Universität Wien

250060 VO Algebraic Number Theory (2024W)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik
Moodle
Fr 08.11. 13:15-14:45 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß

Registration/Deregistration

Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).
Register/Deregister for this course

Details

Language: English

Lecturers

Classes (iCal) - next class is marked with N

  • Friday 04.10. 13:15 - 14:45 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 07.10. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 11.10. 13:15 - 14:45 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 14.10. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 18.10. 13:15 - 14:45 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 21.10. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 25.10. 13:15 - 14:45 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 28.10. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 04.11. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 11.11. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 15.11. 13:15 - 14:45 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 18.11. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 22.11. 13:15 - 14:45 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 25.11. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 29.11. 13:15 - 14:45 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 02.12. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 06.12. 13:15 - 14:45 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 09.12. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 13.12. 13:15 - 14:45 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 16.12. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 10.01. 13:15 - 14:45 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 13.01. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 17.01. 13:15 - 14:45 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 20.01. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 24.01. 13:15 - 14:45 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 27.01. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 31.01. 13:15 - 14:45 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.

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

Neukirch "Algebraische Zahlentheorie"
P. Samuel "Algebraic Theory of Numbers"
Koch "Algebraische Zahlentheorie"
Lang "Algebraic number theory"
I. Stewart, D. Tall, Algebraic Number Theory and Fermat's Last Theorem
D.A. Marcus, Number Fields
W. Narkiewicz, Elementary and Analytic Theory of Algebraic Numbers

Association in the course directory

MALZ

Last modified: Mo 07.10.2024 12:46