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.
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Here you will find important dates, deadlines and other relevant information.
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.
Pre-courses
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!
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 (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 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
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) ma.tum.de. Please write us some date suggestions to choose from.
Profile: The essentials for the Bachelor’s program
Conditions of study
The Bachelor's degree course in Mathematics at TUM is a full-time program. The teaching language is German. Students have to pass the Grundlagen- und Orientierungsprüfung (GOP) within the first year of the program. The standard duration of study is six semesters. A dual study program together with a position in business is not possible.
Commencing the degree program
The Bachelor's program in Mathematics begins in the winter semester. If you would like to switch from another university to TUM, it is possible to do so in both the winter and the summer semesters.
Small groups
The material from the lectures is revised, supplemented, and elaborated upon in small learning groups of around 15 students depending on demand and interest amongst participants.
Commencing your studies
You commence your program in Mathematics with introductory courses in "Analysis" as well as "Linear Algebra and Discrete Structures." In the process, you acquire fundamental knowledge of methodology and theory. These topics provide the basis for all further mathematical modules in the program.
Minor
Beginning in the first semester, you will cover one of the following minors: Electrical Engineering, Computer Science, Physics, or Economics. Upon registering for the examination, you commit to your minor. In exceptional circumstances, the Examination Board for Mathematics can approve a special minor at TUM: We are happy to advise you.
Elective studies
Beginning in the third semester, you will cover elective modules from the comprehensive areas of abstract and applied mathematics. In the third academic year you specialize by choosing a specialty in the area of Abstract Mathematics, Mathematical Finance, Management and Mathematics, Mathematics in Science and Engineering, or Data Analysis.
Academic content
Suggestions as to when you should choose which modules can be found in our overview, which is divided into semesters and also gives consideration to the choice of specialty in the previous academic year. Please note the prerequisites in the moduls descriptions.
Timetable
In TUMonline you can create your own individual timetable, which you can save digitally. Please note our tips on creating your timetable. Examples of timetables can be found here and on the German website.
Seminars
In the second semester, you hold a short presentation in one of the Workshops and, in this way, learn to communicate mathematics to others. In the final year, you complete the Seminar. When making your selection here, please keep in mind that the topic frequently feeds directly into your Bachelor’s thesis.
Professional internship
A four-week professional internship is integrated into the program. The accompanying Internship Seminar offers you the opportunity to inform yourself about suitable occupations and to discuss the experiences made during the professional internship. You can also use the Careers Service.
Intradisciplinary competence
You can round off your personal competence profile by choosing modules from the field of intradisciplinary competencies. Related to your personal interests, you can choose modules from a wide range of soft skills or language courses on offer.
Abroad
During your Bachelor's program, you can spend one to two semesters abroad at one of TUM's partner universities. In this case, the recognition of modules completed abroad is often possible. As with everything to do with the semester abroad: do inform yourself in good time!
Bachelor's thesis
The area in which you acquire advanced knowledge during the degree course helps to make your choice of topic for your Bachelor’s thesis. This is often based on the topic of the Advanced Seminar. Read everything you need to know about the Bachelor’s thesis here.
Degree and graduation certificate
You have fulfilled all the requirements? Congratulations! Please confirm with us which achievements should appear on your Bachelor's certificate. Please note: the date of completion for the degree program is the date of the last examination.
Bachelor – and then?
Once you have received your Bachelor's degree then, regardless of your chosen specialty, you are very well-prepared for one of the five mathematical Master’s programs at TUM. Direct entry into professional life is also an option. Come and take our congratulations at the Graduation Ceremony.
Academic and examination regulations
Please note the general information concerning examinations. Here you will also find all examination rules and regulations. Here you can read the current readable version of the Examination and Academic Regulations (in German):
Prerequisites
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:
- Mathematics has always been easy for me at school.
- 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.
- I often try out new things, I like thinking laterally and out-of-the-box.
- 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.
- I like working in groups and can integrate well in a learning team.
Suitable?
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:
- submitting a mathematical essay (approximately one page in length) with the online application,
- submitting a letter of motivation (no more than one page) with the online application,
- in the event that we invite you to it, a personal orientation interview.
Important!
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.
Essay
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
- for the Bachelor’s program in Mathematics and, in particular,
- 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 card | Upload |
| 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) ma.tum.de.
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.
APSO, FPSO, and ECTS?
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.
Minor
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.
Winter semester
- WI001056_1 – Principles of Economics in English, 6 Credits
Recommendation: 1st Semester - WI000729 – Foundations of Business Administration 2, 3 Credits
Recommendation: 1st Semester - WI000219 – Investment and Financial Management, 6 Credits
Recommendation: 5th Semester - WI000275_E – Management Science in English, 6 Credits
Recommendation: 5th Semester - WI000231 – Asset Management in English, 6 Credits
Recommendation: 5th Semester
Required: Knowledge in statistics - WI001059_E – Financial Accounting in Englisch, 6 Credits
Overlapping is possible
Summer semester
- WI001132 – Cost Accounting, 6 Credits
Recommendation: 2nd Semester
Remark: Online course
If you want to attend lectures in person please note the dates of course WI001057. - WI000728 – Foundation of Business Administration 1, 3 Credits
Recommendation: 2nd Semester - WI000820 – Marketing and Innovation Management, 6 Credits
Recommendation: 4th Semester - WI001060 – Production and Logistics, 6 Credits
Overlapping is possible
Winter semester
- PH0001 – Experimental Physics 1, 9 Credits
Recommendation: 1st Semester - PH0003 – Experimental Physics 3, 9 Credits
Recommendation: 5th Semester
Required: PH0001, PH0002 - PH0006 – Theoretical Physics 2 (Elektrodynamics), 9 Credits
Recommendation: 5th Semester
Required: PH0001, PH0002, PH0005
Summer semester
- PH0002 – Experimental Physics 2, 9 Credits
Recommendation: 2nd Semester
Required: PH0001 - PH0005 – Theoretical Physics 1 (Mechanics), 9 Credits
Recommendation: 4th Semester
Required: PH0001 - PH0007 – Theoretical Physics 3 (Quantum mechanics), 9 Credits
Recommendation: 6th Semester
Required: PH0001, PH0002, PH0005, PH0006
Winter semester
- IN0008 – Fundamentals of Databases, 6 Credits
Recommendation:
– 1st Semester (Begin of studies in winter semester 2018/19)
– 3rd Semester (Begin of studies winter semester 2017/18 at the latest) - IN0001 – Introduction to Informatics, 6 Credits
Recommendation:
– 1st Semester (Begin of studies winter semester 2017/18 at the latest)
– 3rd Semester (Begin of studies in winter semester 2018/19)
Should be attended together with IN0002. - IN0002 – Fundamentals of Programming (Exercises & Laboratory), 6 Credits
Recommendation:
– 1st Semester (Begin of studies winter semester 2017/18 at the latest)
– 3rd Semester (Begin of studies in winter semester 2018/19)
Should be attended together with IN0001. - IN0009 – Basic Principles: Operating Systems and System Software, 5 Credits
Recommendation: 5th Semester
Required: IN0001, IN0004 - IN0004 – Introduction to Computer Organization and Technology - Computer Architecture, 8 Credits
Overlapping is possible
Summer semester
- IN0007 – Fundamentals of Algorithms and Data Structure, 6 Credits
Recommendation: 2nd Semester
Required: Very good programming knowledge - IN0011 – Introduction to Theory of Computation, 8 Credits
Recommendation:
– 2nd Semester (Begin of studies in winter semester 2018/19)
– 4th Semester (Begin of studies winter semester 2017/18 at the latest)
Required: Basic programming knowledge - IN0006 – Introduction to Software Engineering, 6 Credits
Recommendation:
– 2nd Semester (Begin of studies winter semester 2017/18 at the latest)
– 4th Semester (Begin of studies in winter semester 2018/19)
Required: IN0002 - IN0003 – Functional Programming and Verification, 5 Credits
Recommendation: 4th Semester
Required: IN0001 - IN0010 – Fundamentals of Databases, 6 Credits
Recommendation: 4th Semester
Required: IN0001, IN0002, recommended IN0003
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.
Mandatory
- IN0001 – Introduction to Informatics, 6 Credits
Recommendation: 3rd Semester (or 1st Semester)
Should be attended together with IN0002. - IN0002 – Fundamentals of Programming (Exercises & Laboratory), 6 Credits
Recommendation: 3rd Semester (or 1st Semester)
Should be attended together with IN0001.
For students with minor in Computer Science the module "Introduction to Programming" MA0010 is not mandatory.
Winter semester
- IN0008 – Fundamentals of Databases, 6 Credits
Recommendation: 1st Semester - IN0009 – Basic Principles: Operating Systems and System Software, 5 Credits
Recommendation: 5th Semester
Required: IN0001, IN0004 - IN0004 – Introduction to Computer Organization and Technology - Computer Architecture, 8 Credits
Overlapping is possible
Summer semester
- IN0011 – Introduction to Theory of Computation, 8 Credits
Recommendation: 2nd Semester
Required: Basic programming knowledge - IN0007 – Fundamentals of Algorithms and Data Structure, 6 Credits
Recommendation: 2nd Semester
Required: Very good programming knowledge - IN0003 – Functional Programming and Verification, 5 Credits
Recommendation: 4th Semester - IN0006 – Introduction to Software Engineering, 6 Credits
Recommendation: 4th Semester
Required: IN0002 - IN0010 – Fundamentals of Databases, 6 Credits
Recommendation: 4th Semester
Required: IN0001, IN0002, recommended IN0003
- Mandatory: EI0901 – Engineering Practice for Mathematicians, 10 Credits
Recommendation: 5th - 6th Semester
Graded essay and presentation
Further information and links can be found on the corresponding webpage.
Combining the practical part with the internship of the module "Professional Internship" might be possible (longer internship). Please ask Kathrin Ruf.
Winter semester
- EI29821 – Principles of Information Engineering, 5 Credits
Recommendation: 1st Semester - EI0625 – Communication Networks, 5 Credits
Recommendation: 3rd Semester
Summer semester
- EI5356 – Measurement Systems and Sensor Technology for Mathematicians, 6 Credits
Recommendation: 2nd Semester - EI4692 – Introduction to Signal Processing for MA, 5 Credits
Recommendation: 4th Semester
Requried: Elementary knowledge in probability theory - EI0308 – Communications Systems 1, 5 Credits
Recommendation: 4th Semester
Required: Basic knowledge in probability theory and statistics - EI5183 – Control Theory (MSE) in English, 4 Credits
Recommendation: 4th Semester
Required: Basic knowledge in ordinary differential equations
Repeat exams will usually take place in the subsequent semester.
Mandatory
- EI29821 – Principles of Information Engineering, 5 Credits
Recommendation: 1st Semester - EI5356 – Measurement Systems and Sensor Technology for Mathematicians, 6 Credits
Recommendation: 2nd Semester - EI09011 – Engineering Practice for Mathematicians, 6 Credits
Recommendation: 4th - 6th Semester
Graded essay and presentation
Further information and links can be found on the corresponding webpage.
It is recommended to combine the practical part with the internship of the module "Professional Internship" by doing a longer internship after prior consultation.
Winter semester
- EI0625 – Communication Networks, 5 Credits
Recommendation: 5th Semester
Summer semester
- EI4692 – Introduction to Signal Processing for MA, 5 Credits
Recommendation: 4th Semester
Requried: Elementary knowledge in probability theory - EI00440 – Communications Systems, 5 Credits
Recommendation: 4th Semester
Required: Basic knowledge in probability theory and statistics - EI5183 – Control Theory (MSE) in English, 4 Credits
Recommendation: 4th Semester
Required: Basic knowledge in ordinary differential equations
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.
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) 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) together with the registration of the thesis to bachelor (at) ma.tum.de.
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) ma.tum.de.
Length
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) ma.tum.de 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) ma.tum.de 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.
Date
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.
Extension
In the event that you need more time to work on your thesis, you must submit an application to bachelor (at) ma.tum.de 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.
LaTeX
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.
Logos
Corporate design and use of TUM and TUM Department of Mathematics logos.
Thesis Templates for LaTeX
LaTeX-Vorlagen für die Abschlussarbeit
Literature
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
- JADE – Journal Articles Database
- ERAM – Electronic Research Archive for Mathematics
- Online database at Zentralblatt MATH
- Mathematics Education Database
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.
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