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# Algebra

## Module MA2010

This Module is offered by TUM Department of Mathematics.

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

### Module version of WS 2021/2 (current)

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.

available module versions
WS 2021/2SS 2021WS 2019/20

### Basic Information

MA2010 is a semester module in German language at Bachelor’s level which is offered in summer semester.

This Module is included in the following catalogues within the study programs in physics.

• Further Modules from Other Disciplines
270 h 105 h 9 CP

### Content, Learning Outcome and Preconditions

#### Content

This course covers basic algebraic structures such as groups, rings and fields. More specifically: subgroups, generation, quotient groups, solvable groups, homomorphisms, group actions, ideals, quotient rings, prime ideals, unique prime factorization, field extensions, finite fields, Galois theory, solvable polynomials.

#### Learning Outcome

Upon completion of the module, students are able to deal abstractly and computationally with various axiomatic structures, and to apply this in different contexts. They can use modern algebraic terminology, and they can find their own proofs for statements about algebraic structures. These structures include groups, rings and fields. Students are able to identify such structures and can apply the theorems and methods covered in the course to them.

#### Preconditions

MA0004 Linear Algebra 1, MA0005 Linear Algebra 2 und Discrete Struktures

### Courses, Learning and Teaching Methods and Literature

#### Courses and Schedule

VO 5 Algebra [MA2010] Himstedt, F. Liedtke, C. eLearning
UE 1 Algebra (Questions Session) [MA2010] Himstedt, F. Liedtke, C. Wed, 16:15–17:45, virtuell
and dates in groups
eLearning
UE 2 Algebra (Exercise Session) [MA2010] Himstedt, F. Liedtke, C. dates in groups eLearning

#### Learning and Teaching Methods

lecture, exercise module, assignments
The module is offered as lectures with accompanying practice sessions. In the lectures, the contents will be presented in a talk with demonstrative examples, as well as through discussion with the students. The lectures should animate the students to carry out their own analysis of the themes presented and to independently study the relevant literature. Corresponding to each lecture, practice sessions will be offered, in which exercise sheets and solutions will be available. In this way, students can deepen their understanding of the methods and concepts taught in the lectures and independently check their progress. At the beginning of the module, the practice sessions will be offered under guidance, but during the term the sessions will become more independent, and intensify learning individually as well as in small groups.

blackboard

#### Literature

Ch. Karpfinger, K. Meyberg, Algebra - Gruppen, Ringe, Körper, Spektrum Akademischer Verlag, Heidelberg 2008.
G. Fischer, Lehrbuch der Algebra, Vieweg, Wiesbaden, 2., überarb. Auflage 2011.

### Module Exam

#### Description of exams and course work

The module examination is based on a written exam (90 minutes). Students have to know basic axiomatic structures of groups, rings and fields and deal with them. They are able to apply theorems and methods in limited time and to argue with mathematical precision.

#### Exam Repetition

The exam may be repeated at the end of the semester.

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