Universität Wien FIND

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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