Math 5-385 Syllabus

Math 5-385 Fall 2001
Course Syllabus

MWF 11:15 AM
Vincent 364

Instructor: Professor Joel Roberts

Vincent 351
625-1076
e-mail: roberts@math.umn.edu
URL:http://www.math.umn.edu/~roberts
Office hours
(These may be changed if some variation would be more compatible with the students' schedules.)
- MW 1:25 p.m.
- Open lab hours, to be arranged.
  (Probably on Tuesday or Thursday)
- 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:

Algebra and geometry:
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. Some theory about varieties and ideals.
5. Introduction to projective algebraic geometry.
Use of computer packages:
- Matlab for visualization of implicitly defined curves.
- Maple for Gröbner basis calculations

Prerequisite:

Sophomore level linear algebra, and polynomials in several variables including partial derivatives -- for instance,
Math 2243/63 or Math 2373/74.

Required work:

Homework assignments (including small computer projects): About 2 assignments each 3 weeks.
Two midterm tests: Dates are Wednesday, October 24 and Wednesday, November 28
(Note the revised dates of both tests.)
Take-home exam/final project: Due Monday, December 17

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.