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Modul
Algebraic Number Theory [M-MATH-101725]
Credits
8Recurrence
UnregelmäßigDuration
1 SemesterLanguage
Level
4Version
1Responsible
Organisation
- KIT-Fakultät für Mathematik
Part of
Bricks
Identifier | Name | LP |
---|---|---|
T-MATH-103346 | Algebraic Number Theory | 8 |
Competence Certificate
oral examination of ca. 30 minutes
Competence Goal
Students are able to
- understand basic structures and concepts from algebraic number theory,
- apply abstract concepts to concrete problems,
- read research papers and write a thesis in the field of algebraic number theory.
Prerequisites
none
Content
- Algebraic number fields: rings of integers, Minkowski theory, class-groups and Dirichlet's unit theorem,
- Extensions of number fields: Ramified primes, Hilbert's ramification theory,
- Local fields: Ostrowski's theorem, valuation theory, Hensel's lemma, extensions of local fields,
- analytic methods: Dirichlet series, Dedekind's zeta function, L-series
Recommendation
The contents of the module "Algebra" are strongly recommended.
Workload
Total workload: 240 hours
Attendance: 90 h
- lectures, problem classes and examination
Self studies: 150 h
- follow-up and deepening of the course content,
- work on problem sheets,
- literature study and internet research on the course content,
- preparation for the module examination