Math 250B - Algebra
Winter 2011

Instructor: Brian Osserman

Lectures: MWF 10:00-10:50, Physics 148.

CRN: 30184

Office: MSB 3218, e-mail:

Office Hours: W 11:00-12:00, Th 1:00-2:00

Prerequisites: Math 250A

Textbook: Lang, Algebra

Syllabus: The three main topics for the quarter will be tensor products, representation theory, and field theory. See also the department syllabus.

TA: Patrick Dragon

Discussion: Tu 10:00-10:50, MSB 2112

TA Office Hours: Tu 1:00-2:00, Th 2:00-3:00, in MSB 2145

Grading: 50% homework, 20% midterm, 30% final exam

Homework: Problem sets assigned weekly


Welcome to Math 250B: Algebra

Aside from containing many subfields in its own right, algebra is of fundamental importance in many other areas of mathematics, including number theory, algebraic geometry, algebraic topology, and representation theory. We will begin with the subject of tensor products, which are important in all of the above fields, as well as in differential geometry (and by extension, general relativity). We will then move on to the basics of representation theory, and finally we will cover the theory of algebraic field extensions.


Lecture notes

I will post notes here to supplement Lang as seems appropriate.

  • Semisimplicity: A self-contained exposition of the material we covered from the chapter on semisimplicity.
  • A Galois theory example: The lattices of subgroups and intermediate fields for the splitting field of x2-2 over Q.


Problem sets

Problem sets will be posted here each Friday, due the following Friday in class. You are encouraged to collaborate with other students, as long as you do not simply copy their answers.


Exams

There will be one in-class midterm exam, on Friday, February 4. The final exam is scheduled for Friday, March 18 1:00-3:00 PM.