Algebra
Module MA2010
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 2019/20
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 2021/2 | SS 2021 | WS 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
| Total workload | Contact hours | Credits (ECTS) |
|---|---|---|
| 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
| Type | SWS | Title | Lecturer(s) | Dates | Links |
|---|---|---|---|---|---|
| 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.
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.
Media
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.
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.