Week 1


September 23

 Read Chapter 2, pp. 40  48: Definitions and Examples of Groups

September
25

 Read Chapter 2, pp. 48  50: Elementary Properties of Groups
 Written Homework (Due 10/2): pp. 52  54: 3,
7, 8, 22, 23, 35; pp. 64  69: 2, 4, 10, 19, 37, 56; pp. 81  82: 5, 11, 18

Week
2


September 28

 Read Chapter 3, Finite Groups and Subgroups: pp. 57  64

September 30

 Read
Chapter 4, Cyclic Groups: pp. 72  81 (skip Thm. 4.2 and Cor. 2 (pp. 75, 76)

October 2 
 Continue with Cyclic Groups and Read Chapter 5, Permutation Groups: pp. 95  bottom of 106 and the table on p. 107
 Written Homework (Due 10/9): pp. 81  85: 24, 29, 39, 42, 64; pp. 113  116: 4, 24, 26, 27, 28, 43; pp. 133  134: 2, 4, 5, 10

Week
3


October
5

 Continue with Permutation Groups

October
7 
 Read
Chapter 6, Isomorphisms: p. 122  Thm. 6.4 on p. 131)

October
9 
 Read
Chapter 7, Cosets and Lagrange's Theorem: pp. 138  147
 Written Homework (Due 10/16): p. 133: 24, 32, 33; p. 149: 1, 2, 12, 28, 40, 49; p. 167: 6, 8, 9, 24, 34

Week
4


October
12

 Continue with Cosets and Lagrange's Theorem

October
14 
 Read
Chapter 8, External Direct Products: p. 155  middle of p. 159

October 16 
 Read
Chapter 9, Normal Subgroups and Factor Groups: pp. 178  186
 Written Homework (Due 10/23): p. 193: 10, 14, 27, 52, 70, 74; p. 211: 7, 15, 19, 21, 37, 50

Week
5


October 19 
 Read Chapter 10, Group Homomorphisms: p. 200  middle p. 208

October
21


October
23 
 Read Chapter 12, Introduction to Rings: 237  242


Week
6


October 26 
 Read Chapter 13, Integral Domains: pp. 249  254

October 28 
 Read Chapter 14, Ideals and Factor Rings: pp. 262  269

October 30

 Read Chapter 15, Ring Homomorphisms: pp. 280  285 (up to Field of Quotients)
 Written Homework (Due 11/6): p. 242: 2, 15, 17, 23; p.255: 5, 16, 22, 38, 44; p. 269: 6, 8, 17, 27, 35; p. 287: 10, 30 (reduce mod 3), 44 (binomial theorem), 46

Week
7


November 2 
 Read Chapter 16, Polynomial Rings: pp. 293  300

November
4 
 Continue Polynomial Rings

November
6 
 Read Chapter 17, Factorization of Polynomials: pp. 305  313 (up to Unique Factorization in Z[x])

Week
8


November
9

 Continue Factorization of Polynomials
 Written Homework (Due 11/16): p. 301: 10, 12, 18, 22, 33, 34; p. 317: 4, 5, 10abc, 13, 15, 16, 24; p. 335: 2, 12 (Hint: problem 10), 28, 30, 36

November
11 
 Read Chapter 18, Divisibility in Integral Domains: pp. 322  331 (skip Euclidean Domains pp. 331  334)

November
13 
 Read Chapter 20, Extension Fields: pp. 354  366 (skip middle p. 362  366)

Week
9


November 16

 Read Chapter 21, Algebraic Extensions: pp. 370  378 (skip Theorem 21.6)
 Written Homework (Due 11/23): p. 366: 3, 7, 8, 10, 20, 34; p. 378: 10 (ignore the second sentence), 11, 18 (Hint: quadratic formula), 20, 24, 37, 38

November
18 
 Continue Algebraic Extensions

November
20 
 Read Chapter 24, Sylow Theorems: pp. 403  414

Week
10


November
23 
 Continue Sylow Theorems
 No written homework, but see Announcements on the home page.


THANKSGIVING BREAK: NOVEMBER 2529

Week
11


November
30 

December
2

 LAST CLASS
 Questions, Course Evaluations, etc.
