Computational Science and Engineering
Master of Science (M.Sc.)
Computational Science and Engineering (CSE) is a rapidly developing field that brings together applied mathematics (especially numerical analysis), computer science, and scientific or engineering applications. CSE focuses on developing problem-solving methodologies and robust tools for numerical simulation. To understand phenomena and processes in science and engineering, we no longer have to rely solely on theories and experiments, but can also use computations. Numerical simulations can complement experiments and can even enable the study of systems and problems that would be too time-consuming, too expensive, or too dangerous (if possible at all) using experiments alone.
The high level of detail and realism of these simulations requires advanced skills in mathematical modeling, numerical analysis, efficient algorithms, computer architecture, software design and implementation, as well as validation and visualization of results. This program equips engineering, science, or mathematics graduates with the skills needed for a successful professional or academic career in CSE.
For more details:
- The talk on "Computational Science Education at the Technical University of Munich" by the CSE program director Prof. Hans-Joachim Bungartz (from 2016) provides a broader perspective on the CSE study program.
- The TED talk about Computational Science and Engineering by Karen Willcox (from 2022) provides a more up-to-date view.
Type of Study: Full-time
Standard Duration of Studies: 4 Semesters
Credits: 120 ECTS
Main Locations: Garching
Start of Degree Program: Winter Semester
Language of Instruction: English
Costs: semester fee, no tuition fees
Professional Profile: Informatics
The Master’s program in Computational Science and Engineering is a multidisciplinary program where the first three semesters focus on lectures, tutorials, and seminars, and the fourth semester is reserved for the Master's thesis.
The program covers a wide range of subjects and research areas, including numerical analysis, computer science, scientific computing and various applications such as computational physics, computational fluid dynamics, visualization, and many more. To ensure a broad range of topics as well as excellent expertise in each area, the CSE program is offered in cooperation with several TUM departments across three TUM schools (CIT, NAT, and ED).
All mandatory modules of the program are taught in English, but some modules within the application areas may be offered bilingually (German lectures and English course material, or vice versa) or be conducted in German, which would allow a broader choice of application areas.
With the degree in M.Sc. in Computational Science and Engineering, you will have a comprehensive portfolio of skills in computer science, numerical analysis, scientific computing, and their relevant applications, methods, and techniques.
The Computer Science curriculum includes the core subjects Advanced Programming and Parallel Programming, as well as a choice between Computer Architecture and Networks, Basic Algorithms, Scientific Visualization, and Patterns in Software Engineering.
In Numerical Analysis, the focus is on Numerical Programming and Numerical Algorithms for High Performance Computing.
In addition, you will have acquired both theoretical and practical skills in scientific computing and will be able to apply your theoretical knowledge to current research questions in your individual area of focus.
Graduates of the Master's program in Computational Science and Engineering can look forward to inspiring careers in this important and dynamic field. Computational Science and Engineering is an emerging discipline that spans all the fields from which it evolved – applied mathematics, engineering and science applications, high-performance computing, and many more. Consequently, the employment opportunities and career paths available to graduates of the program are diverse, constantly exploring new areas of application, and typically characterized by a high degree of interdisciplinarity.
Thanks to their computational skills, advanced programming skills, and understanding of sophisticated models and algorithms, graduates in Computational Science and Engineering are in demand to solve large-scale problems that were once considered unsolvable.
Application and Admission
The program is open to students with a bachelor's or master's degree in a science or engineering discipline as well as applied mathematics and, in some cases, computer science.
Please note that CSE is not a computer science program, and students who wish to pursue such a program are not encouraged to apply to CSE. If you are interested in computer science or computer engineering, the Informatics Master's program is for you. The same is true if your primary interest is Robotics or Machine Learning, as these other programs would likely be a better fit for you.
If you have a degree in a computer-related or mathematical discipline, you will need to demonstrate sufficient expertise in an engineering or science subject. This can be accomplished, for example, by completing an appropriate minor.
In addition, you will have to demonstrate the following skills
- A solid understanding of mathematics at an advanced level (see "Solid basic knowledge of mathematics" below).
- Knowledge of a modern programming language, e.g. C++, Java, Python, Fortran (see "Solid basic programming skills" below)
- Very good English language skills (see here)
The aptitude test assessment the M.Sc. Computational Science and Engineering is a two-stage process in which we assess your qualifications with regard to the special qualitative requirements of this Master's program. Depending on the results of the first stage, you may be accepted directly, rejected directly, or invited to a telephone interview for the second stage of the selection process.
Winter semester: 1 January – 31 May 2023
Note: International applicants are advised to apply early (e.g. by 31 March 2023) to avoid delays in visa procedures and other formal processes. You can still apply by the usual deadline, but risk missing introductory events (if further steps take longer).
You have to apply for the Master's degree via TUMonline. After you have created your account in TUMonline, please enter the requested personal data and information about your education, and upload the required documents. The application is completely electronic.
Prospective students with a Bachelor's degree from outside the European Union have to request a preliminary examination documentation from uni-assist (VPD) in advance.
Only in case of admission you will have to submit some additional documents as certified copies for enrollment.
Application for a Master's program - step by step
The following documents have to be submitted for the application (the required documents may vary depending on the applicant):
- A personal statement (letter of motivation) explaining why you have chosen this particular Master’s program and TUM specifically. Please use this form.
- Two letters of recommendation. Please use this form.
- Analysis of Curriculum. Please use this form.
- Your CV/résumé (Europass and other formats are accepted)
- Bachelor's degree certificate, including a list of courses and grades OR an official transcript of records. Documents not issued in German or English must be translated and notarized by a sworn translator.
- Proof of your English language proficiency
- GRE or Gate score for applicants with a B.Sc. degree from Bangladesh, China, India, Iran, Pakistan (original scorecard or have the score transmitted directly via ETS)
- Preliminary documentation from uni-assist for all applicants with a Bachelor's degree from outside the EU/EEA
- APS certificate for applicants with a Bachelor's from China, Vietnam or India
- A passport photo
- A copy of your passport
Optional admission documents:
The following documents are not mandatory but help us to get a better impression of the applicant:
- A statement certified by your university to confirm your ranking on your former program, e.g. 3rd best student in a class of 50 graduates
- Certificates from professional training or additional qualifications related to the program (e.g. participation in research competitions, internships, etc.)
- Description of the grading system of your former university
- Certified copy of university entrance qualification
Attention: If you did not obtain your Bachelor's degree in a country within the EU/EEA, you have to upload a preliminary documentation from uni-assist (VPD). In order to get the VPD, you must send the required documents (some as notarized copies!) to uni-assist via post! Uni-assist still needs the documents in paper. As the issuance of the VPD can take up to 4 weeks, we highly recommend sending the necessary documents to uni-assist very early. More information on Preliminary Documentation (VPD) by uni-assist.
Also, candidates from specific countries are subject to additional requirements (as indicated above). For more information, check this page.
Please do check the requirements for Notarization, especially for translations!
Special requirements for documents apply for certain countries.
The admissions office checks whether your uploaded documents are complete and correct. If this is the case, the department can view your application and forward it to the admissions committee. The admissions committee decides whether your application will be admitted, rejected or forwarded to the second stage of the aptitude assessment.
For your convenience, a checklist of all documents which are required to apply for CSE can be found here. Please use it, and do not forget any mandatory documents, because this hinders the processing of your application (i.e., it will not be forwarded to the admission committee until complete).
We have also created a detailed application guide which should answer the most common questions. The guide can be downloaded here. Please read it carefully.
NOTE: All fields in the forms provided are digitally fillable, except for the signature fields. If the fields do not display properly or behave unexpectedly (values disappear or are duplicated), please download the file again using a different browser: Firefox is known to work, while there are problems with Chromium-based browsers.
If you have any trouble, please check our FAQs.
Preliminary documentation from uni-assist (VPD)
Applicants who have not acquired their qualification for postgraduate studies (usually Bachelor) in a country within the EU/EEA must apply for a preliminary documentation (VPD) at uni-assist, in addition to the TUM application.
Which documents have to be submitted to uni-assist?
- Completed application form for VPD (see Downloads)
- a copy of your degree certificate (if available)
- a copy of your Transcript of Records
- a translation, if the original documents are not in German or English
- if required: Certificate of the German Academic Evaluation Center (APS)
You do not have to submit an complete application for a specific program to uni-assist, you only have to apply for the general preliminary documentation (VPD).
An application for a VPD via uni-assist alone does not qualify as an application for a degree program at TUM.
GRE and GATE
Applicants with a Degree from Bangladesh, China, India, Iran or Pakistan have to submit a GRE (General) Test. We have defined required minimum scores, lower scores will not be accepted.
The required scores are:
- Verbal reasoning: (will not be taken into account anymore)
- Numerical reasoning: 164 (effective 1 September 2022)
- Analytical writing: 4.0 (effective 1 September 2022)
Institution Code: 7806, Department: 5199 ("all other departments").
For Applicants from India:
As an applicant from India, you can submit a scorecard of the Indian GATE test (in an engineering field!) as an alternative if you are not from an IIT. The minimum qualifying score for the relevant year is required. Students from an IIT can directly upload their transcript in the application portal instead of GRE or GATE.
Certificate from the German Evaluation Center (Akademischen Prüfstelle, APS)
Applicants with an undergraduate degree from China, India and Vietnam have to submit a certificate from the German Evaluation Center (APS).
The program is open to students who have earned a Bachelor's or Master's degree in one of the following disciplines:
- Engineering (e.g. mechanical, civil, electrical, etc.)
- Science (e.g. physics, biology, chemistry, etc.)
- Informatics / computer science (be aware that CSE is not Computer Science, M.Sc. Informatics)
- Applied mathematics
- an equivalent subject
If you have a degree in a computer-related or mathematical discipline, you must demonstrate sufficient knowledge in an engineering or science subject. This can be done, for example, by taking the appropriate subject as a minor.
In addition, you will need to prove you have the following skills:
Solid basic knowledge in mathematics
Solid basic knowledge in mathematics is indispensable for participation in the CSE Master's program. You should be able to demonstrate good knowledge in the topics taught in the mathematics courses of a German Bachelor in Engineering, i.e. linear algebra and integral and vector calculus, in the best case also numerics and stochastics. Please have a look at the bachelor programs at TUM and the corresponding number of ECTS in mathematical subjects:
- Mechanical Engineering has 19 ECTS in math-related subjects + electives.
- Engineering Science has 27 ECTS in math-related subjects+ electives.
- Electrical Engineering has 32 ECTS in math-related subjects+ electives.
If your profile is different, this does not mean that you cannot apply for CSE. However, please make sure that your math background is in the range of the programs listed above.
Solid basic programming skills
Besides the solid basic knowledge in mathematics, skills in a modern (object-oriented) programming language (e.g., C++, Java, Python, Fortran, Julia, Rust, etc.) are needed. They can be demonstrated by courses taken as part of a previous degree program, by additional certificates, or by work experience indicated in the curriculum vitae.
Timetable and Deadlines
Online application and submission of required documents
For the winter semester:
January 1 – March 31, 2023: recommended application deadline for applicants who need a visa
January 1 – May 31, 2023: compulsory application deadline
No submission of missing application documents after the official application deadline will be accepted!
Time frame for interviews: April – September
Start of program (lecture period)
Winter semester: October 2023
Check here for exact dates.
During your Studies
All important information for the start of the program will be covered in the Informatics-wide orientation program.
For the successful completion of the Master's program in Computational Science and Engineering, 120 credits are required:
- Lectures, exercises, and practical courses from required and elective modules (90 Credits)
- Master's Thesis (30 Credits)
Detailed information can be found below. For more information, see Degree Program Contents.
- Computer Science, required (Section A): 10 Credits
- Scientific Computing (Section C): 31 Credits
This includes a seminar (5 ECTS) and a practical course (10 ECTS) which can be chosen according to your interests.
To complete the CSE program, you must attend 49 ECTS of elective courses. The area of elective modules is split into 4 parts:
- Computer science – electives (section A)
- Applied mathematics (section B)
- Application areas of CSE (section D). This section is further split into 6 different catalogs
- Other electives (section E)
A minimum number of ECTS must be obtained from each of the first three sections: 10 for Computer Science, 16 for Applied Mathematics, and 8 from a single catalog in section D. The remaining (up to 15) ECTS can be covered by elective modules from any section or catalog.
Thus, the above can be summarized as follows:
You must earn a total of at least 49 ECTS from elective modules, subject to the following rules.
- You must earn at least 10 ECTS from the section A electives.
- You must earn at least 16 ECTS from the section B electives.
- You must earn at least 8 ECTS from one D catalog.
- Remaining ECTS (up to 15) can be earned from any section or catalog.
The advanced practical course (lab) is a mandatory module in which CSE students choose a practical lab course with a topic suitable for CSE. Students then usually work in groups on a larger project. Such a lab course has 10 ECTS and provides a large amount of practical and social skills.
Registration for practical courses typically follows the matching process. Read more about this under "Course registration".
The Seminar Scientific Computing is a special type of module, different from usual lectures or lab courses: It involves studying a selected topic with the individual guide of a TUM researcher. Students are then usually asked to write a scientific report and give a talk for the rest of the seminar participants. The grade is often determined by both the report and the talk.
Registration for seminar courses typically follows the matching process. Read more about this under "Course registration"
The Bavarian Graduate School of Computational Engineering (BGCE) is an association of three master’s programs:
- Computational Science and Engineering (CSE, i.e., this program; taught at TUM)
- Computational Mechanics (COME, taught at TUM)
- Computational Engineering (CE) (at University Erlangen-Nuremberg)
The BGCE Honors Track, an elite program within the Bavarian Elite Network, offers additional courses to the most capable and dedicated students in each of the partner's degree programs. The Honors Track program aims to enhance both the academic training and personal skills of the selected students. The additional effort, in addition to outstanding performance in the regular master's program, is rewarded with excellent networking opportunities and the designation "with honors," a hallmark of academic excellence.
The following documents contain the regulations for obtaining the "Master of Science" with honors degree:
- The examination regulations from 2019 apply to students who started the Honor's Program in 2019 or later.
- The examination regulations from 2016 apply to students who started the Honor's Program in 2017 or later.
- The examination regulations from 2012 apply to students who started the Honor's Program in 2013 or later.
- The examination regulations from 2005 apply to students who started the Honor's Program in 2012 or earlier.
For more details on the honors program and its curriculum, please see the program website.
Detailed information can be found under Examinations.
The following regulations apply to all students:
- The General Examination and Study Regulations of TUM (Allgemeine Prüfungs- und Studienordnung, APSO - latest version from Aug. 04, 2022)
- The program-specific Academic and Examination Regulations (Fachprüfungs- und Studienordnung, FPSO - latest version from Sept. 09, 2021)
The applicable version will depend on when you started:
Please note that the German versions of each set of regulations are the official documents; only the German text is legally binding. Where available, English translations of the regulations are provided for your convenience.
For the full list of examination regulations, please check Statutes & Regulations on tum.de.
It is possible to transfer credits from your previous studies (or from an exchange program) to your CSE degree plan. Recognition is regulated by APSO §16. There are three types of recognition:
- Recognition of examinations taken at a higher education institution abroad, e.g. from your previous studies.
- Recognition of examinations taken during a stay abroad during your CSE studies.
- Consecutive recognition of examinations taken during a Bachelor's or Master's program at TUM.
The following information holds true for the first type of recognition. If you want to transfer examination results according to point two or three, please see below.
Regulations for recognition (from previous studies)
It is only possible to apply for a recognition during the first year of your CSE studies.
Documents for recognition
To obtain a recognition, you should submit the following four documents:
- The application form for recognition. Please complete it and sign it.
- Detailed descriptions for the content of each examination from your previous degree program (ideally, an official course syllabus).
- A Transcript of Records verifying that you have successfully taken the exam and listing the grade you received in the exam.
- A grading table specifying the maximum possible grade and the minimum passing grade for the course. This will be used to transfer your grade into the German grading system.
In the application form, please specify which CSE modules you would like to get recognized. You should also indicate which previous examination results you would like to be considered. It is possible to combine several previous examinations to fulfill the requirements of one CSE module. It is also possible to apply for more than just one module recognition. Please submit a form for each CSE module you wish to obtain recognition for.
The most important documents are the descriptions of the examinations from your previous studies. These should be as detailed possible to ensure that the contents of the examinations (lecture, exercise, seminar, practical course, etc.) cover all the contents of the CSE module. If your former university does not provide such a document, you will have to write the description yourself. You should sign the document to confirm that the description is accurate. The more detailed the description is, the greater the chances that it will be approved.
To prove that you actually passed the examination you want to get recognized for CSE, you must provide a transcript of records that includes the title of the exam, the scope of the course (amount of credits and/or duration) and the grade you received in the exam. The transcript must be either the original or a certified copy.
To transfer your previous grade into the German grading system, we need a grading table. This grading table must provide at least the following information: best possible grade, worst possible grade, and minimum grade to pass the examination.
Process of Recognition
Fill out the application form completely. Provide all required documents listed above and submit them to the CSE coordinators. To get an acceptance or rejection as soon as possible, please submit the application within the first four weeks of the winter term.
After checking the formal requirements for the documents, they will be forwarded to the lecturers responsible for the respecitve module. They will check whether the content and scope of your previous examinations cover the content of the TUM module.
You will be informed by the secretary of CSE about the result and the transferred grade.
Finally, you can decide whether to accept the recognition or not, e.g. to get a better grade in the TUM module. Once you have accepted the recognition, you cannot retake the TUM module exam to improve the transferred grade.
Regulations for recognition (from a stay abroad)
The recognition should be discussed individually with the CSE coordinators before the planned stay. Otherwise, chances are that the modules taken might not be recognized for the CSE.
Regulations for recognition (from another study at TUM)
Free/additional courses (not used in the previous study's curriculum) or mandatory CSE modules (which have already been passed) can be transferred 1:1, meaning that you transfer a module from the former study program at TUM into the same module from the CSE program. In this case, please only fill out the application form for recognition.
The master's thesis should preferably be started after all other program courses have been completed, but this is not a must. However, if the number of missing credits is too high, registration can and will be declined. As a policy, a person at TUM always defines the topic officially, but you can conduct your thesis in a variety of settings and get advice from people outside TUM:
- Under the supervision of a TUM chair
This is the most common choice for CSE students. Visit the website where TUM thesis offers are published. Not all thesis offers are posted on this website, and not all offers on the page apply to CSE! Also visit the websites of the research groups that interest you and contact them directly: It never hurts to ask!
- At another university or research institute
Visit the university's or institute's website to search for an topic of interest.
- At a company
Many of our students start their thesis at a company where they have worked as an intern or a Werkstudent, for example.
In the last two cases, you will have to make sure that you still find an examiner at TUM from one of the CSE-related schools (formerly, one of the 7 related departments):
- TUM School of Computation, Information, and Technology (CIT): comprising the former departments of Informatics (IN), Mathematics (MA), and Electrical and Computer Engineering (EI)
- TUM School of Engineering and Design (ED): comprising the former departments of Mechanical Engineering (MW), and Civil, Geo and Environmental Engineering (BGU), and
- TUM School of Natural Sciences (NAT): comprising the former departments of Physics (PH) and Chemistry (CH).
They will sign the registration form and grade your thesis. In such a setting, often an external person acts as an assistant advisor.
The CSE program coordinators often receive thesis offers from institutes at universities, various companies, or former CSE students. External offers for theses are usually posted at the bulletin board in front of the chair.
Each thesis must be examined by one (or two) professor(s) (with “Prof.” or “PD” in their title), at least one of whom must be a faculty member at TUM. If you wish to complete your thesis at an external company, please make sure to find suitable examiners in time. Past students have experienced that it can be difficult to find professors willing to act as examiners for the master's thesis if they did not propose the topic.
To register for your master's thesis, you will need to send your thesis proposal to the Examination Board (via email to the secretary of the CSE examination board) using this registration form.)
The registration form must include the topic and the intended start date, and it must be signed by the examiner and the student. This form should be submitted as soon as the topic and schedule are decided, as it will help to narrow down the content of the paper and set a deadline for submission. Please note that the title provided in this form is preliminary and can be changed without further consultation (provided the topic does not stray too far off the initial proposal).
We highly recommend that you submit an abstract of the thesis before submitting the registration form, in order to ensure that the topic is appropriate for CSE. This is especially important if the thesis will be written at an external university, a company, or a non-CSE chair at TUM. Only topics that are related to CSE will be accepted.
The master's thesis should be written in English. The Examination Board may accept another language, but in that case a summary in English must be included. The summary should not exceed one page (15–20 lines are sufficient).
Need help writing in English? The English Writing Center offers free one-on-one English writing consultation to all members of the TUM community. This is a great offer that can improve the quality of your final thesis. Take a look at their website and feel free too book an appointment!
For a general overview of all formalities regarding the master's thesis, refer to this information. In particular, note that you must be enrolled throughout the working time of the thesis, up to the moment you submit (see thesis).
Submitting your Master's Thesis
The master's thesis must be submitted no later than six months after the start date. The start date is indicated on the registration form.
Note: Please make sure in advance that the chosen topic can be handled within the required timeframe. This is especially important if you plan to write your thesis at another university or an external institution, as they may be used to having more time to complete a thesis project.
You must submit identical copies of your thesis:
- one official copy for the Examination Board (printed hard-copy)
- one copy for each of your examiners (can be digital if your examiner allows it)
The official copy for the Examination Board must be submitted to the CSE coordinators (in person or to our mailbox). You may give the additional copies directly to the examiner(s) or submit the copies via the coordinators, who will forward them to the examiner(s) for grading.
If an in-person submission is not possible, you may submit the thesis via postal services. In such a case, the postmark date will be the submission date. Please send your documents to the following address:
Institut für Informatik 5
Please note: All copies must be submitted by the submission deadline.
The use of a proper typesetting system like LaTeX is strongly recommended. Please refer to the thesis guidelines and rules for form and delivery while you are working on the thesis. Since these thesis guidelines hold for theses of the Informatics programs, make sure you adapt them for CSE. Most importantly, ensure that all relevant information appears in the title pages, and make sure to include the signed Declaration of Own Work.
An unofficial template that fulfills all formal requirements for CSE can be found here (provided by Walter Simson).
After you submit your thesis, the coordinators will send a request for grading to the examiners. The examiners usually need a few weeks for reviewing and grading. When having more than one examiner, the thesis grade is calculated by averaging the value of the two grades given by the examiners.
CSE regulations do not require thesis presentations, but some examiners choose to make them mandatory. If your examiner requires you to present your thesis, he/she will determine the presentation format, and you will be responsible for finding a date and room for the presentation. You are welcome to use the SCCS Colloquium for this purpose.
Please note: The submission date of your thesis is the official last date of your thesis work. Even if your presentation takes place after this date, the submission date will still be used for official purposes.
Extension of deadline
If you are unable to meet the submission deadline for any reason outside your control (i.e. access to resources/facilities, software/hardware failure, medical conditions, ...), you can request an extension via the secretary of the Examination Board with appropriate documentation supporting your argument. Please send such a request as soon as issues arise, and at least one week before the deadline, so that the extension can be processed in a timely manner.
In general, if you are ill and prevented from working on the thesis, the working period will be paused according to the received medical certification. Please refer to the following link describing what the medical note must include in order to be considered valid.
In all other cases, your supervisor must agree to the extension or, better yet, issue a statement acknowledging the reasons for the extension.
After successfully completing the course requirements and master’s thesis, you will graduate with a Master of Science (M.Sc.) degree and begin your professional life. For tips and advice on graduation and your next steps, see Graduation.