Algebra II

Spring Semester 2013



Instructor: Matt Kerr
Office: Cupples I, Room 114
e-mail: matkerr [at] math.wustl.edu
Office Hours: Tuesday/Thursday 12-1, and by appointment

Course Outline:

I. Galois Theory
II. Bilinear Forms and the Classical Groups
III. Representation Theory
IV. Commutative Rings
V. Categories and Homological Algebra (time permitting)

This is the second half of a year-long course which forms the basis for the Ph.D. qualifying examination in algebra.

Prerequisites: Math 5031, or permission of the instructor.

Class Schedule:

Lectures are on Monday, Wednesday and Friday, from 3-4 PM, in Cupples I Rm. 113. First class is Monday Jan. 14 and last class is Friday April 26. Spring Break is the week of March 11, and Monday Jan. 21 is a holiday.

Midterm Exam: Wednesday March 6 (in class) [solutions]
Final/Qualifying Exam: Monday May 6, 3-6 PM, in Rm. 199 (Cupples I). [solutions]


Assignments:

Problem Set 1 (due Monday Jan. 28) (solutions)
Problem Set 2 (due Monday Feb. 4) (solutions)
Problem Set 3 (due Monday Feb. 11) (solutions)
Problem Set 4 (due Monday Feb. 18) (solutions)
Problem Set 5 (due Monday Feb. 25) (solutions)
Problem Set 6 (due Monday Mar. 4) (solutions)
Problem Set 7 (not to hand in, but do over break)
Problem Set 8 (due Monday Mar. 25) (solutions)
Problem Set 9 (due Monday Apr. 1) (solutions)
Problem Set 10 (due Wed. Apr. 10) (solutions)
Problem Set 11 (due Wed. Apr. 17) (solutions)
Problem Set 12 (due Fri. Apr. 26) (solutions)

These will be collected on Mondays in class and returned by the end of the week. Solutions will also be posted and will include students' work. Please feel free to come to office hours to discuss problem sets.

Grader: Ryan Keast

Books:

Nathan Jacobson, Basic Algebra I (2nd Ed.); Dover

and the companion volume Basic Algebra II are the recommended textbooks, which means I will follow them or assign problems from them when possible.

There are many other excellent standard texts, including

D.J.H. Garling, A Course in Galois Theory; Cambridge Univ. Press,

Thomas Hungerford, Algebra; Springer-Verlag,

Serge Lang, Algebra; Springer-Verlag,

and

Joseph Rotman, Advanced Modern Algebra; Prentice-Hall.

Grading Policy:

Your final grade for the semester is determined as follows: HW 40%, midterm 20%, final exam 40%. I will drop the lowest two grades you receive on homework.

Homework and examination grades will be regularly updated on blackboard.