**Math 5-385 Fall 2008Course 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.}

- Office hours

**Text:** *Ideals, varieties and Algorithms*(**3**^{rd}
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
**R**² and surfaces and curves in**R**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, as time permits.

- Affine varieties (particularly curves in
- 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:

`Homework assignments`(including small computer projects): About 2 assignments each 3 weeks.

- Two midterm tests: Dates are
and*Wednesday, October 15**Wednesday, November 19*

- Take-home exam/final project: Due
*Tuesday, December 16*

**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:**

will be accepted until*Late homework*of the next Tuesday after thedue date, but*12 noon*be accepted after that time.*will not*

We can, however, drop missing assignments up to the equivalent of 1^{1}/_{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`

`
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