Universität Wien
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250013 VO Matrix groups (2022S)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik
Moodle

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Details

Language: German

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Tuesday 01.03. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 03.03. 11:30 - 13:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 08.03. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 10.03. 11:30 - 13:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 15.03. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 17.03. 11:30 - 13:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 22.03. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 24.03. 11:30 - 13:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 29.03. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 31.03. 11:30 - 13:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 05.04. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 07.04. 11:30 - 13:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 26.04. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 28.04. 11:30 - 13:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 03.05. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 05.05. 11:30 - 13:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 10.05. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 12.05. 11:30 - 13:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 17.05. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 19.05. 11:30 - 13:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 24.05. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 31.05. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 02.06. 11:30 - 13:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 09.06. 11:30 - 13:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

IN particular in their role as symmetry groups, matrix groups play an important role in mathematics and theoretical physics. The theory of matrix groups exhibits surprising connections between the contents of the basic courses on analysis and linear algebra. While the basic concepts of matrix groups come from the side of (linear) algebra, the main tool to study these groups is differential calculus. The connection to linear algebra leads to a new view on differential calculus and to substantial applications of analytical techniques. Many explicit examples of matrix groups that play an important role in mathematics and theoretical physics will be discussed in detail.

Assessment and permitted materials

Oral exam after the end of the course.

Minimum requirements and assessment criteria

Students should know about the fundamentals of the theory of matrix groups, in particular the relations between a matrix group and its Lie algebra and between smooth homomorphisms between such groups and their derivatives. They should be able to discuss several important examples of such groups and homomorphisms. The level of the course follows the usual standards of advanced courses in the bachelor program.

Examination topics

The contents of the course as collected in the lecture notes.

Reading list

I will provide lecture notes (in German) which contain all the material needed to complete the course. As additional reading, there are several introductory books on matrix groups, for example "Matrizen und Lie-Gruppen" by W. Kühnel (Springer 2011, in German) or "Matrix Groups for Undergraduates" by K. Tapp (AMS 2005, in English). Of course, these differ in content from the course and partly cover quite a bit of additional material.

Association in the course directory

ZWM

Last modified: We 15.03.2023 13:28