| Date |
Topic |
Book Sections |
Homework/Additional Files |
| Aug 22 |
Introduction to Algebraic Geometry |
|
Homework #1 -- Due 8:30 am on Aug 29 |
| Aug 27 |
Ideals and varieties |
Section 3.1 |
|
| Aug 29 |
Ideals and varieties |
Section 3.1 |
|
| Sep 3 |
Grobner bases |
Section 2.1 |
Homework #2 -- Due 8:30 am on Sep 10 |
| Sep 5 |
Grobner bases |
Sections 2.1 and 2.2 |
|
| Sep 10 |
Normal forms and Hilbert's basis theorem |
Sections 2.3 and 2.4 |
|
| Sep 12 |
Buchberger criterion |
Section 2.5 |
Homework #3 -- Due 8:30 am on Sep 19 |
| Sep 17 |
Zariski topology and morphisms |
Sections 3.2 and 3.3 |
|
| Sep 19 |
Elimination and graphs |
Sections 4.1 |
|
| Sep 24 |
Eliminating orders and rational maps |
Sections 4.1 and 3.4 |
Homework #4 -- Due 8:30 am on Oct 1 |
| Sep 26 |
Rational maps and elimination |
Section 4.2 |
|
| Oct 1 |
Joins |
Section 4.3 |
|
| Oct 3 |
Scrolls and resultants |
Sections 4.3 and 5.1 |
|
| Oct 8 |
Resultants and elimination theory |
Sections 5.1, 5.2, and 5.3 |
Midterm Exam Available |
| Oct 10 |
Fall Break |
|
|
| Oct 15 |
Irreducible varieties |
Sections 6.1 and 6.2 |
Midterm Exam Due at 8:30 am |
| Oct 17 |
Intersection and field extensions |
Sections 6.4 and 6.5 |
|
| Oct 22 |
Nullstellensatz |
Section 7.1 |
Homework #5 -- Due 8:30 am on Oct 31 |
| Oct 24 |
Real Nullstellensatz and Positivstellensatz |
|
|
| Oct 29 |
Radical ideal membership and prime decomposition |
Sections 7.6 and 8.1 |
|
| Oct 31 |
Primary decomposition and quotients |
Sections 8.2 and 8.3 |
|
| Nov 5 |
Saturation and projective space |
Sections 8.2 and 9.1 |
Homework #6 -- Due 8:30 am on Nov 12 |
| Nov 7 |
Homogenization and projective varieties |
Sections 9.2 and 9.3 |
|
| Nov 12 |
Homogenization and affine patches |
Section 9.4 |
|
| Nov 14 |
Projective Nullstellensatz |
Section 9.5 |
|
|
| Nov 19 |
Morphisms and products |
Sections 9.6 and 9.7 |
Homework #7 -- Due 8:30 am on Nov 26 |
| Nov 21 |
Projective elimination theory |
Chapter 10 |
|
| Nov 26 |
Hilbert function and polynomial |
Sections 12.1 and 12.2 |
|
| Nov 28 |
Thanksgiving Day |
|
Homework #8 -- Due 8:30 am on Dec 5 |
| Dec 3 |
Invariants and Bezouts Theorem |
Sections 12.3, 12.4, and 12.6 |
|
| Dec 5 |
Invariants and Bezouts Theorem |
Sections 12.3, 12.4, and 12.6 |
|
|
| Dec 17 |
Final Exam: 8 - 11 am |
|
|
