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 3.

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 - NOT DUE FOR A GRADE
  • Read Chapters 1 and 2.
  • Chapter 1 19,22,28.
  • Chapter 2 - 4,5.
  • Extra Practive Problems (Not Required) - Ch 1: 18,21,24,25,29. Ch 2: 8

    • Homework 3 - Due Mon. Sept 20.
  • Chapter 2 - 16,18(use 16),22,27.
  • Chapter 3 - 27(use induction),30.
  • Extra Practive Problems (Not Required) - Ch 2: 21 and Ch 3: 1,2,4,6,7,10,14,26,31,33.

    • Homework 4 - NOT DUE FOR A GRADE
  • Chapter 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 - Mon. Sept. 27 - Covers Homeworks 2-4 (work out the extra problems) - list of topics

    Homework 5a - NOT DUE FOR A GRADE
  • Chapter 4 - 1(a-d),2,3(a,b,d,h,j,k),4(a-d),5,8,9,10,11,12.

    • Homework - Due Fri. Oct 8.
  • Exam 1 Corrections.

    • Homework 5b - Due Fri. Oct 15.
  • Chapter 4 - 20,23,24,25,26,31,37,40,43.
  • Extra Fun (Not Required) - Ch. 4 - 1e,17,18,19,21,27

    • Homework 6a - NOT DUE FOR A GRADE
  • Chapter 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 6b - Due Fri. Oct 22.
  • Chapter 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 7a - NOT DUE FOR A GRADE
  • Chapter 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. 29
  • Chapter 6 - 1,2,12, Complete these problems
  • Extra Fun (Not Required) - Ch. 6 - 16,17,18,19

    • Homework 8 - NOT DUE FOR A GRADE
  • 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.
  • Chapter 9 - Complete these problems.
  • Extra Fun (Not Required) - 2,3,4,5,6,8 (Recall Ch. 4#1c - \(\mathbb{Q}\) is not cyclic ),34,35,36
  • More Challenging Fun - Ch. 9 - 41 Challenge: 11,12,14

    • Exam 2 - Fri. Nov. 5 - Covers Homeworks 5-8 (work out the extra problems) - list of topics

    Homework 9a - NOT DUE FOR A GRADE
  • Chapter 9 - 15,16,47,48,50,52

    • Homework 9b - Due Fri. Nov 19.
  • Chapter 9 - Complete these problems
  • Extra Fun (Not Required) - Ch. 9: 31 Challenge: 37-42

    • Homework 10 - NOT DUE FOR A GRADE.
  • Complete These problems, and
  • Chapter 10 - 5,6,8.
  • Extra Fun (Not Required) - Ch. 10: 7,9-14

    • Homework 11 - NOT DUE FOR A GRADE.
  • Chapter 11: 1,2,3,4,8,9,19

    • Exam 3 - Mon. Dec. 6 - Covers Homeworks 9-11 (work out the extra problems) - list of topics

    Homework 12 - NOT DUE FOR A GRADE - NOT included on the final exam. tr>
  • Chapter 13: 1,2,3
  • Chapter 16: 1,2,3

    • Final Exam - Mon. Dec. 13 3pm-5pm in our normal room - Covers Exams 1-3 Topics above