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 Jan 30

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) - 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 Feb 6 - 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)
  • Read Chapters 2 and 3.
  • Ch 3 - 1,2,4,6,7,10,14,26.

    • Homework 3 (part 2) - Due Feb. 13.
  • 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 20 - Covers Homeworks 2-4 (work out the extra problems)

    Homework 5 (part 1)
  • 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)
  • Read Chapters 4 and 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 5 (part 3) - Due Mar 13
  • Read Chapters 4 and 5.
  • Ch 4 - 20,23,24,25,26,31,37,40,43.
  • Ch 5 - 11,17,18,24,27,34,35.
  • Extra Fun (Not Required) - Ch. 4 - 1e,17,18,19,21,27
  • Extra Fun (Not Required) - Ch. 5 - 10(for remaining n=7,8,9,10),14,31,36

    • Homework 6 (part 1)
  • 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 6 (part 2) - Due Mar 27
  • Read Chapter 6.
  • Ch 6 - 1,2,12, Complete these problems
  • Extra Fun (Not Required) - Ch. 6 - 16,17,18,19

    • Homework 7 - Due April 3
  • Read Chapter 9.
  • Ch 9 - Complete these problems.

    • Homework 8
  • 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 - 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. Apr. 3 - Covers Homeworks 5-8 (work out the extra problems)

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

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

    • Homework 10 - Due Apr 24
  • Read Chapter 10
  • Complete These problems, and then: Ch 10 - 5,6,8.
  • Extra Fun (Not Required) - Ch. 10: 7,9-14

    • Homework 11 - Due May 1
  • Read Chapter 11
  • Ch 11: 1,2,3,4,8,9,19

    • Exam 3 - Mon. May 6 - Covers Homeworks 9-11 (work out the extra problems)