# 21-238: Math Studies Algebra II, Spring 2017

Lectures MWF 3:30 - 4:20 in SH 208

## Course Description

We will study modules, vector spaces, matrices, inner product spaces, and aspects of representation theory. And maybe some other stuff -- if you have something in particular that you'd like to hear more about, or have a particular reason to be interested in algebra, let me know and we'll see if we can squeeze it in.
## Textbook:

*Abstract Algebra, 3rd Edition* by Dummit and Foote.
## Handouts:

Finitely generated modules over a PID.

The structure of semisimple rings.
## Office Hours:

Tuesday 1:30-3:00 or by appointment in 7121 Wean Hall.
## Grades:

Your grade will be determined as follows:

20% homework (see below for details),

20% each of two midterms,

40% final exam.

## Recommended Reading:

Week of Jan 16: D&F 10.1, 10.2.

Week of Jan 23: D&F 10.3, 11.1.

Week of Jan 30: D&F 12.1

Week of Feb 6: D&F 12.2, 12.3.

Week of Feb 13: D&F 10.4, 10.5.

Week of Feb 20: No relevant textbook chapters.

Week of Feb 27: D&F 18.1, 18.2.

## Homework:

Homework will typically be assigned on Wednesday and due the subsequent Wednesday. Collaboration is encouraged on the assignments, but each student is expected to write up his or her own solutions. Occasionally there will be a starred problem as discussed below. Use of external resources (on non-starred problems) is also permitted, but in the interest of academic honesty please be sure to cite your sources.

Each assignment may contain a single starred problem for which no collaboration nor external resource is allowed. You may consult only the text and your notes. Please obey these terms -- homework is graded on completeness anyway so there should be little incentive to cheat.

## HW1 (due FRIDAY Jan 27)

Solutions

## HW2 (due Feb 1)

Solutions

## HW3 (due Feb 8)

Solutions

Solutions

## HW5 (due Mar 1) [UPDATED Feb 26]

Solutions

## HW6 (due Mar 29)

Solutions

## HW7 (due Apr 7)

Solutions

## HW8 (due Apr 12)

Solutions

## HW9 (due NEVER)

Solutions

Clinton T. Conley

clintonc[at]andrew.???.edu