Math 71 Syllabus and Homework Assignments
Fall 2010
 Updated: Nov. 20


There may be last minute 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 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
  • 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
    • Read Section 13.2, Algebraic Extensions +, pp. 520 - 529
    December 1
    • LAST CLASS
    • Wrapping it up: Questions, Comments, etc.