## Module Handbook

• Dynamischer Default-Fachbereich geändert auf MAT

# Course MAT-12-21-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 SuSe [3] Bachelor (Core) [DE] German Fieker, Claus, 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

## Possible Study achievement

• Verification of study performance: proof of successful participation in the exercise classes (ungraded)
• Examination number (Study achievement): 83170 ("Exercise Class Elementary Number Theory")
• Details of the examination (type, duration, criteria) will be announced at the beginning of the course.

## Contents

• Unique prime decomposition in ℤ, linear diophantine equations,
• Euler's phi function, structure of the primary residual class group (ℤ/nℤ)*,
• Gaussian reciprocity law,
• quadratic number fields, decomposition behaviour of prime numbers, sums of squares.

## Competencies / intended learning achievements

The students know the basic concepts, statements and methods of number theory. In particular, an advanced ability of abstraction was promoted.

## Literature

• R. Remmert, P. Ullrich: Elementare Zahlentheorie,
• R. Schulze-Pillot: Einführung in die Algebra und Zahlentheorie,
• T. Apostol: Introduction to Analytic Number Theory.

## 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-12-21-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)