Wintersemester 2004/2005

**Vorlesungsankündigung - Survey of Lectures**

Franz Winkler

Franz Winkler

Time: Tue 15:30 - 18:00, Place: HS 14

first lecture: October 5

A theoretical introduction into the area of computer algebra is presented. Some of the main topics will be algorithms for basic algebraic domains (like integers, polynomials, finite fields, algebraic extension fields), computation by homomorphic images using the Chinese remainder algorithm, greatest common divisors of polynomials, factorization of univariate polynomials over finite fields, and the basic theory of Gröbner bases for polynomial ideals.

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. The course is a combination of lecture and exercises (KV). The exercise part will be supervised by Dr. Günter Landsmann.

Time: Thu 14.30 - 16.00 Place: Seminarraum Hagenberg

first meeting: October 7

We discuss new results (by our group and also by others) in computer algebra, symbolic computation, computer aided geometric reasoning, and related topics. Participants give lectures in the seminar, and sometimes guest speakers are invited to present their work.

Time: Mon 13.30 - 14.30 (see announcements), Place: Seminarraum Hagenberg

Invited guest speakers present their research work in symbolic computation.

We read and discuss recent publications in computer algebra.

Implementation of algorithms in computer algebra and constructive algebraic geometry.

I discuss ongoing work with my doctoral and diploma students. In my working group students are encouraged to work out diploma and phd theses on topics such as computer algebra, algebraic geometry, computer aided geometric design, and symbolic methods in analysis.