Math 5385 (Intro to Computational Algebraic Geometry)
MWF 11:15 AM
Vincent 311

Instructor: Professor Joel Roberts

• Vincent 351
• 625-1076
• e-mail: roberts@math.umn.edu
• URL: http://www.math.umn.edu/~roberts
• Office hours
• MW 2:30 p.m.
• Friday 9:05 a.m.
• Tuesday and/or Thursday office hours may be set up later.
  Also, if the established hours don't fit your schedule, please get in touch with me
  (625-1076 or roberts@math.umn.edu) to arrange an appointment.

Text: Ideals, varieties and Algorithms(2^nd edition), by Cox, Little, and O'Shea. Springer, 1997

Class webpage: http://www.math.umn.edu/~roberts/math5385/
Check this page regularly for important information about the class
and for software downloads and instructions.

Subject matter:

1. Affine varieties (particularly curves in ² and surfaces and curves in ³), parametrizations, ideals.
2. Monomial orderings, division algorithm, Gröbner bases and basic properties.
3. Applications of Gröbner bases: elimination theory, singular points, envelope of a family of curves, etc.
4. Introduction to some theory in algebraic geometry.
5. Polynomial and rational functions on a variety.

• Use of computer packages:
  • Matlab for visualization of implicitly defined curves.
  • Maple for Gröbner basis calculations

Prerequisite:

• Homework assignments (including small computer projects): About 2 assignments each 3 weeks.
   
• Two midterm tests: Tentative dates are Wednesday, October 18 and  and Friday, December 1
  (Note the revised test dates)
   
• Take-home exam/final project: Due Monday, December 18
  

Grading policies:

• Each midterm test will count for 20% of the grade.
• The the take-home final and project will count for 30% of the grade.
• Remaining homework will count for 30% of the grade.

Other policies:

• Late homeworkwill be accepted until the third class meeting after the due date, but will notbe accepted after that time.
  We can, however, drop up to 2 missing assignments or the 2 lowest homework assignment grades.
   
• Exams must be taken on the scheduled date except for serious emergencies, for example illness that requires medical attention.
  Prompt notification is required.
   
• An Incomplete is given only when most of the required work for the course has been completed with passing grades and there is a reasonable expectation that the missing work can be made up.
   

Comments and questions to:  roberts@math.umn.edu

Back to the class homepage.