Math 5-385 Fall 2006
Course Syllabus
Last update {office hours} on September 7, 2006
MW 3:35 p.m. to 4:50 p.m.
Vincent Hall 364
Instructor: Professor Joel Roberts
- Vincent 351
- 625-1076
- e-mail:
roberts@math.umn.edu
- URL:
http://www.math.umn.edu/~roberts
- Office hours
- Office hours:
- Tuesdays, 2:30 to 3:20 p.m.
- Wednesdays, 9:30 to 11 a.m. and 1:25 to 2:45 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(2nd 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:
- Affine varieties (particularly curves in
2 and surfaces and curves in
3), 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, such as envelopes, tangent cones, etc.
{Based partly on material in the text,
and partly on handouts
which also will be posted on the class webpage.}
- 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:
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 the third class
meeting after the due date, but will not be 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.