- Office hours: F 2-4
- Office: 219B LOM
Announcements
- Dec. 3: Office hours 2-4pm.
- Nov. 22: Office hours semi-cancelled. If I'm around, you can stop by, but no guarantees.
- Sep. 19: No class on Sep. 30 or Oct. 21. Make-up classes on Friday, Sep. 27 and Friday, Oct. 18 at 9:45-11:00am in 431 DL.
- Sep. 17: Starting this week, Wednesday office hours will be replaced by extended office hours on Friday.
Final exam
Here are solutions to the final exam.Homeworks
Homework is due most Mondays and the assignments will be posted here. Solutions or partial solutions to some of these assignments are available on request.
- Problem set 1, due Sep. 9, 2013.
- Problem set 2, due Sep. 16, 2013.
- Problem set 3, due Sep. 23, 2013.
- Problem set 4, due Wednesday, Oct. 2, 2013.
- Problem set 5, due Oct. 7, 2013.
- Problem set 6, due Oct. 14, 2013.
- Problem set 7, due Oct. 28, 2013.
- Problem set 8, due Nov. 4, 2013.
- Problem set 9, due Nov. 11, 2013.
- Problem set 10, due Nov. 20, 2013.
- Problem set 11 due the week of Dec. 2-6, 2013.
Schedule
The approximate schedule for future classes is given in the following table. All readings are from Eisenbud.
| Date | Reading | Topics |
| Aug. 28 | Ch. 0 (and 1) | origins of commutative algebra |
| Aug. 30 | 2.1 | localization and Hom |
| Sep. 4 | 2.2 | tensor products and flatness of localization |
| Sep. 9 | 2.3, 2.4 | radical, modules of finite length |
| Sep. 11 | 3.1, 3.2 | prime avoidence, associated primes |
| Sep. 16 | 3.3 | primary decomposition |
| Sep. 18 | none | localization of primary decomposition, Nullstellensatz |
| Sep. 23 | 4.1 | integrality and Nakayama's lemma |
| Sep. 25 | 4.2,4.4 | primes in integral extensions |
| Sep. 27 | 4.5 | proof of Nullstellensatz |
| Oct. 2 | 5.1 | finish Nullstellensatz, associated graded |
| Oct. 7 | 5.2, 5.3, 6.1 (optional), 6.2 | Artin-Reese Lemma, Krull Intersection Theorem, flatness, Tor |
| Oct. 9 | 6.3 (through Cor. 6.3), 6.5 | criterion for flatness, Rees algebra |
| Oct. 14 | 7.1, 7.2, 7.5 | completions |
| Oct. 16 | 7.6 | flatness of completion, maps from power series |
| Oct. 18 | 9.0, 10.0 | statement of Cohen structure theorem, Krull dimension, PIT |
| Oct. 28 | 10.1, 10.2 | systems of parameters, going down theorem |
| Oct. 30 | 10.3, 11.1 | regular local ring, DVRs |
| Nov. 4 | 11.2 | Serre's criterion, class group |
| Nov 6 | 11.6 | Krull-Akizuki theorem |
| Nov. 11 | 12 | Hilbert-Samuel polynomial |
| Nov. 13 | 13.1 | Noether normalization |
| Nov. 18 | 13.1 | Consequences of Noether normalization |
| Nov. 20 | 13.3 | finiteness of integral closure |
| Dec. 2 | 15.1, 15.2, 15.3 | monomials and division |
| Dec. 4 | 15.4, 15.8 | Gröbner bases |