- 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 |