Main content
This entry is from Winter semester 2016/17 and might be obsolete. You can find a current equivalent here.
Algebra
(dt. Algebra)
Level, degree of commitment | Advanced module, depends on importing study program |
Forms of teaching and learning, workload |
Lecture (4 SWS), recitation class (2 SWS), 270 hours (90 h attendance, 180 h private study) |
Credit points, formal requirements |
9 CP Course requirement(s): Written or oral examination Examination type: Successful completion of at least 50 percent of the points from the weekly exercises. |
Language, Grading |
German,The grading is done with 0 to 15 points according to the examination regulations for the degree program B.Sc. Mathematics. |
Subject, Origin | Mathematics, B.Sc. Mathematics |
Duration, frequency |
One semester, each winter semester |
Person in charge of the module's outline | Prof. Dr. Thomas Bauer, Prof. Dr. István Heckenberger, Prof. Dr. Sönke Rollenske, Prof. Dr. Volkmar Welker |
Contents
Elementary theory of groups and rings. Basic theorems on the structure of subgroups and ideals. Constructions of groups and rings (e.g.; quotient structures). Special classes of groups and rings and their theory (e.g. Abelian groups, factorial and Euclidean rings). Connections to number theory or algebraic geometry. Beginnings of field theory.
Qualification Goals
Students will be able to
- understand basic principles of elementary algebraic objects,
- derive simple properties of axiomatically defined algebraic structures,
- recognize algebraic structures in other mathematical areas.
They practice
- mathematical working methods (development of mathematical intuition and its formal justification, training of abstraction skills, proofs),
- in the exercises, oral communication skills through discussion and free speech in front of an audience
Prerequisites
Translation is missing. Here is the German original:
Keine. Empfohlen werden die Kompetenzen, die in den Basismodulen vermittelt werden
Recommended Reading
- M. Artin, Algebra, Birkhäuser, 1993.
- S. Bosch, Algebra, 8. Aufl., Springer, 2013.
- G. Fischer, Lehrbuch der Algebra, 3. Aufl,, Spektrum 2013.
- S. Lang, Algebra, Addison-Wesley, 1984.
Please note:
This page describes a module according to the latest valid module guide in Winter semester 2016/17. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:
- Winter 2016/17
- Summer 2018
- Winter 2018/19
- Winter 2019/20
- Winter 2020/21
- Summer 2021
- Winter 2021/22
- Winter 2022/23
- Winter 2023/24
The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.
The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.