Math 421: Abstract Algebra I
Fall 2009

Homework Assignments & Tentative Schedule


Date
Section
Assignment
M
8/31
Introduction
Homework #1
W
9/2 0.1, 0.2 Handy facts
Homework #2: Read Section 0.3 as needed, also read pages 13-14, and do a first reading (this means skip the details and read for the big picture) of Section 1.1. In Section 0.3 do Problems #12, #13, #14.
F
9/4
0.3 The integers mod n and definition of a group
Homework #3: Please do a more detailed reading of Section 1.1. Also complete Problems #5 and #15bd in Section 0.3, as well as Problems #9, #25 in Section 1.1.
M
9/7
LABOR DAY
NO CLASS
W
9/9
1.1 Definition of a group
Homework #4
F
9/11
1.2 Dihedral groups
Homework #5
M
9/14
1.3 Symmetric groups
Homework #6
W
9/16
1.4 Matrix groups and 1.5 Quaternion Group
Homework #7: Please read Section 1.4 as needed as well as Section 1.5. Please do Problems #3, #11 in Section 1.4 and in Section 1.5 Problem #2 ONLY for D8 and Q8. How do these two groups compare?
F
9/18
1.6 Homomorphisms and isomorphisms
M
9/21
1.6 More homomorphisms and isomorphisms
Homework #8: Please do a first reading of Section 1.7 before class on Wednesday. Please do Problems #3, #4, #7, #8, #17, #23*.
W
9/23 1.7 Group actions
Homework #9: Read Section 1.7 as needed. Please do Problem #20 in Section 1.6 and Problems #3, #8 and #9 in Section 1.7.
F
9/25
1.7 More group actions

M
9/28
Presentations by generators and relations
Homework #10
W
9/30
Midterm 1: Combo In Class/Take Home
 
F
10/2
2.1 Definition of a subgroup
Take Home portion of Midterm 1 due by 5:00 p.m. today
M
10/5
2.2 Important subgroups
Homework #11: Please read Section 2.2 as needed. Here are the exercises - Section 1.7 #19; Section 2.1 #4, #11ac; Section 2.2 #4 for S3 only.
W
10/7
2.2 Important subgroups continued
Homework #12: Please do a first reading of Section 2.3 before class Monday. The following problems are due on the Wednesday after break: Section 2.1 #10; Section 2.2 #12abc, #14.
F
10/9
FALL BREAK
NO CLASS
M
10/12
2.3 Cyclic groups

W
10/14
Flexible use
F
10/16 Flexible use
Homework #13: Read Chapter 2 as needed. Section 2.2 #12def; Section 2.3 #1, #5, #9, #12; Section 2.4 #14.

M
10/19
2.4 Generating subgroups  
W
10/21
2.5 Subgroup lattice
Homework #14: Skim Section 3.1 (so read the definitions and statements of theorems and propositions, skip proofs and details). The following problems are due Monday next week: Section 2.3 #26 (phi is the Euler phi function, see p.7); Section 2.5 #6, #9a and Z45; Section 3.1 #6, #9.
F
10/23
3.1 Quotient groups
 
M
10/26
3.1 Quotient groups Homework #15: Section 3.1 #3, #4, #5.
W
10/28
3.2 Cosets and Lagrange's Theorem
 
F
10/30
Flexible use
Homework #16: Section 3.1 #38, #39 and Section 3.2 #4, #16.
M
11/2
3.3 The Isomorphism Theorems
W
11/4
3.3 The Isomorphism Theorems
Midterm 2 distributed today by 5:00 p.m.
F
11/6 Flexible use
M
11/9
Diversion into geometry and topology Midterm 2 due by 5:00 p.m. today
W
11/11
3.5 The alternating group
Homework #17
F
11/13
3.5 The alternating group

M
11/16 5.4ish Fundamental Theorem of Finite Abelian Groups Homework #18
W
11/18
7.1 Definition of a ring

F
11/20
7.1 Types of rings
Homework #19: Read Section 7.1 as needed. In Section 7.2 please read the part about polynomial rings. For Wednesday please do a first reading of Section 7.3. The following problems are due Wednesday next week: Section 7.1 #7, #13 (for part c see p.225 example 6); and Section 7.2 #1, #2.
M
11/23
7.2 Polynomial rings
W
11/25
Flexible use  
 
F
11/27
THANKSGIVING BREAK NO CLASS
M
11/30
7.4 Properties of ideals  
W
12/2
7.5 Rings of fractions  
F
12/4
Flexible use  
M
12/4
7.6 The Chinese Remainder Theorem

W
12/9
Flexible use Take Home Final distributed today by 5:00 p.m.
Wed
12/16

Take Home Final due today at 5:00 p.m.