# Difference between revisions of "742"

(New page: '''Math 742''' Commutative Algebra and Galois Theory Prof: [http://www.math.wisc.edu/~andreic Andrei Caldararu] Grader: [http://www.math.wisc.edu/~dummit/personal.html Evan Dummit] Ca...) |
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Grader's office hours: Monday 4pm. Late homework may be given directly to the grader, along with either (i) the instructor's permission, or (ii) a polite request for mercy. | Grader's office hours: Monday 4pm. Late homework may be given directly to the grader, along with either (i) the instructor's permission, or (ii) a polite request for mercy. | ||

− | This course, the second semester of the introductory graduate sequence in algebra, will cover the basic aspects of commutative ring theory and Galois theory. The textbook we'll use for the Commutative Algebra portion will be Atiyah-Macdonald "Commutative Algebra". For Galois Theory I plan on using | + | This course, the second semester of the introductory graduate sequence in algebra, will cover the basic aspects of commutative ring theory and Galois theory. The textbook we'll use for the Commutative Algebra portion will be Atiyah-Macdonald "Commutative Algebra". For Galois Theory I plan on using Emil Artin's notes which are available [http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.ndml/1175197041 here,] but I may change my mind before we start on it. |

==SYLLABUS== | ==SYLLABUS== |

## Revision as of 15:24, 28 January 2013

**Math 742**

Commutative Algebra and Galois Theory

Prof: Andrei Caldararu

Grader: Evan Dummit

Caldararu's office hours: Monday 1:30pm.

Grader's office hours: Monday 4pm. Late homework may be given directly to the grader, along with either (i) the instructor's permission, or (ii) a polite request for mercy.

This course, the second semester of the introductory graduate sequence in algebra, will cover the basic aspects of commutative ring theory and Galois theory. The textbook we'll use for the Commutative Algebra portion will be Atiyah-Macdonald "Commutative Algebra". For Galois Theory I plan on using Emil Artin's notes which are available here, but I may change my mind before we start on it.

## SYLLABUS

In this space we will record the theorems and definitions we covered each week, which we can use as a list of notions you should be prepared to answer questions about on the Algebra qualifying exam. The material covered on the homework is also an excellent guide to the scope of the course.

**WEEK 1**:

Commutative rings and homomorphisms, integral domains, fields. Ideals, prime and maximal. Existence of maximal ideals. Local rings. Some geometric pictures (Spec and Specm). Nilradical.

Below you will find a repository of homework problems.

## HOMEWORK 1 (due Feb 4)

Atiyah-Macdonald, page 10: 1, 2, 6, 10, 12, 15, 16, 17, 18, 21