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. Sept. 4

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 Wed. Sept 9 (try for Fri. Sept. 4) - 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 Fri. Sept 11 - 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 Wed. Sept 16
  • Read Chapters 2 and 3.
  • Ch 3 - 1,2,4,6,7,10,14,26.

    • Homework 3 (part 2) - Due Fri. Sept 18.
  • 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 - Due Fri. Sept 25
  • 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 - Fri. Sept. 25 - Covers Homeworks 2-4 (work out the extra problems)

    Homework 5 (part 1) - Due Wed. Sept 30
  • 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 Fri. Oct 2.
  • Read Chapter 4.
  • 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 Wed. Oct. 7
  • 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 Fri. Oct 9.
  • Read Chapter 5.
  • Ch 5 - 11,14,17,18,24,27,31,34,35.
  • Extra Fun (Not Required) - Ch. 5 - 10(for remaining n=7,8,9,10),36

    • Homework 7 (part 1) - Due Wed. Oct. 14
  • 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 Fri. Oct 16.
  • Read Chapter 6.
  • Ch 6 - 1,2,12, Complete these problems
  • Extra Fun (Not Required) - Ch. 6 - 16,17,18,19

    • Homework 8 - Due Fri. Oct. 23
  • Read Chapter 9.
  • Ch 9 - Complete these problems.

    • Homework 9 - Due Wed. Oct. 28
  • 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 - Fri. Oct. 30 - Covers Homeworks 5-9 (work out the extra problems)

    Homework 10 (part 1) - Due Wed. Nov 4.
  • Read Chapter 9 (this week focuses on 9.2)
  • Ch 9 - 15,16,47,48,50,52

    • Homework 10 (part 2) - Due Fri. Nov 6.
  • Read Chapter 9.
  • Ch 9 - Complete these problems
  • Extra Fun (Not Required) - Ch. 9: 31 Challenge: 37-42

    • Homework 11 - Due Fri. Nov 13.
  • Read Chapter 10
  • Complete These problems, and then: Ch 10 - 5,6,8.
  • Extra Fun (Not Required) - Ch. 10: 7,9-14

    • Homework 12 - Due Fri. Nov 20.
  • Read Chapter 11
  • Ch 11: 1,2,3,4,8,9,19

    • Homework 13 - Due Wed. Dec. 2
  • Read Chapter 13
  • Ch 13: 1,2,3

    • Exam 3 - Fri. Dec. 4 - Covers Homeworks 10-13 (work out the extra problems)

    Homework 14 - This will not be graded, but you should do these!
  • Read Chapter 16
  • Ch 16: 1,2,3