**Instructor:** Brian Osserman

**Lectures:** MWF 11:00-11:50am, MSB 3106

**CRN:** 52761

**Office:** MSB 3218, e-mail:

**Office Hours:** M 10-11, W 3-4

**TA:** Chris Berg MSB 3206 and Eddie Kim MSB 2131

**Discussion:** R 11:00-11:50am, Veihmeyer 116

**TA Office Hours:** Chris R 2-3, Eddie W 10:00-11:00

**Prerequisites:** 250AB or permission of instructor

**Required Text:** Dummit and Foote, *Abstract Algebra*

**Syllabus:** We will begin with a rapid review of basic
group theory, and then move on to more advanced topics in group
theory, including free groups and presentations, the Sylow theorems, the
Jordan-Holder theorem, solvable groups, semidirect products, and profinite
groups. We then cover field theory and Galois theory,
and if time allows, we will also discuss supplementary topics in
commutative algebra such as Grobner bases, Artin rings, and Dedekind
domains.

**Grading:** 100% homework

**Homework:** Homework will be assigned roughly weekly

Homework assignments and supplementary notes will be posted here as the course progresses. We will not necessarily follow the textbook closely, so attendance at lecture is strongly encouraged.

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

- Problem set #1, due 4/11.
- Problem set #2, due 4/18.
- Problem set #3, due 4/25.
- Problem set #4, due 5/2.
- Problem set #5, due 5/9.
- Problem set #6, due 5/16.
- Problem set #7, due 5/23.
- Problem set #8, due 5/30.

I will post here supplemental lecture notes on topics which are not covered in the textbook.

- 4/18: Free and amalgamated products
- 4/21-23: Inverse limits and profinite groups
- 5/28: Infinite Galois theory
- 5/30-6/4: Groebner bases