Computer Science Department - Technische Universität München Chair for Efficient Algorithms

Computational Algebra II (WS 05/06)

• Lecturer:
  Dr. Peter Ullrich

• Area:
  4 lectures per week in area III (Theoretical Computer Science)
  advanced course, topic algorithms

• Time and Place:
  Mon 12:15 - 13:45, lecture hall MI 00.06.011 (Hörsaal 3)
  Tue 16:15 - 17:45, lecture hall MI 00.04.011 (Hörsaal 2) Tue, 17.01. and 31.01. in MW0350 !!!

• Exercises:
  none

• Audience:
  graduate students of computer science or mathematics
  students with computer science as minor

• Prerequisites:
  1st and 2nd year courses.
  Knowledge of ''Computational Algebra I (SS'05)'' would be helpful (or e.g. chap.1-3 in [CLO]).
  In the first lesson, however, I will give a brief summary of the main results of part I.

• Recommended for:
  In-depth knowledge in topic Algorithms

• Contents:
  Complexity of Groebner Bases, improvements of Buchberger's algorithm,
  syzygies, Groebner Bases for modules, homogeneous Groebner Bases and projective geometry,
  multivariate resultants, dimension and Hilbert function.

• Related and Advanced Lectures:
  Computational Algebra I

• Lecture Notes:
  Lecture Notes (07/02/06).

• References:
  [CLO] Cox, Little, O'Shea: Ideals, Varieties and Algorithms, Springer Verlag
  Mishra: Algorithmic Algebra, Springer Verlag
  Greuel, Pfister: A Singular Introduction to Commutative Algebra, Springer Verlag
  Becker, Weispfenning: Gröbner Bases, GTM 141, Springer Verlag
  Kreuzer, Robbiano: Computational Commutative Algebra 1, Springer Verlag
  Cox, Little, O'Shea: Using Algebraic Geometry, GTM 185, Springer Verlag
  Winkler: Polynomial Algotithms in Computer Algebra, Springer Verlag

• Office Hours:
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