Math 320

Fall 2010

Homework, Schedule, Assignments

“F” means Farmer; “P” means Pinter. “P2A4” means problem 4 in set A in chapter 2 of Pinter; “F2.3.4” means exercise 2.3.4 in Farmer.

Due Date

Have done before class

Presentations

9/13/10, Mon

  1. Complete the reading and tasks in Sections 3.1 and 3.2 of Farmer.
  2. Read Chapter 3 in Pinter.
    1. Why do we remove 0 from the set Q to form the group ⟨ Q , ·⟩? Why not just ⟨Q, ·⟩?
    2. If you consider Z7 to be the set {0, 1, 2, 3, 4, 5, 6}, is it a group under multiplication? Why or why not? If not, can you fix it? How about Z6 ?
    3. How can you tell from a glance at the table on page 29 that the group is not commutative?

Exercises in Pinter: 3A2 (why the x ≠ 0 restriction on the elements of the set?), 3B2, 3B4, 3C1, 3C2, 3C3.

9/15/10, Wed

Problem Set 1 due:

  1. Tasks 2.3.1 and 2.3.2 from Farmer.
  2. Two tasks of your choice from Farmer Section 2.5.
  3. Pinter 2B6.
  4. One exercise of your choice from Pinter set 3B.
Solutions to most problems in this set are here.

9/20/10, Mon

Read P ch. 4; P3A3, P3B5, P3D(all), P4A2, P4A4, P4B1, P4C2

AG: P3A3; AN: P3B5; CB: P3D; TC: P4A2; SL: P4C2

9/22/10, Wed

Read P ch. 5; P4G1; P4G2; P4H4; P5A1; P5A4

MD: P4B; JW: P4C; KJ: P4D; JC: P4E; BA: P4F

9/27/10, Mon

Review P ch 6 as needed; Read P ch. 7; P5B1; P5B4; P5C1 (does this work if G is not Abelian?); P5C4; P5D1; P5D3; P5D5; P7A(all)

SS: P5E1,3,5; KD: P5D1,3; JR: P5B4,6; EB: P5G; AV: P7B1,2,3; BJ: P7F2,3,4

9/29/10, Wed

Read P ch. 8; P6D3; P7B1; P7B4; P7C1; P7F1; P7I1,2; P8A(all)

AG: P7C2; AN: P7H1; CB: P7G1,2; TC: P8B2,4; SL: P8E1,2

10/4/10, Mon

Read P ch. 9; P8B1,2,3; P8D1; P8E1; P9B1; P9E1

BA: P8C3,4; JC: P8F1,2,3; MD: P8C1,2; SS: P9B2; JW: P8D4,5

10/6/10, Wed

Reread P Ch. 9; P9A(all); P9C1,2,4; P9D1; P9H2; P9H3

EB: P9C5,6; KD: P9D2,3; KJ: P9E4; BJ: Proof of Cayley's Theorem pp. 95--7; AV: P9H1

10/11/10, Mon

Read P Ch. 10; P9E2,3,5; P9B3; P9G3; P9I1,2; P10A1; P10B1,2,4,6; P10D1

JR: P9E2,5; AG: P9I3; AN: P10B5,7; SL: P10C5,6

10/13/10, Wed

Problem Set 2 Due: P5D6; P7H3; P8F1,2,4; P9A3; P9H4; Read P Ch. 11.

10/18/10, Mon

Read P Ch. 11. Work on Sample Midterm

10/20/10, Wed

Midterm I. Covers Farmer chapters 1-3, Pinter chapters 1-10 (note: not 11)

10/25/10, Mon

Reread P Ch 11; P10C1,2,3,5; P10D4; P11A(all); P11B2,3

KJ: P10C2; AV: P10C7; SS: P10D2,3; JW: P10D5; BJ: P10G1; TC: P11A4,5; EB: P11B5

10/27/10, Wed

Read P Ch 12; P11C1,2,5; P11D1,2; P11E1,2,3; P11F1,2; P12A1; P12B1,2

BA: P11E4,5; AG: P11E6,7; JC: P12A1; MD: P11C8; KD: P11F1,2; SL: P12B2; AN: P12D1

11/1/10, Mon

Read P Ch 13; P12B5,6; P12D1,3; P12C1; P12E3; P13A1,2,3(see p. 71 for definitions); P13B1,2; P13C1,2

EB: P12B8; SS: P12D2; JW: P12C2; TC: P12C3; AG: P13(Theorem 3); BJ: P13(Theorem 4); AV: P13A3,5

11/3/10, Wed

Read P Ch 14 ; P13D2,3,4; P13E1,2,6; Read Cauchy's Theorem p. 131; P13F1; P14A1,2,5; P14D1

KJ: P13B4,6 (the operation on R* is multiplication; on R, addition); KD: P13D3,4; MD: P13E1,2; BA: P13F2,3; SL: P14B1,2

11/8/10, Mon

Read P Ch 15; P14A3, P14B3, P14C1,2,4,8,9; P14D1,2,3,6; P14G1,2,3; P15A1,2,3

JC: P14C3; MD: P14C4; AN: P14D5; SS: P14E1; TC: P14E3; AV: P14I1,2

11/10/10, Wed

Problem Set 3 due: P11D3; P12D4; P13G(all); P13D1; P13I1,2

11/15/10, Mon

Read P Ch 16; P15A1,2; P15C1,2,6; P15D1

JC: P15A3; BA: P15B1,2,3; EB: P15C1,3; KD: P15E1; KJ: P15E3; BJ: P15H(all)

11/17/10, Wed

Read P Ch 17; P16A2,5; P16B1; P16D2; P16E1; P16I1; P17A1,2,4

JW: P16A1,3; TC: P16F2,4; MD: P16F1,3; AN: P16C1,2,3; SS: P16I1,2

11/22/10, Mon

Read P Ch 18; P17A1,4,5; P17B1,3,4; P17C1,2; P17H1,2,4,5; P17I2

AV: P17A1,6; SL: P17B1,2; AG: P17C3; KD: P17H3; JC: P17I3; CB: P17I5

11/24/10, Wed

No Class - Thanksgiving Break

11/29/10, Mon

Read P Ch 19; P18A2,3; P18B1,2,5; P18C1,3,4; P18D1,3; P18E1,3,4; P18F1,2,3; P18I3

BA: P18B6; KJ: P18C5,6; BJ: P18D2; JW: P18E4; MD: P18F2; EB: P18I2

12/1/10, Wed

Problem Set 4 due: P14F1,2; P14I6 (may assume P14I1-5); P15C5; P16F(all); P17I5

12/6/10, Mon

Read P Ch 20; P19A1,3; P19B1,4; P19C1,3; P19D1,2; P19E1,2,4; P19G2; P19H1

TC: P19A1,3; KD: P19C1,2; AG: P19E2,3; SS: P19H2

12/8/10, Wed

12/13/10, Mon

Final Exam, Darwin 31, 8:00-10:00 a.m.

Sample Final