Week 1


September 22

 Read Section 1.1, pp. 16  21: Definition and Properties of Groups +
 Written Homework: pp. 21  23: 1, 3, 6, 12, 19, 25, 31

September
24

 Read Section 1.2, pp. 23  middle 26: Dihedral Groups and Generators and Relations 
 Written Homework: pp. 27  28: 1b, 3, 4

Week
2


September 27

 Read Section 1.3, Permutation Groups (also called Symmetric Groups), pp. 29  32
 Written Homework: p. 28: 7; p. 33: 2, 3 (do 2 and 3 just for sigma, tau and sigma squared),
6, 11, 16
 NOTE: Homework from Week 1 due Wednesday (Change of date)

September 29

 Read
Section 1.4, 1.5, Matrix Groups and the Quaternion Group  , pp. 34  36
 Written Homework: p. 35: 1, 2, 5; p. 36: 2 (just do S_3), 3

October 1 
 Read Section 1.6, Homomorphisms and Isomorphisms, pp. 36  38 (up to 6 lines from bottom)
 Written Homework: pp. 39  41: 1, 2, 4, 7, 20, 23

Week
3


October
4

 Read Section 2.1, Subgroups, pp. 46  48
 Written Homework: p. 40: 13; pp. 48  49: 1b,d,e, 2ad, 5, 9, 13, 15

October
6 
 Read
Section 2.3, Cyclic Groups +, pp. 54  59
 Written Homework: p. 60: 1, 3, 11, 13a, 18
 NOTE: Homework assignment from Week 2 due today. This assignment covers only the written homework listed for Week 2 (contrary to what was said in class).

October
8 
 Read
Section 2.4, Subgroups Generated by a Subset  , pp. 61  64
 Written Homework: p. 65: 2, 8 (you may assume the result that is stated in the middle of p. 64), 11 (you may assume that SL(2,Z_3) has 24 elements), 13, 14, 19

Week
4


October
11

 Read Section 3.1 (this section is quite verbose), Cosets and Homomorphisms, pp. 73  85
 Written Homework: pp. 85  89: 1, 5, 9, 10, 14ab, 22, 32, 34, 35, 38 (you may use the First Isomorphism Theorem in problems 34, 35, 38.)

October
13 
 Read Sections 3.1 and 3.2, Cosets and Homomorphisms and Cosets and Lagrange's Theorem, pp. 73  85 and pp. 89  93 (skip 93  95)
 No Written Homework from today's class
 NOTE: Homework assignment from Week 3 due today.

October 15 
 Read
Cosets and Lagrange's Theorem and the First Isomorphism Theorem, pp. 89  93 and p. 97 up to and including Corollary 17
 Written Homework: pp. 95  96: 5, 8, 11, 12, 15

Week
5


October 18 
 Read Section 3.5, Transpositions and the Alternating Group, pp. 106 110
 Written Homework: pp. 111: 3  5, 11  14 (Possible hint for 12: Look at n = 5.)

October
20

 Read Sections 1.7 and 4.1, Group Actions, pp. 41  44 and pp. 112  116
 Written Homework: pp. 44  45: 4, 16, 18; pp. 116  117: 1  4
 NOTE See the Announcements on the Math 71 home page regarding the homework for Week 4 which is due today.

October
22 
 Read Section 4.2 : Groups Acting on Themselves by Left Multiplication, pp. 118  121
 Written Homework: pp. 121  122: 1, 3a, 4, 8, 9, 11

Week
6


October 25 
 Read Section 4.3, Groups Acting on Themselves by Conjugation, pp. 122  129 (skip Theorem 12)

October 27 
 Read Section 4.3, Sylow's Theorems, pp. 139  146

October 27 
 TAKEHOME MIDTERM EXAM, handed out

October 29

 Sylow's Theorems (continued), pp. 139  146

Week
7


November 1 
 Read Section 7.1, Rings, pp. 223  229 (skip Example p. 229)
 Written Homework: pp. 230  231: 5, 7, 8, 11, 14, 15, 17

November
3 
 Read Section 7.2, Examples of Rings, pp. 233  237 (skip Group Rings, pp. 236  237)
 Written Homework: pp. 146  147: 7, 18, 30 (see definition of 'simple' on p. 102); pp. 237  238: 1c, 3b,c, 4 (assume that R is a commutative ring with 1 in these problems)

November
5 
 Read Section 7.3, Ring Homomorphisms and Quotients +, pp. 239 247 (skip Theorem 8, middle  end of p. 246)
 Written Homework: pp. 247  249: 1, 2, 4, 6, 10, 13, 18

Week
8


November
8

 Read Section 7.4, Ideals , pp. 251  256
 Written Homework: pp. 256  258: 710, 19, 23 (possible hints: (1) prove 2a = 0 (2) consider the quotient), 25, 27

November
10 
 Read Handout given in class; skim Sections 8.1 and 8.2 (euclidean and Principal Ideal Domains), but read material on the euclidean algorithm and the greatest common divisor, pp. 270  277 and pp. 279  281
 Written Homework: pp. 277  278: 1d (use the euclidean algorithm), 3 (use the definition of norm on p. 270)

November
12 
 Read Sections 9.1 and 9.2, Polynomials, pp. 295 298 and pp. 299  301
 Writtten Homework: p. 301: 6abc (you do not have to answer the part about characteristics); pp. 146  147: 6, 13, 15

Week
9


November 15

 Read Section 8.3, Unique Factorization Domains+ (Optional but interesting reading: Factorization in Gaussian Integers pp.289  292), pp. 283  292
 Written Homework: pp.292  293: 1, 2

November
17 
 Read Section 9.3, Unique Factorization Polynomial Rings, pp. 303  306
 Written Homework: p. 301: 1, 8, 9; p. 306: 3

November
19 
 Read Section 9.4, Irreducibility Criteria , pp. 307  310
 Written Homework: pp. 311  312: 1d, 3, 9, 14, 16

Week
10


November
22 
 Read Section 13.1, Field Extensions +, pp. 510  519


THANKSGIVING BREAK: NOVEMBER 2428

Week
11


November
29 
 Read Section 13.2, Algebraic Extensions +, pp. 520  529

December
1

 LAST CLASS
 Wrapping it up: Questions, Comments, etc.
