Fall 2015-16

**Instructor:** Dan Abramovich

**Class meeting:** Mondays, Wednesdays and Fridays at 11:00-11:50am in Kassar 105

**Office:** Kassar 118

**Telephone:** (401) 863 7968

**E-mail:** `abrmovic ( at ) math (period) brown (dot) edu`

**Web site:**
`http://www.math.brown.edu/~abrmovic/MA/f1516/251/index.html`

**Preliminary Office hours:** Monday, 2:00-3:00, Wednesday and Friday 10:00-10:50

**Text:** ALGEBRA by Serge Lang, 3rd rev. ed. 2002. Corr. 4th printing, 2005.
ISBN: 0-387-95385-X

**Topics:** Groups and group actions; Categories and functors; Rings
and modules; Fields and Galois theory.

** Homework:**

problem set 1, due: Monday Sep 21.

problem set 2: Lang Chapter 1 ex 12, 14, 28, 29, 32, 39, 41, 42,
46. due: Friday Oct 2.

problem set 3, due: Friday Oct 9.

**Exposition of modules ofver a PID.** due: Friday Nov 6.

problem set 4, due: Friday Nov 13.

problem set 5: Lang Chapter VI ex. 1aefhkmn, 3ac, 9, due: Friday Nov 20.

problem set 6: Lang Chapter VI ex. 17,18,19,22,35,37,44,45, due: Monday November 30.

Presentations:

Daniel Keliher's notes on
the simplicity of the alternating group.

Will Kochanski's notes on
the Jordan-Holder theorem.

Brad Benz's notes on
the simplicity of PSL2(F).

Kavi Duvvoori's notes on
the simplicity of PSLn(F).