Module MA4803-KP05
Number Theory (ZahlThKP05)
Duration
1 Semester
Turnus of offer
irregularly
Credit points
5
Course of studies, specific fields and terms:
- Master CLS 2023, optional subject, mathematics
- Bachelor CLS 2023, optional subject, mathematics
- Minor in Teaching Mathematics, Master of Education 2023, optional subject, mathematics
- Minor in Teaching Mathematics, Master of Education 2017, optional subject, mathematics
- Master CLS 2016, optional subject, mathematics
- Bachelor CLS 2016, optional subject, mathematics
Classes and lectures:
- Number Theory (exercise, 1 SWS)
- Number Theory (lecture, 2 SWS)
Workload:
- 15 hours exam preparation
- 60 hours private studies
- 45 hours in-classroom work
- 30 hours work on project
Contents of teaching:
- Divisibility of integers, Farey sequencees, Fibonacci Numbers
- Approximation of real numbers by rational numbers
- Modulo operations: Complete and reduced residue system, Theorems of Euler and Fermat
- Representation of natural numbers sums of 2, 3 or 4 squares
- Quadratic residues
- Quadratic reciprocity
- Prime number criteria and pseudo prime numbers
- Pythagorean triples
- Rational points on curves of degree 2
- Number theoretic functions
- Prime number theorem, prime numbers in arithmetic progression
- Riemann zeta function and its functional equation
- Known problems and conjectures, i.e. Goldbach conjecture
- Stochastic prime numbers
Qualification-goals/Competencies:
- Theoretical knowledge of the mentioned topics
- Historical and most recent issues
- Solve questions in this filed
- Recognize interdisciplinary aspects
Grading through:
- exercises, project, oral or written exam
Responsible for this module:
Literature:
- Chandrasekharan : Einführung in die analytische Zahlentheorie Springer Lecture Notes 2008
- Bundschuh : Einführung in die Zahlentheorie Springer 1992
- Menzer : Zahlentheorie: Fünf ausgewählte Themenstellungen der Zahlentheorie Oldenbourg Wissenschaftsverlag 2010
- Remmert u. Ullrich : Elementare Zahlentheorie Birkhäuser 1995
- Rempe : Primzahltests für Einsteiger: Zahlentheorie - Algorithmik - Kryptographie Vieweg+Teubner 2009
- Scharlau, Opolka : Von Fermat bis Minkowski: Eine Vorlesung über Zahlentheorie und ihre Entwicklung Springer 2009
- Scheid : Zahlentheorie Spektrum 2003
- Schmidt : Einführung in die algebraische Zahlentheorie Springer 2009
- Weil : Zahlentheorie Spektrum 1992
- Winogradow : Elemente der Zahlentheorie Prestel-Verlag 1956
Language:
- offered only in German
Notes:
Admission requirements for taking the module:- None (The competencies of the modules listed under 'Requires' are needed for this module, but are not a formal prerequisite)
Admission requirements for participation in module examination(s):
- Successful completion of homework assignments as specified at the beginning of the semester
Module exam(s):
- MA4803-L1: Number Theory, written exam (90 min) or oral exam (30 min), 100 % of module grade
Last Updated:
22.02.2022