Universität Wien

250060 VO Algebraic number theory (2021W)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik
REMOTE
Moodle

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Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

The lecture will be held digitally via Moodle.

  • Monday 04.10. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 06.10. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 11.10. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 13.10. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 18.10. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 20.10. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 25.10. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 27.10. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 03.11. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 08.11. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 10.11. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 15.11. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 17.11. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 22.11. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 24.11. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 29.11. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 01.12. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 06.12. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 13.12. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 15.12. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 10.01. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 12.01. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 17.01. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 19.01. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 24.01. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 26.01. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 31.01. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

Number theory is a branch of pure mathematics devoted to the properties of integers and integer-valued functions
in the broadest sense. It is one of the oldest sciences. The main subdivisions of number theory are
elementary number theory, analytic number theory, algebraic number theory, Diophantine geometry,
probabilistic number theory, arithmetic combinatorics and computational number theory.
The aim is to give an introduction to algebraic number theory and to cover some of the classical topics, like rings of integers, norm, trace and discriminant, ideals of Dedekind rings, finiteness of the class number, Dirichlet's unit theorem, splitting and ramification, cyclotomic fields, valuations and local fields, and as a bonus, the Theorem of Kronecker-Weber.

Assessment and permitted materials

Written exam at the end of the lecture.

Minimum requirements and assessment criteria

Passing the exam.

Examination topics

Rings of integers, norm, trace and discriminant, ideals of Dedekind rings, finiteness of the class number, Dirichlet's unit theorem, splitting and ramification, cyclotomic fields, valuations and local fields.

Reading list

[BUR] D. Burde, Commutative Algebra, 2009.
[COH] H. Cohen, A course in computational algebraic number theory, 1993.
[KOC] H. Koch, Algebraic number theory, 1997.
[LAN] S. Lang, Algebraic number theory, 1994.
[NEU] J. Neukirch, Algebraic number theory, 1999.
(WAS] L. C. Washington, Introduction to cyclotomic fields, 1997.

Association in the course directory

MALZ

Last modified: Fr 12.05.2023 00:21