Mathematics as a sciencific discipline is above all concerned with the study of abstract structures and their inner connections. These structures are explored with the help of logical thinking. Within mathematics one may distinguish the two areas of abstract and applied mathematics. The first is divided into Algebra, Analysis, Geometry, Topology and Number Theory, in the second, one can find Numerical Mathematics, Mathematical Optimization and Stochastics.
While studying Mathematics, you do not only acquire a lot of mathematical expertise and learn about typical mathematical methods. Over and above that, you develop skills like the ability to think analytically, to approach complex problems in a systematic, yet creative manner and to adapt an exact way of operation. These skills are all highly demanded in many professional fields.
Courses and modules of the study program Mathematics B.Sc.
During the first three semesters of your Bachelor studies in Mathematics you obtain basic knowledge in the fields of Linear Algebra, Analysis and Numerical Mathematics. These Basic Modules are obligatory for every student, some of them are visited side by side with students of Mathematical Finance, Physics or students in the Bachelor of Education. Beginning with the fourth semester you can start to choose different areas of specialisation. All obligatory modules are listed below.
The following tables exemplarily show you how your studies can look like with different areas of specialisation. It is of course also possible to combine the possible areas of specialisation in a different way. For further information, please have a closer look at the examination regulations.
Obligatory Modules (86 ECTS)
- Analysis I/II (18 ECTS), consisting of
- Analysis I (9 ECTS)
- Analysis II (9 ECTS) - Linear Algebra I/II (18 ECTS), consisting of
- Linear Algebra I (9 ECTS)
- Linear Algebra II (9 ECTS) - Applied Mathematics I (18 ECTS), consisting of
- Computer based Mathematics (4,5 ECTS)
- Mathematical Modelling (4,5 ECTS)
- Numerical Analysis (9 ECTS) - Analysis III (9 ECTS), consisting of
- Ordinary Differential Equations (4,5 ECTS)
- Measure Theory (4,5 ECTS) - Algebra I (9 ECTS)
- Probability Theory (4,5 ECTS) and Statistics (4,5 ECTS)
- Applied Mathematics II (5 ECTS)
One may chose one of the following lectures
- Numerics of Ordinary Differential Equations (5 ECTS)
- Optimization I (5 ECTS)
Mathematical Modules of Choice (36 - 54 ECTS)
Besides the Obligatory Modules, one has to choose mathematical Modules of Choice to the extend of at least 36 ECTS. Additional 18 ECTS can be chosen according to ones preferences either from further mathematical courses or also non-mathematical courses.
The choice of mathematical Modules of Choice has to be done in such a way that two of the following areas of specialisation are covered (the combination of Stochastics and Statistics being excluded):
Analysis and Numerical Analysis
- Functional Analysis (5 ECTS)
- Theory and Numerics of Partial Differential Equations (9 ECTS)
Geometry and Algebra
- Algebra II (5 ECTS)
- Algorithmic Algebraic Geometry (9 ECTS)
Stochastics
- Functional Analysis (5 ECTS)
- Stochastic Processes (4,5 ECTS)
- Stochastic Analysis (4,5 ECTS)
Statistics
- Functional Analysis (5 ECTS)
- Mathematical Statistics I (9 ECTS)
Differential Geometry
- Ordinary Differential Equations with Applications to Geometry (5 ECTS)
- Differential Geometry I (9 ECTS)
It is possible to choose two areas of specialisation with the component Functional Analysis. In this case, 23 ECTS of the Modules of Choice are covered by areas of specialisation, otherwise 28 ECTS. The remaining ECTS can be covered by further Modules of Choice. The following are taught on a regular basis:
- Complex Analysis (5 ECTS)
- Optimization I (5 ECTS, possible as Module of Choice, if not chosen as Applied Mathematics II)
- Numerics of Ordinary Differential Equations (5 ECTS, possible as Module of Choice, if not chosen as Applied Mathematics II)
- Funktional Analysis (5 ECTS)
- Algebra II (5 ECTS)
- Algebraic Number Theory (5 ECTS)
- Theory and Numerics of Partial Differential Equations (9 ECTS)
- Algorithmic Algebraic Geometry (9 ECTS)
- Stochastic Processes (4,5 ECTS)
- Stochastic Analysis (4,5 ECTS)
- Mathematic Statistics I (9 ECTS)
- Differential Geometry I (9 ECTS)
- Ordinary Differential Equations with Applications in Geometry (5 ECTS)
Minor Subject (18 - 36 ECTS)
One has to obtain 18 ECTS in one and the same non-mathematical subject whilst studying Mathematics. These ECTS can be obtained in the following areas of study:
- Biology
- Chemistry
- Computer Science
- Life Science
- Philosophy
- Physics
- Linguistic
- Economics
After discussing appropriate lectures with the respective areas of study, these will be published in a notice (on F4).
Seminars and Bachelor Thesis (22 ECTS)
Over the course of the Bachelor of Mathematics, one has to participate in a proseminar (3 ECTS, typically in the third semester) and a main seminar (4,5 ECTS, typically in the fifth semester).
As a part of the Bachelor thesis (14,5 ECTS, typically in the sixth semester), one has to deliver a presentation about the topic of the thesis.
In the following you can find all the required modules. For further information, please have a look at the examination regulations.