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German original

Number Theory
(dt. Zahlentheorie)

Level, degree of commitment in original study programme Intermediate module, compulsory elective module
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: 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 study course B.Sc. Mathematics.
Original study programme B.Sc. Mathematik / Mathematik Wahlpflichtmodule
Duration,
frequency
One semester,
Regelmäßig im Wechsel mit anderen intermediate moduleen
Person in charge of the module's outline Prof. Dr. István Heckenberger, Prof. Dr. Sönke Rollenske

Contents

  • Fundamental theorem of arithmetic,
  • g-adic expansion and divisibility,
  • elementary theory of primes,
  • Examples of public-key cryptographic methods,
  • Diophantine equations,
  • Modular arithmetic, power residues, reciprocity laws.

Qualification Goals

The students shall

  • learn the basics of classical number theory,
  • recognize the links to methods from algebra and analysis,
  • practice mathematical working methods (development of mathematical intuition and its formal justification, training of abstraction and formulating proofs),
  • improve their oral communication skills in the exercises by practicing free speech in front of an audience and during discussion.

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.


Recommended Reading

  • Remmert, Ullrich: Elemetare Zahlentheorie, Birkhäuser.
  • Everest, Ward: An Introduction to Number Theory, GTM, Springer (hier insbesondere Kapitel 1-3)
  • Stein: Elementary Number Theory: Primes, Congruences, and Secrets (a computational approach), UTM, Springer.



Please note:

This page describes a module according to the latest valid module guide in Sommersemester 2021. 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.