MATH 434: Algebraic Geometry and Groebner Bases

SPRING 2007

Instructor: Professor Lauren Rose

Office: Albee 305, x 7362

Class Meetings: T/Th 10:30-11:50, Albee 106

Office Hours: TBA

Text: Ideals, Varieties and Algorithms, 2^nd edition, by Cox, Little and O’Shea

Course Requirements: Your grade will be based on homework, presentations, attendance, and class participation.

Homework: Homework problems will be discussed in class, and several proofs will be handed in each week.
Presentations: In addition to presenting homework problems at the board and material from the book, there will be 1 major presentation 30 minute lecture and a 3-5 page written report. For the project, you will present new material from the book that we won’t cover in class. Presentations will take place during the last few of weeks of the semester, and may be done alone or in pairs.
I expect you to read the textbook on a regular basis, and to become comfortable using Mathematica or another computer algebra system.

MATH 434 Assignments, Spring 2007

Assignment		Problems for class discussion due		Hand in Due
1	Read 1.1. Read the proof of Proposition 5 1.1: 2	2/1		2/1
2	Read 1.2 and 1.3 1.2: 1,2*, 4, 5, 6, 9, 11 1.3: 1, 2, 3, 4	2/6		2/8
3	Read 1.4 1.3: 6, 12, 13 1.4: 1, 3, 4, 5, 6, 7, 8*, 9	2/13		2/15
4	1.5: 3, 5, 8, 9 2.1: 2b, 3b, 4* Find a polynomial in one variable, f , such that < f > = < x+1, x-1 >	2/20		2/22
5	Read 2.2 - 2.4 2.2: 2, 3, 4, 10, 11 2.3: 1, 2, 3	2/27		3/1
6	2.3: 5 2.4: 3, 8, 11 2.5: 1, 4, 7	3/6		3/8
7	2.5: 13, 17 2.6: 2, 4, 5, 9	3/13		3/15
8	2.6: 3,12 2.7: 2, 3, 9, 11	3/20		3/22
9	2.7: 1, 3, 5, 7, 11a	3/27		3/29
Spring Break	Spring Break		Spring Break
10		4/11		4/13
11		4/18		4/20
12		4/25		4/27
13		5/1		5/3
	Extra/Presentations	5/8	Presentations	5/10
	Presentations	5/16	Presentations	5/17
	Presentations/Final exam due	5/22