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 |
- TAKE-HOME 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: 7-10, 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 24--28
|
Week
11
|
|
November
29 |
|
| | | | | | | | | | | | | | | |