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This entry is from Winter semester 2018/19 and might be obsolete. You can find a current equivalent here.

Algebra
(dt. Algebra)

Level, degree of commitment Advanced module, required module
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.
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 can

  • understand basic principles of elementary algebraic objects,
  • derive simple properties from axiomatically defined algebraic structures,
  • recognize algebraic structures in other mathematical areas.

You practice

  • mathematical methods (development of mathematical intuition and its formal justification, training of abstraction and formulation of proofs),
  • in the recitation classes, oral communication skills through discussion and presentation 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.


Applicability

The module can be attended at FB12 in study program(s)

  • B.Sc. Computer Science
  • B.Sc. Mathematics
  • M.Sc. Computer Science

When studying B.Sc. Mathematics, this module must be completed in the study area Advanced Modules in Mathematics (Core Subjects).

The module can also be used in other study programs (export module).


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 2018/19. 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:

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.