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# Scientific Computing (Master)

Scientific Computing (SC) is an international **mathematical master program** with special focus on applied mathematics and in particular on numerical analysis. Since the needed mathematical skills are quite broad, the program is mainly addressed to mathematicians but it is also open for applicants from other disciplines as long as they have a **strong mathematical background** and/or a high affinity towards mathematics. The language of instruction is English.

## Current Information for the Winter Semester 2022/23

- The master program "Scientific Computing" has
**new study and exam regulations**which become valid with the**winter semester 2022/2023**. Before you apply to the program, please read the following paragraphs carefully and keep the**mathematical focus**of the master program in mind. - Registration for the
**Mathematics Prep-Course for Scientific Computing**(by Prof. Jörg Liesen) is now open. More information on the course topics can be found here.

## Admission Requirements (as of winter 2022/23)

The specific requirements of the SC program are a Bachelor in mathematics ("Mathematik", "Wirtschaftsmathematik", "Technomathematik") or a Bachelor in another field of studies with a **sufficiently strong mathematical component. **A field of studies is considered to have a sufficiently strong mathematical component if it contains **a minimum of**

- 18 credits from the area "Analysis/Linear Algebra"
- 6 credtis from the area "Differential Equations"
- 9 credits from the area "Numerical Analysis"

with a **level of competence **comparable to a typical engineering program obtained at the Technical University of Berlin. In particular, the individual areas should have dealt with the following topics:

*Analysis/Linear Algebra:* sets and mappings; induction; real and complex numbers; (convergence of) sequences and infinite series; differential calculus of scalar functions: mean value theorem, higher derivatives, extremal values, Taylor polyomial/series; integral calculus of scalar functions: (in)definite integrals, Fourier series; differential calculus of multivariate functions: partial derivatives, higher derivatives, extremal values; integral calculus of multivariate functions: contour integrals, integration on surfaces, integral theorems of Gauß and Stokes; linear systems and Gaussian elimination; vector spaces, linear mappings, determinants and eigenvalues

*Differential Equations:* systems of linear and nonlinear ordinary differential equations (existence, uniqueness and stability of solutions), linear partial differential equations, boundary and eigenvalue problems, Laplace transformationfloating point arithmetic, solving linear and nonlinear systems of equations, least squares, polynomial interpolation, numerical integration, quadrature, approximation of solutions of ordinary differential equations

Numerical Analysis:

**List of relevant mathematical courses**: applicants without a Bachelor in mathematics are required to hand in the following **document** providing information on the mathematical level of competence.

Additionally, a **proof of English language profiency of level B2** (Common European Framework of Reference for Languages) or equivalent is mandatory. German language skills are not required. Since SC is a non-restricted Master’s program there is no further selection process among the candidates who fulfill these admission requirements.

Please note that the admission requirements need to be fulfilled when applying to the program. There is no possibility of catching up on prerequisite courses after the admission.

**Retention of the old and change to the new study and exam regulations: **Beginning with the winter term 2022/23, currently enrolled students of the master studies Scientific Computing have the possibility to change to the new study and exam regulations. Similarly, continuation and completion according to the old study and exam regulations until the summer term 2025 is possible. The required declaration for this process has to be submitted to the examination office and can be found here. Note that with the new study and exam regulations, the (now) **compulsory** modules "Numerical Linear Algebra (10 LP)" and "Scientific Computing (10 LP)" have slightly changed. Students interested in changing from old to new study and exam regulations should particularly take into account:

- if the former module "Scientific Computing (7 LP)" has been passed successfully, it will automatically be recognized as equivalent to the new module "Scientific Computing (10 LP)"
- in order to get the new module "Numerical Linear Algebra (10 LP)" recognized, students must have successfully passed both former modules "Numerical Linear Algebra I (5 LP)" and "Numerical Linear Algebra II (5 LP)"

## Structure of the Program (as of winter 2022/23)

The SC program consists of 120 ECTS and is subdivided into **mandatory (30 ****ECTS), elective (44 ****ECTS), free choice (16 ****ECTS) **courses** **and the** master thesis (30 ECTS).**

**Mandatory courses** (30 ECTS): Scientific Computing, Numerical Linear Algebra I, Numerical Mathematics II for Engineers

**Elective courses** (26+18 ECTS): Different modules for a total of **26 ECTS in applied mathematics** have to be chosen; additionally, modules for a total of **18 **** ECTS in an applied discipline** have to be chosen, see the MOSES platform for a list of modules (module descriptions only available in German). Within the applied discipline, it is also possible to bring in courses attended at other Berlin universities.

**Free choice** (16 ECTS): Here, the student can choose from all modules offered by TU Berlin. To search for appropriate modules, the MOSES platform can be used. Additionally, it is also possible to bring in courses attended at other Berlin universities.

**Master thesis** (30 ECTS): The master thesis should be designed considering the current state of research. This is guaranteed by intensive research work of the teaching staff. The topic of the master thesis can be chosen in the field of applied mathematics as well as in the applied discipline.

## Application Process (as of winter 2022/23)

The application is possible **only for the winter semester**. The application deadline can be found here (see “Application for master's programs with free admission”). For students who did not receive their Bachelor from TU Berlin the application process is done via uni-assist, see here for more details. Note that applicants without a Bachelor in mathematics are required to hand in the following **document** providing information on the mathematical level of competence.

## Study and Exam Regulations

**Caution**: The study and exam regulations will **change** with the **winter semester 2022/23**.

The study and exam regulations **(for students admitted after summer semester 2022)** contain all regulations which are specific to the SC program:

The former study and exam regulations **(for students admitted before winter semester 2022/23)** contain all regulations which are specific to the SC program:

Furthermore, the regulations governing general study and examination procedures (in German *Ordnung zur Regelung des allgemeinen Studien- und Prüfungsverfahrens (AllgStuPO)*) are also valid for the SC program:

## Structure of the Program (before winter 2022/23)

The SC program consists of 120 ECTS and is subdivided into seven areas:

**Area 1: Scientific Computing** (27 ECTS)

Here, the student can choose among different modules, mostly in numerical mathematics, see the MOSES platform for a list of modules (module descriptions only available in German). The module Wissenschaftliches Rechnen^{*} (in English *Scientific Computing*) is mandatory.

**A****rea 2: Applied Mathematics** (20 ECTS, in German *Angewandte Mathematik*)

Here, different modules in applied mathematics can be chosen, see the MOSES platform for a list of modules (module descriptions only available in German).

**A****rea 3: Applied Discipline** (19 ECTS)

The student chooses one applied discipline among the fields physics, chemistry, engineering sciences, biology and medicine and selects modules of the chosen discipline. These modules are usually offered by departments which are not part of the institute of mathematics and, thus, we cannot provide a complete list of modules. To search for appropriate modules, the MOSES platform can be used.

**Area 4: Free Choice** (5 ECTS)

Here, the student can choose from all modules offered by TU Berlin. To search for appropriate modules, the MOSES platform can be used.

**Area 5: Mathematical Seminars** (12 ECTS)

Here, the student has to take two seminars. The seminars offered in the next semesters can be found on the list *L**ong-**T**erm **C**ourse **P**lanning **in Mathematics* (only available in German), see the News section of the institute's website.

**Area 6: Internship** (7 ECTS)

A full-term internship of at least six weeks is compulsory and usually is completed during the lecture-free period after the third semester. As far as scientific supervision is ensured the internship can be done at an institution outside the university.

**Area 7: Master thesis** (30 ECTS)

The master thesis should be designed considering the current state of research. This is guaranteed by intensive research work of the teaching staff. The topic of the master thesis can be chosen in the field of applied mathematics as well as in the applied discipline.

^{*} The name of this module is "Wissenschaftliches Rechnen" and it consists of the course "Scientific Computing", see the corresponding description on Moses. It should not be confused with the identically named module offered by the Institute of Computer Engineering and Microelectronics.

## Mentoring (before winter 2022/23)

Before students can register for the first exam, they are obliged to create a study plan indicating which courses are planned to be attended in which semester. This study plan needs to be discussed with a mentor of the student’s choice. The mentor can be any professor of the institute of mathematics, e.g., a lecturer of a course which is attended by the student.

## Contact Persons

Bernhard Höveler is a student advisor who can be contacted for general questions concerning the SC program.

Prof. Tobias Breiten is the chairman of the SC examination board and can be contacted for questions about the approval of a specific course or about a specific admission decision.

For questions regarding the application and admission process at TU Berlin, please contact the office of student affairs.

## Helpful Links

- information on application and enrollment: office of student affairs
- information on modules: MOSES
- information on mathematical courses offered in the next semesters: Long-Term Course Planning
- general information in currently offered courses: MOSES
- detailed information on currently offered courses: ISIS (only available after admission)