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This entry is from Winter semester 2020/21 and might be obsolete. You can find a current equivalent here.
Number Theory
(dt. Zahlentheorie)
Level, degree of commitment | Advanced module, depends on importing study program |
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(s): 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 the degree program B.Sc. Mathematics. |
Subject, Origin | Mathematics, B.Sc. Mathematics |
Duration, frequency |
One semester, Regularly alternating with other advanced modules |
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 Winter semester 2020/21. 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
- Summer 2018
- Winter 2018/19
- Winter 2019/20
- Winter 2020/21
- Summer 2021
- Winter 2021/22
- Winter 2022/23
- 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.