Math 331-2: MENU: Abstract Algebra Winter
All reading and homework is from Dummit and Foote. Since I will make changes in the schedule, you should make a point of checking frequently to be sure you have the most up to date list of assigned problems and due dates.

The listed exercises should be handed in at the beginning of lecture on the due date indicated.

Note that there are two reading/review assignments on material from linear algebra.

# Assignments Last updated: December 22, 2014

Lecture # Date Topic(s) Sections Homework, due following Monday
1 Mon 1/5 Basic Definitions: Units, Zero Divisors, Nilpotents; Integral Domains, Fields 7.1 1, 11
2 Wed 1/7 Properties of Subrings 7.1 13, 14, 17, 18
3 Fri 1/9 Subrings of Integral Domains are Integral Domains; Finite Integral Domains are Fields 7.2
4 Mon 1/12 Homomorphisms (definition) 7.2 2, 3, 4, 8
5 Wed 1/14 Homomorphisms; Quotients 7.3 5, 6, 8, 10
6 Fri 1/16 Homomorphisms; Quotients, Prime Ideals 7.3 13, 16, 17 19, 26, 28
MLK Day Mon 1/19 No Class   Fun Problem
7 Tue 1/20 Properties of Ideals 7.4 7, 8, 10, 33* (* = hard)
8 Wed 1/21 Maximal Ideals 7.5 5
9 Fri 1/23 Rings of Fractions, Euclidean Domains 8.1 10
No Class 1/26-1/28
10 Fri 1/30 Principal Ideal Domains 8.2 3, 4, 5
11 Mon 2/2 Unique Factorization Domains 8.3 (pp. 283-289 only) 8a
12 Tue 2/3 Basic Properties of Polynomial Rings 9.1 4, 5, 6, 13
13 Wed 2/4 Polynomials over Fields
Gauss' Lemma
9.2
pp. 303-304
1, 2, 7, 8

HT Fri 2/6 Midterm
14 Mon 2/9 Irreducibility
Polynomials over fields, II
9.4
9.5
1,3,4

16 Wed 2/11 Modules: Basic definitions 10.1 3, 5, 8, 18, 19, 20
17 Fri 2/13 Quotients and homomorphisms 10.2 1, 3, 7, 8, 10
18 Mon 2/16 Generation of modules, etc. 10.3 4, 6
19 Wed 2/18 Generation of modules, etc. 10.3 22a
Reading/review   Definitions; basic theory 11.1 1, 6, 7
Reading/review   Matrix of a linear transformation 11.2 (pp. 415-420 only)
20 Fri 2/20 Modules over PIDs: Basic theory 12.1
21 Mon 2/23 Modules over PIDs: Basic theory 12.1 2, 3, 5, 6, 11
22 Wed 2/25 Modules over a PID 12.2 11,19
23 Fri 2/27 Abelian Groups: Smith Canonical Form 12.3
24 Mon 3/2 F[T]-modules 12.3 2, 22, 26
25 Wed 3/4 Jordan Canonical Form 12.3
26 Fri 3/6 Catch up day
Mon 3/9 -
Fri 3/13