## Module Handbook

• Dynamischer Default-Fachbereich geändert auf MAT

# Course MAT-12-11-K-2

## Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
- K Lecture with exercise classes and tutorials (V/U/T) 5.5 CP 109 h
2 V Lecture 28 h
2 U Exercise class/tutorial (in small groups) 28 h
(2V+2U) 5.5 CP 56 h 109 h

## Basedata

SWS 2V+2U 5.5 CP = 165 h 1 Sem. in WiSe/SuSe [2] Bachelor (Fundamentals) [DE] German Fieker, Claus, Prof. Dr. (PROF | DEPT: MAT) Gathmann, Andreas, Prof. Dr. (PROF | DEPT: MAT) Horn, Max, Prof. Dr. (PROF | DEPT: MAT) Lassueur, Caroline, Jun. Prof. Dr. (PROF | DEPT: MAT) Malle, Gunter, Prof. Dr. (PROF | DEPT: MAT) Schulze, Mathias, Prof. Dr. (PROF | DEPT: MAT) Thiel, Ulrich, Prof. Dr. (PROF | DEPT: MAT) [MAT-GRU] Mathematics (B.Sc. year 1 and 2) [NORM] Active

## Notice

The course is also offered as distance learning course as part of the early entrance programme FiMS, see https://fims.mathematik.uni-kl.de

## Possible Study achievement (Übungsschein Algebraic Structures)

• Verification of study performance: proof of successful participation in the exercise classes (incl. written examination)
• Examination number (Study achievement): 82025 ("Exercise Class Algebraic Structures")
• Details of the examination (type, duration, criteria) will be announced at the beginning of the course.
Qualified certificate of successful participation in the exercise classes through active participation, successful completion of homework and passing the final exam for the exercise classes.

## Contents

• fundamental algebraic structures: groups, rings, fields (in particular: symmetric group),
• substructures and factor structures (in particular: normal subgroups, isomorphism theorems),
• principal ideal domains: ℤ, polynomial ring K[t] (in particular: Euclidean algorithm).

## Literature

• G. Fischer: Lineare Algebra,
• H.-J. Reiffen, G. Scheja, U. Vetter: Algebra,
• H.-D. Ebbinghaus, et al.: Zahlen,
• S. Lang: Algebraische Strukturen.

## Materials

Further literature will be announced in the lecture(s); exercise material is provided.

## Registration

Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de).

None

None

## References to Course [MAT-12-11-K-2]

Module Name Context
[MAT-12-10A-M-2] Pure Mathematics A P: Obligatory in Obligatory-Modulteil #A (Algebraic Structures) 2V+2U, 5.5 LP
[MAT-12-10L-M-2] Fundamentals of Mathematics C: Geometry, Elementary Algebra and Number Theory P: Obligatory in Obligatory-Modulteil #A (Algebraic Structures) 2V+2U, 5.5 LP