Math 25800: Abstract Algebra
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: January 1, 2016

Lecture # Date Topic(s) Sections Homework, due following Monday
1 Mon 1/4 Basic Definitions: Units, Zero Divisors, Nilpotents; Integral Domains, Fields 7.1 1, 11
2 Wed 1/6 Properties of Subrings 7.1 13, 14, 17, 18
3 Fri 1/8 Subrings of Integral Domains are Integral Domains; Finite Integral Domains are Fields 7.2 2, 3, 4, 8;
4 Mon 1/11 Homomorphisms (definition) 7.3  
5 Wed 1/13 Homomorphisms; Quotients 7.3 5, 6, 8, 10
6 Fri 1/15 Homomorphisms; Quotients, Prime Ideals 7.3 13, 16, 17 19, 26, 28
MLK Day Mon 1/18 No Class   Fun Problem
7 Wed 1/20 Properties of Ideals, Maximal Ideals 7.4 7, 8, 10, 33* (* = hard), 7.5: 5
8 Fri 1/22 Rings of Fractions, Euclidean Domains 8.1 10
9 Mon 1/25 Principal Ideal Domains 8.2 3, 4, 5
10 Wed 1/27 Unique Factorization Domains 8.3 (pp. 283-289 only) 8a
HT Fri 1/29 Midterm
11 Mon 2/1 Linear Algebra 11.1  
12 Wed 2/3 Linear Algebra 11.1 1,2,6
13 Fri 2/5 Linear Algebra 11.2 1,2,3,4,11,12,19,21(e),25,26,29,35,36
14 Mon 2/8 Determinants    
15 Wed 2/10 Linear Alebra Summary Part I:   Homework
Relax Fri 2/12 No Class
16 Mon 2/15 Basic Properties of Polynomial Rings 9.1 4, 5, 6, 13
17 Wed 2/17 Polynomials over Fields
Gauss' Lemma, CRT
9.2, 9.4, 9.5
pp. 303-304
9.2: 1, 2, 7, 8; 9.4: 1,3,4
 
HT Fri 2/19 Midterm
18 Mon 2/22 Modules: Basic definitions 10.1 3, 5, 8, 18, 19, 20
19 Wed 2/24 Quotients and homomorphisms 10.2 1, 3, 7, 8, 10
20 Fri 2/26 Generation of modules, etc. 10.3 4, 6
21 Mon 2/29 Generation of modules, etc. 10.3 22a
22 Wed 3/2 Modules over PIDs: Basic theory 12.1  
23 Fri 3/4 Modules over PIDs: Basic theory 12.1 2, 3, 5, 6, 11
24 Mon 3/7 Modules over a PID 12.2 11,19
25 Wed 3/9 Abelian Groups: Smith Canonical Form 12.3  
26 Fri 3/11 F[T]-modules, Jordan Canonical Form 12.3 2, 22, 26
  Fri 3/10
Fri 3/11
Reading Period - NO LECTURES
Review ? Review session, TBA
FINAL Fri 3/18 Final examination in E 203, 10:30-12:30

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Copyright © 1999 - 2007 Michael R. Stein