Class: Tue 3:15 Thu 2:15 Fri 10:00 Williams Theatre
Office hours: Tue 4:15 5:45, Fri 11:00-12:30 Richard Berry 169
| Lecture | Date | Summary | Homework | Suggested reading |
| 1 | 01/03 | Tensor product of modules | Review definition, brush up on categories and functors | Wikipedia or Bourbaki, MacLane (categories), Taufik also recommends the book by Goldblatt on topoi. |
| 2 | 03/03 | Tensor products of modules, continued | Work through the list of examples from class | |
| 3 | 04/03 | Symmetric and exterior powers | ||
| 4 | 08/03 | Determinants | Consolidate our definition with the one you knew | defintion of determinant in linear algebra |
| 5 | 10/03 | Manifolds, tangent and cotangent vectors, 1-forms | ||
| 6 | 11/03 | A slower review of the material of Thursday's class | Spivak, Galot-Hulin-LaFontaine | |
| 7 | 15/03 | Kaehler differentials | Matsumura | |
| 8 | 17/03 | Kaehler differentials, continued | Matsumura | |
| 9 | 18/03 | prime ideals and maximal ideals | Atiyah and Macdonald | |
| 10 | 22/03 | Jacobson and Nilradical | Atiyah and Macdonald | |
| 11 | 24/03 | The prime spectrum of a ring | Assignment 1 due Tuesday 12/04 Solutions | Atiyah and Macdonald |
| 12 | 05/04 | Localisation | Atiyah and Macdonald | |
| 13 | 07/04 | Local properties | Atiyah and Macdonald | |
| 14 | 08/04 | Localisation, contraction and extension of ideals | Atiyah and Macdonald | |
| 15 | 12/04 | Localisation, contraction and extension of ideals | Atiyah and Macdonald | |
| 16 | 14/04 | Localisation, contraction and extension of ideals | Atiyah and Macdonald | |
| 17 | 15/04 | Primary ideals | Atiyah and Macdonald | |
| 18 | 19/04 | Primary decomposition | Atiyah and Macdonald | |
| 19 | 21/04 | Primary decomposition | Atiyah and Macdonald | |
| 20 | 22/04 | Primary decomposition, first uniqueness theorem | Atiyah and Macdonald | 21 | 26/04 | Primary decomposition, second uniqueness theorem | Atiyah and Macdonald |
| 22 | 28/04 | Integral dependence | Assignment 2 due Tuesday 10/05 in class | Atiyah and Macdonald |
| 23 | 29/04 | Going-up | Atiyah and Macdonald | |
| 24 | 03/05 | Starting to go down | Atiyah and Macdonald | |
| 25 | 05/05 | Going down | Atiyah and Macdonald | |
| 26 | 06/05 | Going down | Atiyah and Macdonald | |
| 27 | 10/05 | Zariski's Lemma implies the Nullstellensatz | Wikipedia | |
| 28 | 12/05 | Valuation rings | Atiyah and Macdonald | |
| 29 | 13/05 | Valuation rings | Atiyah and Macdonald | |
| 30 | 17/05 | Proof of Zariski's Lemma | Assignment 3, due on Friday, 27 May, consists of the exercises 1, 10 -- 14 and 28 in Chapter 5 of Atiyah Macdonald. | Atiyah and Macdonald |