Universität Wien
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250066 VU Applications of algebra (2013S)

7.00 ECTS (4.00 SWS), SPL 25 - Mathematik
Continuous assessment of course work

Details

Language: German

Lecturers

Classes (iCal) - next class is marked with N

  • Monday 04.03. 14:00 - 16:00 Seminarraum
  • Thursday 07.03. 14:00 - 16:00 Seminarraum
  • Thursday 14.03. 14:00 - 16:00 Seminarraum
  • Monday 18.03. 14:00 - 16:00 Seminarraum
  • Thursday 21.03. 14:00 - 16:00 Seminarraum
  • Monday 08.04. 14:00 - 16:00 Seminarraum
  • Thursday 11.04. 14:00 - 16:00 Seminarraum
  • Monday 15.04. 14:00 - 16:00 Seminarraum
  • Thursday 18.04. 14:00 - 16:00 Seminarraum
  • Monday 22.04. 14:00 - 16:00 Seminarraum
  • Thursday 25.04. 14:00 - 16:00 Seminarraum
  • Monday 29.04. 14:00 - 16:00 Seminarraum
  • Thursday 02.05. 14:00 - 16:00 Seminarraum
  • Monday 06.05. 14:00 - 16:00 Seminarraum
  • Monday 13.05. 14:00 - 16:00 Seminarraum
  • Thursday 16.05. 14:00 - 16:00 Seminarraum
  • Thursday 23.05. 14:00 - 16:00 Seminarraum
  • Monday 27.05. 14:00 - 16:00 Seminarraum
  • Monday 03.06. 14:00 - 16:00 Seminarraum
  • Thursday 06.06. 14:00 - 16:00 Seminarraum
  • Monday 10.06. 14:00 - 16:00 Seminarraum
  • Thursday 13.06. 14:00 - 16:00 Seminarraum
  • Monday 17.06. 14:00 - 16:00 Seminarraum
  • Thursday 20.06. 14:00 - 16:00 Seminarraum
  • Monday 24.06. 14:00 - 16:00 Seminarraum
  • Thursday 27.06. 14:00 - 16:00 Seminarraum

Information

Aims, contents and method of the course

We present three selected topics in the area of applications of algebra. They are
algebra and symmetry, algebra and coding, and algebra and equations.
The emphasis of the first topic lies on group theory, of the second topic on
finite fields, and of the third topic on Groebner bases in polynomial rings of
several variables.

1.) 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.

2.) 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.

3.) 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.

Assessment and permitted materials

Benotung VU

Minimum requirements and assessment criteria

Knowledge of important 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

BMA

Last modified: Mo 07.09.2020 15:40