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This entry is from Winter semester 2019/20 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): Successful completion of at least 50 percent of the points from the weekly exercises.
Examination type: Written or oral examination
Language,
Grading		 German,
The grading is done with 0 to 15 points according to the examination regulations for the degree program B.Sc. Mathematics.
Origin 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

None. The competences taught in the following modules are recommended: either Foundations of Mathematics and Linear Algebra I and Linear Algebra II or Basic Linear Algebra, either Analysis I and Analysis II or Basic Real Analysis.


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 2019/20. 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.