Math 5-385 Fall 2008
Course Syllabus
MW 3:35 p.m. to 4:50 p.m.
Vincent Hall 206
Instructor: Professor Joel Roberts
- Vincent 351
- 625-1076
- e-mail:
roberts@math.umn.edu
- URL:
http://www.math.umn.edu/~roberts
- Office hours, etc.:
- Office hours:
- Monday 1:25 p.m. to 2:15 p.m.
- Tuesday 2:30 p.m. to 3:20 p.m.
- Wednesday 11:15 a.m. to 12:05 p.m.
- Open lab hours, to be arranged when needed.
- 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.
{And I'm often able to answer e-mails.}
Text: Ideals, varieties and Algorithms(3rd
edition), by Cox, Little, and O'Shea. Springer, 2007
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:
- Affine varieties (particularly curves in R² and surfaces
and curves in R³), parametrizations, ideals.
- Monomial orderings, division algorithm, Gröbner bases
and basic properties.
- Applications of Gröbner bases: elimination theory, singular points,
envelope of a family of curves, etc.
- Some theory about varieties and ideals.
- Other topics, as time permits.
- Use of computer packages:
- Matlab for visualization of implicitly defined curves,
and parametrically defined surfaces.
- 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:
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 homework will be accepted until 12 noon
of the next Tuesday after thedue date, but will not be accepted
after that time.
We can, however, drop missing assignments up to the equivalent of
11/2
average size assignments or a comparable number of your lowest homework grades.
- Exams must be taken on the scheduled date except for serious
emergencies or unavoidable absence.
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.