Math 333: Topics in Abstract Algebra: Computational Algebraic Geometry
This syllabus is incomplete and tentative, and will be superseded by later versions as the course evolves. Details on assignments can be found on the assignments webpage.
| Week and Date |
Topic | Notes |
| 1: 9/6 |
Th: Rings, ideals, quotients, varieties |
Lect 1 |
| 2: 9/11-13 |
Tu: Radical ideals, varieties Th: Maximal/prime, field/domain |
Lect 1 HW due |
| 3: 9/18-20 |
Tu: Topology, Zariski topology Th: General points, dimension |
Lect 2 HW due |
| 4: 9/25-27 |
Tu: Maps: regular, rational Th: Maps: regular, rational |
Lect 3 HW due Topic |
| 5: 10/2-4 |
Tu: Products of rings, Making new varieties from old Th: Differentials, tangent space |
Lect 4,5 HW due |
| 6: 10/9-11 |
Tu: No class: fall break Th: Sheaves |
Lect 6 HW due |
| 7: 10/16-18 |
Tu: Sheaves, projective varieties Th: Projective varieties |
Lect 6-7 HW due Outline |
| 8: 10/23-25 |
Tu: Degree, Bezout theorem Th: Special maps |
Lect 8 HW due |
| 9: 10/30-11/1 |
Tu: Divisors Th: Cycles/Intersection theory |
Lect 9, 10 HW due |
| 10: 11/6-8 |
Tu: Cycles/intersection theory Th: Schemes---definition |
Lect 10, 11 HW due Draft |
| 11: 11/13-15 |
Tu: Schemes and varieties Th: Schemes and not varieties |
Lect 12, 13 HW due |
| 12: 11/20-22 |
Tu: Review schemes Th: No class: Thanksgiving |
HW due |
| 13: 11/27-29 |
Tu: Special topic: schemes or Grobner bases Th: Special topic: schemes or Grobner bases |
HW due Practice |
| 14: 12/4-6 |
Tu: Student presentations Th: Student presentations |
|
| 15: 12/11-13 |
Tu: Student presentations Th: Student presentations |