Math 71 Syllabus and Homework Assignments
Fall 2009
Updated: 11/22


Homework will be assigned on Friday and due the following Friday. There may be frequent changes in the syllabus and homework, so check this page before doing any reading or homework.   Jump to Week 1| Week 2|Week 3|Week 4|Week 5|Week 6|Week 7|Week 8|Week 9|Week 10|Week 11 |

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	Review of Groups
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 25--29
Week 11
November 30	Continue Sylow Theorems
December 2	LAST CLASS Questions, Course Evaluations, etc.