MATH 210A: MODERN ALGEBRA

RAVI VAKIL

Lectures: Tuesdays and Thursdays 11–12:15 in Room 380W.

Office hours: in 380-383M (third floor of the math building). Times to be announced.

Grade breakdown:

• Problem sets (7–8) 40%.

• In-class mid-term 20%.

• Final exam 40%.

Course webpage: http://math.stanford.edu/∼vakil/210/

This is the first course in a three-part sequence with the following description from the course guide: “Groups, rings, and fields, Galois theory, ideal theory. Introduction to algebraic geometry and algebraic number theory. Representations of groups and noncommutative algebras, multilinear algebra. Prerequisite: 120 or equivalent.”

We will focus on groups, rings, and fields (including Galois theory), covering roughly to the end of Chapter 5 in Rotman’s Advanced Modern Algebra, although not necessarily in order.

Date: Thursday, September 26.

Questions to ask Greg: Topics. Where do I start? Grader. Grading scheme. Number of problem sets, how hard. Sample ones to look at? (I have old quals.) Grade distribution. (mostly A’s?) Anything I’m forgetting? Is there administration I have to worry about?

Greg’s comments: Roughly 30–40 students. Ignore 3.7. Show existence of a free group? Discussion of finite abelian groups. Define split and semidirect product; Sylow theorems might be a good place for this. Sylow: give the usual order, not Rotman’s! Use it to classify small groups.

Week 1: O1, 3 Week 2: 8, 10 Week 3: 15, 17 Week 4: 22, 24 Week 5: 29, 31 Week 6: 5, 7 Week 7: 12, 14 Week 8: 19, 21 Week 9: 26, 28 Week 10: D3, 5

  E-mail address: vakil@math.stanford.edu