Calendar
Calendar
| Date | Topic | Section | Notes | Due |
|---|---|---|---|---|
| Wednesday, August 25 | Intro to course. What is algebra? What is this course about? | Aug 25 | ||
| Friday, August 27 | Guest speaker: David Cox | |||
| Monday, August 30 | Homework 0 | |||
| Wednesday, September 1 | Polynomials and Affine Space | 1.1 | Sept 1 | |
| Friday, September 3 | Affine Varieties. | 1.2 | Sept 3 | |
| Monday, September 6 | Labor Day. No class | |||
| Tuesday, September 7 | Homework 1 | |||
| Wednesday, September 8 | Parametrizations of Affine Varieties. | 1.3 | Sept 8 | |
| Friday, September 10 | Examples of parametrized varieties | 1.3 | Sept 10 | |
| Wednesday, September 15 | Ideals | 1.4 | Sept 15 | Homework 2 |
| Friday, September 17 | Ideals. Polynomials of One Variable | 1.4-5 | Sept 17 | Term paper initial topic proposal |
| Wednesday, September 22 | Ideals and varieties | 1.4 | Sept 22 | Homework 3 |
| Friday, September 24 | Gröbner bases: Introduction. Orderings on Monomials. | 2.1-2 | Sept 24 | |
| Wednesday, September 29 | Orderings on Monomials. | 2.2-4 | Sept 29 | Homework 4 |
| Friday, October 1 | Division Algorithm. | 2.3 | Oct 1 | Term paper reading report |
| Wednesday, October 6 | Computer Algebra Systems. Monomial Ideals and Dickson’s Lemma. Hilbert Basis Theorem. | 2.4-2.5 | Oct 6 | Homework 5 (WebWork) |
| Friday, October 8 | Properties of Gröbner Bases. Buchberger’s Algorithm. | 2.5-2.7 | Oct 8 | |
| October 11-15 | Midterm exam | |||
| Wednesday, October 13 | Noetherian rings. Buchberger’s Criterion, part 1 | 2.5-2.6 | Oct 13 | |
| Friday, October 15 | Buchberger’s Criterion, part 2 | 2.6 | Oct 15 | |
| Wednesday, October 20 | Buchberger’s Algorithm | 2.7 | Oct 20 | |
| Friday, October 22 | Elimination Theory: Elimination and Extension Theorems | 3.1 | Oct 22 | |
| Wednesday, October 27 | Elimination Theorem. Extension of partial solutions | 3.1 | Oct 27 | Homework 6 (WebWork) |
| Friday, October 29 | Extension Theorem. | 3.1 | Oct 29 | |
| Wednesday, November 3 | Geometry of Elimination | 3.2 | Nov 3 | Homework 7 |
| Friday, November 5 | Implicitization | Nov 5 | Term paper first draft | |
| Wednesday, November 10 | Intersections of ideals. Resultants | 3.6 | Nov 10 | Homework 8 |
| Friday, November 12 | Resultants, discriminants | 3.6 | Nov 12 | |
| Wednesday, November 17 | Discriminants. Nullstellensatz | 4.1 | Nov 17 | Homework 9 |
| Friday, November 19 | Weak Nullstellensatz | 4.1 | Nov 19 | |
| Tuesday, November 23 | Term paper second draft | |||
| Wednesday, November 24 | Thanksgiving Holiday. No class | |||
| Friday, November 26 | Thanksgiving Holiday. No class | |||
| Wednesday, December 1 | Hilbert’s Nullstellensatz | 4.2 | Dec 1 | |
| Friday, December 3 | Ideal-Variety Correspondence | 4.3 | Dec 3 | |
| Wednesday, December 8 | Operations on ideals and varieties | Dec 8 | ||
| Friday, December 10 | Last day of classes | Term paper final version | ||
| Wednesday, December 15 | Final exam, 12pm-2pm | |||
| Tuesday, December 21 | Grades due |