Homework


Homework to be turned in will be yellow.
Other homework assignments will be given, and you should complete them by the due date..

Homework 1 - Due Fri. Jan. 24

Todo:
  • Read the syllabus.
  • Read the following advice for students taking Modern Algebra by Joe Gallian.
  • Read the following advice on proof writing (also by Joe Gallian).
  • Some of you will also find the following interesting: reasons why Modern Algebra is valuable to math education (and math) majors. (also by Joe Gallian).

    • To turn in:
  • Complete the intro sheet.

    • Homework 2 (part 1) - Due Mon. Jan 29 - Keep these problems separate from part 2 (you will not turn these in together).
  • Read Chapters 1 and 2.
  • Ch 1 - 18,21,24,25,29.

    • Homework 2 (part 2) - Due Wed. Jan 31 - Keep these problems separate from part 1 (you will not turn these in together).
  • Read Chapters 1 and 2.
  • Ch 1 - 19,22,28.
  • Ch 2 - 4,5.
  • Extra Fun (Not Required) - Ch 2: 8

    • Homework 3 (part 1) - Due Mon. Feb 5
  • Read Chapters 2 and 3.
  • Ch 3 - 1,2,4,6,7,10,14,26.

    • Homework 3 (part 2) - Due Wed. Feb 7
  • Read Chapters 2 and 3.
  • Ch 2 - 16,18(use 16),22,27.
  • Ch 3 - 27(use induction),30.
  • Extra Fun (Not Required) - Ch 2: 21 and Ch 3: 31,33

    • Homework 4
  • Ch 3 - 37,38(only prove this is a subgroup),39,40.
  • Extra Fun (Not Required) - Ch 3: 38(prove the rest),47,48,54

    • Exam 1 - Wed. Feb. 14 - Covers Homeworks 2-4 (work out the extra problems)

    Homework 5 (part 1) - Due Wed. Feb. 21
  • Read Chapter 4.
  • Ch 4 - 1(a-d),2,3(a,b,d,h,j,k),4(a-d),5,8,9,10,11,12.

    • Homework 5 (part 2) - Due Wed. Feb. 28
  • Read Chapters 4 and 5.
  • Ch 4 - 20,23,24,25,26,31,37,40,43.
  • Extra Fun (Not Required) - Ch. 4 - 1e,17,18,19,21,27

    • Homework 6 (part 1) - Due Mon. Mar. 5
  • Read Chapter 5.
  • Ch 5 - 1,2(e-o),3,4,5(just parts a-c and the question after),7,8,10(only up to n=6).

    • Homework 6 (part 2) - Due Wed. Mar. 7.
  • Read Chapter 5.
  • Ch 5 - 11,17,18,24,27,34,35.
  • Extra Fun (Not Required) - Ch. 5 - 10(for remaining n=7,8,9,10),14,31,36

    • Homework 7 (part 1) - Due Mon. Mar. 19
  • Read Chapter 6.
  • Ch 6 - 5 (Hint: Use the properties of cosets to cut the work down, for example property 4 should help), Prove the following properties from the Properties of Cosets in the lecture notes: Property 4, Property 5, Property 6.

    • Homework 7 (part 2)- Due Wed. Mar. 21
  • Read Chapter 6.
  • Ch 6 - 1,2,12, Complete these problems
  • Extra Fun (Not Required) - Ch. 6 - 16,17,18,19

    • Homework 8 - Due Mon. Mar. 26
  • Read Chapter 9. Note: It is usually easier to show two groups are NOT isomorphic by finding some essential property the groups fail to share. e.g., only one is cyclic, abelian, has element of order 3, etc.
  • Ch 9 - Complete these problems.
  • Ch 9 - 2,3,4,5,6,8 (Recall Ch. 4#1c - \(\mathbb{Q}\) is not cyclic ),34,35,36
  • Extra Fun (Not Required) - Ch. 9 - 41 Challenge: 11,12,14

    • Exam 2 - Wed. Mar. 28 - Covers Homeworks 5-8 (work out the extra problems)

    Homework 9 (part 1) - Due Mon. Apr. 2
  • Read Chapter 9 (this week focuses on 9.2)
  • Ch 9 - 15,16,47,48,50,52

    • Homework 9 (part 2) - Due Wed. Apr. 4.
  • Read Chapter 9.
  • Ch 9 - Complete these problems
  • Extra Fun (Not Required) - Ch. 9: 31 Challenge: 37-42

    • Homework 11 - Due Wed. Apr. 18.
  • Read Chapter 10 and 11
  • Complete These problems, and then: Ch 10 - 5,6,8.
  • Ch 11: 1,2,3,4,8,9,19
  • Extra Fun (Not Required) - Ch. 10: 7,9-14

    • Exam 3 - Wed. Apr. 25 - Covers Homeworks 9-11 (work out the extra problems)

    Homework 12
  • Read Chapter 13
  • Ch 13: 1,2,3

    • Homework 13
  • Read Chapter 16
  • Ch 16: 1,2,3