The problems are from Contemporary Abstract Algebra by Gallian, 6th Edition unless otherwise noted.

1. Homework #1 (Due Tuesday, January 13)
   
   Hand in Problems:
    Chapter 0:     #6, 8, 10, 14, 16, 18*, 19, 22, 24, 36, 48, 50.
                           *First prove that if a and b are positive integers, then a does not divide ab+1.
   
   Extra problems for practice (do not hand in): ∙
   Chapter 0:     #2, 11, 13, 17, 22, 25, 28, 30, 49.

   

2. Homework #2 (Due Tuesday, January 20)
   
   Hand in Problems:
    Chapter 1:     #4, 6, 8, 10.
    Chapter 2:     #6, 11, 12, 14, 16, 20, 22, 24, 28, 33.
                           Note: You may assume without proof in #11 that multiplication of matrices is associative.
   
   Extra problems for practice (do not hand in):
   Chapter 1:     #3, 5, 7, 11, 13.
   Chapter 2:     #1, 7, 13, 17, 18, 19, 21, 25, 33.

   Math 103A Homework 1-2 answers.pdf

   

3. Homework #3 (Due Tuesday, January 27)
   
   Hand in Problems:
    Chapter 3:     #2, 8, 10, 14, 16, 19, 22, 34, 36, 44, 51
   
   Extra problems for practice (do not hand in):
   Chapter 3:     #1, 7, 15, 23, 25, 33, 35, 39, 43
   
   Math 103A Homework 1-3 answers.pdf  -- Joey will supply you with the password for this file after you hand in your homework. I will email the password to the class Wednesday morning as well.
   
   The first Midterm is on Wednesday, January 28, 2009. 
   This midterm will cover Chapters 0 -- 3 of the book.
   Please bring a blue book!
   You may bring one 8 1/2 X 11 sheet (front and back) of notes if you wish.

   

4. Homework # 4 (Due Tuesday, February 3)
   
   Hand in Problems:
   Chapter 4:         #4, 8, 12, 14, 16, 18, 22, 40, 46 (hint: see #45), 54, 56*, 62
   *Hint: show that U(2^n) contains at least two elements of order 2.
   
   Extra problems for practice (do not hand in):
   Chapter 4: #1, 3, 9, 15, 17, 47, 59
   
   Math 103A Homework 1-4 answers.pdf

   

5. Homework # 5 (Due Tuesday, February 10)
   Hand in Problems:
   Chapter 7: #6, 8, 10, 17, 20, 22, 24, 26, 34
   Chapter 10: #2, 6, 14, 20, 24, 32, 50, 54
       Hints:
           #7.10 -- use Exercise 4.54 and Lagrange's theorem.
           #7.20 -- recall the intersection of subgroups is still a subgroup.
           #7.34 -- explain why the elements of order 3 come in pairs.
           #10.20 Think about where 1∈Z₂₀ has to go to in Z₈ .
   
   Extra problems for practice (do not hand in):
   Chapter 7: #3, 5, 7, 9, 15, 17, 19, 23, 25, 27
   Chapter 10:#3, 15, 21, 23, 27

   Math 103A Homework 1-5 answers.pdf

   

6. Homework # 6 (Due Tuesday, February 17)
   Hand in Problems:
   Chapter 10: #2, 6, 14, 15, 20, 24, 26
   Chapter 6: #4, 18, 20, 22*, 24, 25, 30
   *Hint for 6.22 --  exam the elements of order 2.
   
   Extra problems for practice (do not hand in):
   Chapter 10: #3, 21, 23
   Chapter 6: #1, 3, 5
   
   Math 103A Homework 1-6 answers.pdf

   

7. Homework # 7 (Due Tuesday, February 24)
   Hand in Problems:
   Chapter 8:     #2, 4, 6, 8, 12, 26, 28, 40, 50, 56, 58, 64
   Chapter 10:    #9, 32 (Hint use #9)
   
   Extra problems for practice (do not hand in):
   Chapter 8:     #5, 9, 11, 23, 25, 27, 51, 55, 57, 67
   
   Math 103A Homework 1-7 answers.pdf

8. Homework # 8 (Due Tuesday, March 3)
   Hand in Problems:
   Chapter 8:       #50, 56, 58, 64
   Chapter 10:    #32 (Hint use #9 and or see the example involving U(30) in Lecture 22 )
   Chapter 5:      #4, 18, 24, 28, 34, 36, 46
   
   Extra problems for practice (do not hand in):
   Chapter 8:     #51, 55, 57, 67
   Chapter 5:     #5, 37, 41
   
   Math 103A Homework 1-8 answers .pdf
   
    
9. Homework # 9 (Due Tuesday, March 10)
   Hand in Problems:
    Chapter 5: #6, 12
    Chapter 8: #20 (Hint: what are the possible order of the elements of A₄.)
    Chapter 9: #8, 10, 12, 14, 16, 37, 38, 66
    Chapter 10: #30 (Hint: see Theorem 10.2), #44
   
   Extra problems for practice (do not hand in):
   Chapter 5: #7, 9, 15
   Chapter 9: #5, 9, 11, 23, 51, 57
   
   Math 103A Homework 1-9 answers.pdf

The Final Exam is on Friday, March 16 from 3:00 - 6:00 PM.
This final is cumulative.
Please bring a blue book!
You may bring one 8 1/2 X 11 sheet (front and back) of notes if you wish.