Prof. Franz Winkler

Short Description

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.

In the exercise session (Übungen) the students will have to solve both theoretical problems and practical problems with the help of some computer algebra system.

Exercise Problems

• Exercise sheet 0 (Postscript)
• Exercise sheet 1 (Postscript)
• Exercise sheet 2 (Postscript)
• Exercise sheet 3 (Postscript)
• Exercise sheet 4 (Postscript)
• Exercise sheet 5 (Postscript)
• Exercise sheet 6 (Postscript)
• Exercise sheet 7 (Postscript)
• Exercise sheet 8 (Postscript)

Grades for exercise session (Postscript)

Final Exam (Vorlesungsklausur)

• 28 January 2003, 16:15 - 17:45, T 711
• books allowed, no computers
• Results of Final Exam (Postscript)