Main content

Elementary Number Theory
(dt. Elementare Zahlentheorie)

Level, degree of commitment Advanced module, compulsory elective module
Forms of teaching and learning,
workload		 Lecture (3 SWS), recitation class (1 SWS) or lecture (2 SWS), recitation class (2 SWS),
180 hours (60 h attendance, 120 h private study)
Credit points,
formal requirements		 6 CP
Course requirement(s): Successful completion of at least 50 percent of the points from the weekly exercises.
Examination type: Written or oral examination (individual 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.
Duration,
frequency		 One semester,
Regularly alternating with other advanced modules
Person in charge of the module's outline Prof. Dr. Sönke Rollenske, Prof. Dr. István Heckenberger

Contents

  • Euclidean algorithm and greatest common divisor
  • continued fractions
  • Dirichlet convolution and Möbius inversion
  • Prime numbers and cryptography
  • Chinese remainder theorem
  • linear congruence equations
  • Primitive root

Qualification Goals

Students

  • have learned the basics of classical number theory,
  • can formulate concrete problems about numbers in a suitable abstract setting and apply the methods of the setting,
  • recognize the cross connections to methods of algebra,
  • have practiced mathematical ways of working (developing mathematical intuition and its formal justification, training the ability to abstract, reasoning),
  • have improved their oral communication skills in exercises by practicing free speech in front of an audience and in discussion.

Prerequisites

None. The competences taught in the following module are recommended: Foundations of Mathematics.


Applicability

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

  • B.Sc. Data Science
  • B.Sc. Mathematics
  • B.Sc. Business Mathematics
  • M.Sc. Mathematics
  • M.Sc. Business Mathematics
  • LAaG Mathematics

When studying B.Sc. Mathematics, this module can be attended in the study area Compulsory Elective Modules in Mathematics.

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


Recommended Reading

  • Oswald, N., Steuding, J., Elementare Zahlentheorie, Springer, 2014
  • Remmert, R., Ullrich, P., Elementare Zahlentheorie, Springer, 2008



Please note:

This page describes a module according to the latest valid module guide in Winter semester 2023/24. 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:

  • Winter 2016/17 (no corresponding element)
  • Summer 2018 (no corresponding element)
  • Winter 2018/19 (no corresponding element)
  • Winter 2019/20 (no corresponding element)
  • Winter 2020/21 (no corresponding element)
  • Summer 2021 (no corresponding element)
  • Winter 2021/22 (no corresponding element)
  • Winter 2022/23 (no corresponding element)
  • Winter 2023/24

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.