In the winter semester 2026/27, I will read a two-hours lecture course

Computer Algebra B

(with tutorials) for master students. It continues the course Computer Algebra A from the summer term, but is essentially independent of it. On the one hand, the course will introduce some theoretical concepts from commutative algebra and algebraic geometry like the interconnection between polynomial ideals and varieties (the zero sets of polynomials). On the other hand, algorithms for effective computations with ideals and for solving polynomial equations are covered. As fundamental tools for such tasks Gröbner bases will be studied. Prerequisities are only basic notions from algebra like rings and ideals. Further information can be found in Moodle.

Used Literature:

• W.W. Adams, P. Loustaunau: An Introduction to Gröbner Bases, AMS
• T. Becker, V. Weispfenning: Gröbner Bases: A Computational Approach to Commutative Algebra, Springer
• D.A. Cox, J. Little, D. O'Shea: Ideals, Varieties, and Algorithms, Springer
• R. Fröberg: An Introduction to Gröbner Bases, Wiley
• M. Kreuzer, L. Robbiano: Computational Commutative Algebra 1, Springer

Time/Location: Tuesday 11:00-13:00, Room 1252
Beginn: 20. October

Tutorials:

The tutorials are organised by Arne Jenß.