Algebra
Module MA2101
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 2009/10
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 | |||
|---|---|---|---|
| SS 2021 | SS 2020 | WS 2009/10 | SS 2009 |
Basic Information
MA2101 is a semester module in German language at Bachelor’s level which is offered in winter semester.
This module description is valid to SS 2021.
| Total workload | Contact hours | Credits (ECTS) |
|---|---|---|
| 270 h | 90 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 with diverse axiomatic structures, to develop exact arguments and to apply modern algebraic terminology. These structures include groups, rings and fields. Students are able to identify such structures and is in the position to apply the theorems and methods covered in the course.
Preconditions
MA1101 Linear Algebra and Discrete Structures 1
Courses, Learning and Teaching Methods and Literature
Courses and Schedule
WS 2019/20
WS 2018/9
WS 2017/8
WS 2016/7
WS 2015/6
WS 2014/5
WS 2013/4
WS 2012/3
WS 2011/2
WS 2010/1
| Type | SWS | Title | Lecturer(s) | Dates | Links |
|---|---|---|---|---|---|
| VO | 4 | Algebra | Kemper, G. |
Thu, 08:30–10:00, MI HS3 Fri, 10:15–11:45, MI HS3 |
eLearning |
| UE | 2 | Algebra (Exercise Session) | Kemper, G. Reimers, F. |
singular or moved dates and dates in groups |
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., ueberarb. Auflage 2011.
G. Fischer, Lehrbuch der Algebra, Vieweg, Wiesbaden, 2., ueberarb. 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.