Wintersemester 2010/2011
Prof. Franz Winkler
Dr. Günter Landsmann
Computeralgebra (326.017)
| Time: |
Tue 15:30 - 18:00 |
| Place: |
HS 13 |
| First Lecture: |
Tue 05.10.2010, |
HS 13 |
| Exam: |
Tue 25.01.2011, | 16:00 - 17:30 | in HS 17 |
A theoretical and practical introduction into the area of computer algebra will be presented.
In particular we deal with the constructive symbolic solution of systems of algebraic (i.e. polynomial)
equations. We will cover the theory of Gröbner bases, Euclid's algorithm for GDCs of polynomials, and the method of resultants.
The course will follow the appropriate chapters in:
| |
|
F. Winkler: Polynomial Algorithms in Computer Algebra, |
| |
|
Springer-Verlag Wien New York, 1996 |
| |
|
(ISBN 3-211-82759-5) |
Participants are expected to be acquainted with the basic notions in
algebra and algorithm theory.
Lecture mode:
The course is a combination (KV) of
lectures (VO) and
exercises (UE).
The
exercises consist of homework exercises and projects.
There will be
2 exercise sheets which will be available below in pdf-format.
A
project comprises a theme, problems, solutions, examples and an algorithm.
On October 12, after discussing the first bunch of exercises, the projects
will be allocated to groups of students, one project a group. The members of
each group are expected to work out the theme, compile the theory behind,
discuss examples and develop an algorithm capable of solving the corresponding
problems. All this should be summarized in a paper of 5 to 8 pages to be presented on
January 18 in a 15 minutes' talk by a group member.
| Time schedule: | Date | - | Type |
- | Topics |
| 05.10. | | VO | | Kap.1 What is Computer Algebra ? |
| | | | | Kap.2.1 introduction to Gröbner bases |
| | | | | Kap.2.2 Gröbner bases in Robotics |
| 12.10 | | UE | |
1. Exercise sheet, Project organisation |
| 19.10. | | VO | | Gröbner bases, Kap.2.3
|
| 09.11. | | VO | | Gröbner bases, Kap.2.3 |
| 16.11. | | VO | | Gröbner bases, Kap.2.3 |
| 23.11. | | VO | | Gröbner bases, Kap.2.4 |
| 30.11. | | UE | |
2. Exercise sheet |
| 07.12. | | VO | | GCD, Kap.3 |
| 14.12. | | VO | | GCD, Kap.3 |
| 11.01. | | VO | | Resultants, Kap.4 |
| 18.01. | | UE | | Project presentations |
| 25.01. | | VO | | EXAM (KLAUSUR) 16:00 - 17:30 in HS 17 |
| | | | | ohne Unterlagen / no books |
| | |
| |
Klausur-25012011-angaben.pdf |
| | | | |
Klausur-25012011-ergebnis.pdf |
