Universität Wien

250007 VO An overview on algebra (2010W)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik

Details

Language: German

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Thursday 07.10. 15:00 - 17:00 Seminarraum
  • Friday 08.10. 14:00 - 16:00 Seminarraum
  • Thursday 14.10. 15:00 - 17:00 Seminarraum
  • Friday 15.10. 14:00 - 16:00 Seminarraum
  • Thursday 21.10. 15:00 - 17:00 Seminarraum
  • Friday 22.10. 14:00 - 16:00 Seminarraum
  • Thursday 28.10. 15:00 - 17:00 Seminarraum
  • Friday 29.10. 14:00 - 16:00 Seminarraum
  • Thursday 04.11. 15:00 - 17:00 Seminarraum
  • Friday 05.11. 14:00 - 16:00 Seminarraum
  • Thursday 11.11. 15:00 - 17:00 Seminarraum
  • Friday 12.11. 14:00 - 16:00 Seminarraum
  • Thursday 18.11. 15:00 - 17:00 Seminarraum
  • Friday 19.11. 14:00 - 16:00 Seminarraum
  • Thursday 25.11. 15:00 - 17:00 Seminarraum
  • Friday 26.11. 14:00 - 16:00 Seminarraum
  • Thursday 02.12. 15:00 - 17:00 Seminarraum
  • Friday 03.12. 14:00 - 16:00 Seminarraum
  • Thursday 09.12. 15:00 - 17:00 Seminarraum
  • Friday 10.12. 14:00 - 16:00 Seminarraum
  • Thursday 16.12. 15:00 - 17:00 Seminarraum
  • Friday 17.12. 14:00 - 16:00 Seminarraum
  • Thursday 13.01. 15:00 - 17:00 Seminarraum
  • Friday 14.01. 14:00 - 16:00 Seminarraum
  • Thursday 20.01. 15:00 - 17:00 Seminarraum
  • Friday 21.01. 14:00 - 16:00 Seminarraum
  • Thursday 27.01. 15:00 - 17:00 Seminarraum
  • Friday 28.01. 14:00 - 16:00 Seminarraum

Information

Aims, contents and method of the course

We present three selected topics, with emphasis on group theoretic methods for the
first part, ring-theoretic methods for the second part and field-theoretic methods
for the last part. All topics are well known examples for applications of algebra.
The first part, ALGEBRA AND SYMMETRY, deals with crystallographic groups. We first study
group actions and isometry groups of Euclidean spaces. Then we discuss the classification of
wallpaper groups, and more generally of crystallographic groups.
The second part, ALGEBRA AND EQUATIONS, deals with systems of polynomial equations, polynomial rings
in several variables , multivariate division dnd Gröbner bases. We present the Buchberger-
Algorithm for the computation of a Gröbner basis.
The third part, ALGEBRA AND CODING, deals with an introduction to coding theory.
This includes a short repretition of finite fields. We will discuss among other things
linear codes, Reed-Solomon codes, Hamming codes, Golay codes, BCH codes und classical
Goppa codes. Finally we may give an outlook on geometric Goppa codes, which can be constructed from
vector spaces of differentials of algebraic curves.

Assessment and permitted materials

Written exam or oral exam after the end of the lecture.

Minimum requirements and assessment criteria

Overview of algebraic methods in theory and applications

Examination topics

varying

Reading list

1. Janssen, T.
Crystallographic groups.
North-Holland Publishing Co., Amsterdam-London;
American Elsevier Publishing Co., Inc., New York, 1973.

2. Cox, David; Little, John; O'Shea, Donal
Ideals, varieties, and algorithms.
An introduction to computational algebraic geometry and commutative algebra.
Third edition.
Undergraduate Texts in Mathematics. Springer, New York, 2007.

3. Willems, Wolfgang
Codierungstheorie.
De Gruyter Lehrbuch. Berlin: de Gruyter, 250 p. (1999).

Association in the course directory

UEB

Last modified: Mo 07.09.2020 15:40