|class ||Tuesday || 11:45-13:15h, 48-438||class ||Thursday || 11:45-13:15h, 48-438
||tutorial ||Monday || 10:00-11:30h, 48-436
Monomial orderings, division with remainder, normal forms, standard bases, Bucherger's criterion, Mora's algorithm, ideal / module operations
(membership, radicalmembership, intersection, quotient, saturation, elimination, ...),
free resolutions, Hilbert's syzygy theorem, Noether normalization, primary decomposition, Hilbert series/polynomial.
The tutorial will be held by Cornelia Rottner. The deadline for regular signups has ended. For late signups, please contact Cornelia Rottner.
There will be weekly homework assignments posted on this page. Typically assignments will be posted on Thursday, and are due on the next Thursday by 10:00. Please hand in your solutions
by the respective due date in the office of Cornelia Rottner, room 48-427. You may (and you are encouraged to) turn in your homework in teams of 3. However, each of you needs to be able to present your
team's solutions during the tutorial.
In order to obtain an Übungsschein you need to actively participate in the tutorial and achieve a total homework score of at least 40%.
Active participation means regular attendance and presenting a solution of a homework problem (at least once).
For credit points you need to pass an oral exam after the end of the semester.
- G.-M. Greuel, G. Pfister: A Singular Introduction to Commutative Algebra
- D. A. Cox, J. Little, D. O'Shea: Ideals, Varieties, and Algorithms
- H. Schenck: Computational Algebraic Geometry
- W. Decker, Ch. Lossen: Computing in Algebraic Geometry - A Quick Start using Singular