| Class Number |
Date |
Sections in Book |
Brief Description |
| 1 |
Friday, 4/2 |
1.1 - 1.3 |
Course Overview, Polynomial Rings, Affine Varieties |
| 2 |
Monday, 4/5 |
1.4 - 2.1 |
Ideals, Division with Remainder in F[x], The Maps V and I |
| 3 |
Wednesday, 4/7 |
2.2 - 2.3 |
Monomial Orderings, Division with Remainder in k[x_1,...,x_n] |
| 4 |
Friday, 4/9 |
2.4 - 2.5 |
Monomial Ideals, Dickson's Lemma, Hilbert Basis Theorem |
| 5 |
Monday, 4/12 |
2.5 - 2.6 |
Noetherian Rings, Gröbner Bases |
| 6 |
Wednesday, 4/14 |
2.7 - 2.8 |
Computing Gröbner Bases, Reduced Gröbner Bases, Applications |
| 7 |
Friday, 4/16 |
2.9, 3.1 - 3.2 |
The Elimination and Extension Theorems |
| 8 |
Monday, 4/19 |
3.2 - 3.3 |
The Closure Theorem, Implicitization |
| 9 |
Wednesday, 4/21 |
3.4 - 3.5 |
Singular Points, Proof of the Extension Theorem |
| 10 |
Friday, 4/23 |
4.1 |
Weak Nullstellensatz |
| 11 |
Monday, 4/26 |
4.1 - 4.2 |
Strong Nullstellensatz, UFDs and GCDs |
| 12 |
Wednesday, 4/28 |
4.3 - 4.4 |
Operations on Ideals and Varieties |
| 13 |
Friday, 4/30 |
4.4 - 4.5 |
Colon, Prime, and Maximal Ideals in Polynomial Rings |
| 14 |
Monday, 5/3 |
4.6, 4.8 |
Decomposing Varieties and Ideals |
| 15 |
Wednesday, 5/5 |
5.1 - 5.2 |
Polynomial Mappings, Quotients of Polynomial Rings |
| 16 |
Friday, 5/7 |
5.3 |
Computing in Quotients, Vector Spaces and Algebras |
| 17 |
Monday, 5/10 |
5.3 |
Varieties and Quotients of Polynomial Rings |
| 18 |
Wednesday, 5/12 |
5.4 |
The Coordinate Ring of a Variety, Isomorphic Varieties |
| 19 |
Friday, 5/14 |
5.4 |
The Coordinate Ring of a Variety, Isomorphic Varieties, Part 2 |
| 20 |
Monday, 5/17 |
5.5 |
Rational Functions between Varieties, Function Fields |
| 21 |
Wednesday, 5/19 |
- |
Algebra and Computability |