may take a little longer.

In every case, when completing your online application you are asked to indicate your preferred dates for a possible interview, which we will take into consideration as far as possible. There is no entitlement to a specific date. The date specified is binding and you will be notified of it at least one week in advance. Postponement is only possible on the basis of reasonable grounds, such as due to proven illness. 

All interviews take place between mid-June and mid-September, in the department building in Garching. You should allow at least two to three weeks between your online application and your earliest preferred date.  

What does an orientation interview involve? 

The orientation interview lasts about 20 minutes. It is conducted in the presence of an experienced instructor (a professor or long-term member of the scientific staff) and, in addition, normally a member of the student body for mathematics or a (further) member of the scientific staff. 

In the process, we attempt to find out together whether you display a well-founded basic understanding of mathematics beyond straightforward numeracy skills. The mathematical essay can serve as a key point of reference in this regard. Further, the interview covers ideas, expectations, and aims regarding the mathematics degree program, with particular attention paid to the pleasure you take in tackling abstract and application-oriented questions as well as to potential professional perspectives. It is therefore possible that the interview will complement the letter of motivation.

You will be notified of admission to the degree course in Mathematics by e-mail as soon as the Admissions and Enrollment Office has established that all application documents relevant to your admission have been received in due form and in good time, and we have a record of your full participation in the orientation process.

You must then accept the place on the degree program in your TUMonline-account. If you do not want to accept your place, please decline it; this will assist us with planning the courses offered in the first semester of the degree program.

Having accepted an offer of admission, you must pay the semester fees; how to do so is explained in your TUMonline account. Further, you must by now, at the latest, have provided us with all documents relevant to your enrollment (e.g. health insurance verification). Once both of these matters are dealt with, you are officially enrolled. You can then print out your student record from TUMonline and pick up your student ID a few days later from TUM.

If you have any questions, please contact TUM‘s Hotline and Service Desk. In the event of persistent difficulties that cannot be solved via the Hotline and Service Desk, you can also contact us.

Parallel studies

We expressly advise against enrolling in two different degree programs at the beginning of your studies. One particular reason for this is to be found in the regulations concerning the maximum duration of studies at the TUM.

The Bachelor's Degree in Mathematics at the TUM is a full-time program, which means that we expect an average workload of 40 hours per week. Even for outstanding students, parallel studies mean almost double the workload, since only a small portion of academic content in both degree programs can be recognized.

We therefore strongly recommend that you seek advice from us before embarking upon parallel studies, including about the alternatives to parallel studies. We also recommend just as strongly that you speak to the Student Advisory Office of your second discipline.

Simultaneous enrollment in two degree programs from the beginning is not normally required anyway, because most TUM examinations are open for registration to all TUM students and not only to those on a specific degree program.

If you are already enrolled at TUM and would like to embark on parallel studies, you must send an informal parallel studies application to the Student Service Center - Student Admission. 

Lateral entry

For students of mathematics at another institution of higher education 

If you would like to speak about the compatibility of your accomplishments to date, prior to enrollment, you can contact Dr. Carl-Friedrich Kreiner. You are exempt from the study orientation process. 

Subsequent to your online application, you will find the entry “Confirmation of semesters completed” on your document checklist. However, this confirmation can only be provided once you have provided us with details of all the examination requirements you have fulfilled to date. Once you meet the conditions, please contact Dr. Carl-Friedrich Kreiner. We will then pass the confirmation on directly to the Student Service Center - Student Admission.

For students of a subject other than mathematics

You do not have to observe any special conditions. You should apply for the 1st semester in the degree program. In order to make a successful lateral entry in the summer semester, you must provide proof of having fulfilled the examination requirements of our modules in the first semester (or the equivalent thereof).

If you have successfully completed another degree course and would like to commence a second degree program in Mathematics, it is possible that – after your enrollment – certain requirements that you have already fulfilled can be taken into account. Questions that arise prior to enrollment in this regard can be answered by Dr. Carl-Friedrich Kreiner, for those that arise after enrollment you can contact Heike Kudlich or Dr. Kathrin Ruf.

International applications

My secondary school certificate is not from a German school, what must I take into consideration?

Please consult the central TUM information pages on the Higher Education Entrance Qualification. In most cases you have to request a VPD certificate (Preliminary Documentation by uni-assist), which confirms the equivalency of your secondary school certificate to a German secondary school-leaving certificate. Only graduates of German schools abroad are exempt from having to do so.

The application for the issuance of a VPD certificate on uni-assist must also be placed by 15 July

In the event that, in spite of submitting certificates to uni-assist in good time, problems arise relating to the application deadline, please contact bsc-app (at)

I am to receive my certificate after 15 July, what should I do?

With regard to a deadline extension in the event that the certificate cannot be delivered prior to this deadline, please contact Uni-assist and the Service Desk at the Student Service Center - Student Admission.

Do I need verification of language skills?

If the language of instruction at your school was not German, you probably have to provide verification of language skills showing sufficient German language skills. According to the Ministry, this also applies even if your mother tongue is German and you have German citizenship.

My mother tongue is not German, what must I take into consideration? 

If you have a secondary school-leaving certificate from a German-language school, you do not have to observe any special conditions.

If you do not have a secondary school-leaving certificate from a German-language school, then you must provide a verification of language skills. The list of language certificates recognized for this purpose can be found here.

Documents and records

Information on the documents that you require for an application to TUM.


In order to ease your admission to a degree program at TUM, you will find short explanations of key words concerning our studies at TUM.

Grundlagen- und Orien­tierungs­prüfung (GOP)

The Grundlagen- und Orientierungsprüfung (fundamentals and orientation exam) is obligatory for all students starting the bachelor's program Mathematics as from the winter semester 2019/20.

With the Grundlagen- und Orientierungsprüfung (GOP) students have the opportunity to attain basic knowledge of the diverse subject content of the Bachelor program and therefore to orientate themselves for their further studies in mathematics. The course gives students in their first year of study a realistic insight into the demands of mathematical studies. By passing the exam, students demonstrate that they have mastered the essential mathematics foundations, which are prerequisite for the continuation of their mathematical studies. The GOP is also an excellent indicator of the success of each individual's studies. Those students who do not pass the GOP must withdraw from the program. 

The GOP comprises

  • the four foundation modules (written exams):
    MA0001 Analysis 1, MA0004 Linear Algebra 1, MA0002 Analysis 2 and MA0005 Linear Algebra 2 and Discrete Structures and
  • the module MA0007 Foundations in Mathematics (oral exam).

By the end of the second semester, all students must have passed at least two of the four written exam modules, as well as the oral exam "Foundations in Mathematics". For each exam, you have two chances to attain a pass. The two remaining written exams must be passed during the further study program. Not attending the exam without good, documented reasons will count as if you have attended the exam and failed.

Tips on creating your timetable

The timetables at TUMonline, as well as the academic content for each semester are only suggestions. Depending on your personal study situation, you should therefore adapt these suggestions to your individual needs, particularly after a change in degree program, in the event of falling behind in terms of academic progress, a scheduled stay abroad etc.

Please note the following information

  • Mathematics teaching sessions for the Bachelor's program have priority over other subjects.
  • Within the mathematics program: first Required Modules, then Courses in Abstract Mathematics and Courses in Applied Mathematics, then Advanced Courses, Extradisciplinary Courses and further teaching sessions.
  • Please note the prerequisites for each module. You will find these in the TUM Department’s Module Catalog (linked to via each module in your Curriculum).
  • Unfulfilled requirements from previous semesters of enrollment in your current degree program? Are these necessary for successfully completing your Bachelor’s program in Mathematics? Then these have priority.
  • Long-term planning over several semesters makes sense, especially if you envisage a stay abroad or an extended professional internship.
  • Additional teaching sessions can still enhance your profile, even if they cannot contribute to your degree according to the Academic and Examination Regulations. However, do not neglect your Bachelor's program in Mathematics as a result.
  • If you want to choose between modules visiting lectures and exercise courses of these modules in the first two weeks might help you. Take care of your workload. (Benchmark: 30 credits per semester).

Am I doing the right thing?

If in doubt, Kathrin Ruf will be happy to go through your timetable with you.

Modifications in offered modules

In winter semester 2019/20 a new version of our bachelor's program in Mathematics is starting. This leads to modifications in offered modules. These modifications also affect students who started their studies in bachelor Mathematics at TUM until winter semester 2018/19.

Some modules will no longer be offered, others are going to be offered in a different semester. Please pay attention to the information on the German version of this webpage and in the modules descriptions.


Here you can find the current modules available in the standard minors subjects. Further modules will not be added. Depending on your personal study situation, the semester in which you attend a module can vary. For your orientation we have listed some recommendations, as well as the requirements for the modules. A guarantee, that study courses and examinations do not collide can only be given when you take the module in the recommended semester. From your minor subject you must attain between 18 and 27 credits, which count towards your study program achievements. 

Repeat exams will usually take place in the subsequent semester.

Winter semester

Summer semester

Winter semester

Summer semester

For the master's program "Mathematics in Data Science", alongside mathematical competencies,  fundamental knowledge in informatics is also required . You can fully prove your informatics competencies by passing three out of the five modules IN0001, IN0007, IN0008, IN0009, IN0010.

Winter semester

Summer semester

For the master's program "Mathematics in Data Science", alongside mathematical competencies,  fundamental knowledge in informatics is also required . You can fully prove your informatics competencies by passing three out of the five modules IN0001, IN0007, IN0008, IN0009, IN0010.


For students with minor in Computer Science the module "Introduction to Programming" MA0010 is not mandatory.

Winter semester

Summer semester

Repeat exams will usually take place in the subsequent semester.

Winter semester

Summer semester

Repeat exams will usually take place in the subsequent semester.


Winter semester

Summer semester

Scenes of the scientific minor fields electrical engineering, informatics, physics and ecomonics

Bachelor’s Thesis: From planning to submission

In order to successfully complete a Bachelor's degree program at the TUM Department of Mathematics, students must write a scientific work: the Bachelor’s thesis. Here, you will find an overview of everything you need to know about the Bachelor’s thesis, from planning to submission.

Thesis-related questions?

For questions relating to the scientific content of your Bachelor’s thesis, please contact your thesis supervisor or co-supervisor.

When to start

Do you have at least 8 credits in Advanced Courses? Then it is the right moment to commence your Bachelor’s thesis. By the eighth semester of enrollment in your current degree program, at the latest, you must commence your thesis as long as there are no reasonable grounds preventing you from doing so in accordance with section 10 (6) of the APSO.

Time frame

You have three months in which to complete your Bachelor’s thesis. This period begins on the date of registration.
During this period, you should spend an average of at least 30 hours per week on the Bachelor's thesis; an effort equivalent to 12 credits.

Choice of topic

In order to reduce the time needed to familiarize yourself with the topic, it is recommended to choose a topic for your Bachelor's thesis which corresponds to the theme of the Advanced Seminar taken.

Examiner and assessment

The Bachelor’s thesis must be 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 list below. It is the written work that is assessed. The talk you give concerning the content does not affect the grading.

Persons authorized to examine theses (MA)

Registration: When and where?

It is possible to register your Bachelor’s thesis on the 1st and 15th of each month. 

The completed registration form must be submitted in due time as a pdf or photo/scan (readable) to bachelor (at), 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) together with the registration of the thesis to bachelor (at)

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. 
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.

Contact: Please submit your documents for registration to bachelor (at)


The Bachelor’s thesis should not exceed 35 sides.

Language and abstract

The work can be written in the German and English language. It must be prefaced by an abstract in the other language, not the one in which it is written.

Formal considerations

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.

Page 2

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 either on a tablet or as a scan of your original signature). If you do not wish to use a digital signature, you may alternatively submit a separate page with the declaration and your original signature at the Infopoint.

Changing the title

Please write an e-mail containing the new thesis title to bachelor (at) and copy in your co-supervisor and supervisor.

Digital submission

The Bachelor's thesis has to be submitted digitally. Please submit the thesis as a pdf file to bachelor (at) within the deadline. If you have to hand in code or other files, please e-mail all files collected in a zip folder. Printed copies and USB sticks will no longer be accepted.  


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 to bachelor (at) for an extension, at least seven days prior to the planned submission date. This application must have been signed by your thesis supervisor (or you have to send the consent of the supervisor in electronic form). In the event of a second extension, the Chair of the Examination Board must sign the application as well as the thesis supervisor.

Application for an extension, Bachelor’s thesis (pdf)


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.

Thesis Templates for LaTeX

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

English theses

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.

Current news from our Department