## Module Handbook

• Dynamischer Default-Fachbereich geändert auf MAT

# Course MAT-12-22-K-3

## Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
- K Lecture with exercise classes (V/U) 4.5 CP 93 h
2 V Lecture 28 h
1 U Exercise class (in small groups) 14 h
(2V+1U) 4.5 CP 42 h 93 h

## Basedata

SWS 2V+1U 4.5 CP = 135 h 1 Sem. in WiSe [3] Bachelor (Core) [DE] German Fieker, Claus, Prof. Dr. (PROF | DEPT: MAT) Gathmann, Andreas, Prof. Dr. (PROF | DEPT: MAT) Horn, Max, 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

## Possible Study achievement

• Verification of study performance: proof of successful participation in the exercise classes (ungraded)
• Examination number (Study achievement): 83110 ("Exercise Class Introduction to Algebra")
• Details of the examination (type, duration, criteria) will be announced at the beginning of the course.

## Contents

• principal ideal domains, unique factorization domains (UFD),
• groups, operations, Sylow theorems,
• stem and splitting fields,
• fundamental theorem of Galois theory,
• solvability of equations, constructions with compass and ruler.

## Competencies / intended learning achievements

The students understand (using the example of field theory) how the interaction of different areas of algebra leads to new insights (in particular, to answers to classical questions of antiquity). This deepened the fundamental knowledge that different areas of mathematics often have to cooperate for being able to solve concrete problems.

## Literature

• F. Lorenz: Einführung in die Algebra,
• B.L. van der Waerden: Algebra,
• G. Wüstholz: Algebra.

## 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

## References to Course [MAT-12-22-K-3]

Module Name Context
[MAT-12-20L_ERW-M-3] Topic Module A: Mathematics in the Interplay between Abstraction and Concretisation WP: Obligation to choose 2V+1U, 4.5 LP
[MAT-12-20L-M-3] Topic Module A: Mathematics in the Interplay between Abstraction and Concretisation WP: Obligation to choose 2V+1U, 4.5 LP
Course-Pool Name
[MAT-10-KPOOL-3] Pure Mathematics (B.Sc. Mathematics)
[MAT-18-KPOOL-3] Geometry (B.Ed. Mathematics)