Universität Wien

250006 VO Algebraic Number Theory (2025W)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik
Fr 12.12. 13:15-14:45 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß

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Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

The lecture starts on Monday, October 6th.

  • Friday 03.10. 13:15 - 14:45 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 06.10. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 10.10. 13:15 - 14:45 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 13.10. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 17.10. 13:15 - 14:45 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 20.10. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 24.10. 13:15 - 14:45 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 27.10. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 31.10. 13:15 - 14:45 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 03.11. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 07.11. 13:15 - 14:45 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 10.11. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 14.11. 13:15 - 14:45 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 17.11. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 21.11. 13:15 - 14:45 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 24.11. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 28.11. 13:15 - 14:45 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 01.12. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 05.12. 13:15 - 14:45 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 15.12. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 19.12. 13:15 - 14:45 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 09.01. 13:15 - 14:45 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 12.01. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 16.01. 13:15 - 14:45 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 19.01. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 23.01. 13:15 - 14:45 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 26.01. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß

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 of 90 minutes at the end of the lecture. No aids allowed.

Minimum requirements and assessment criteria

At least 50% of the points.

Examination topics

The main topics of the lecture, i.e., 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, Algebraic Number Theory, 2020.
[BUR] D. Burde, Commutative Algebra, 2009.
[MIL] J. Milne, Algebraic Number Theory, 2020.
[WAS] L. C. Washington, Introduction to cyclotomic fields, 1997.

Association in the course directory

MALZ; ML1; MEL

Last modified: Tu 18.11.2025 10:07