The problems are from Contemporary Abstract Algebra by Gallian, 6th Edition
unless otherwise noted.
 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.
 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 12 answers.pdf
 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 13 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.
 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 14 answers.pdf
 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∈Z_{20}
has to go to in Z_{8 }.
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 15 answers.pdf
 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 16 answers.pdf
 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 17 answers.pdf
The second Midterm is on Wednesday, February 25. This midterm will cover
the parts of Chapters 4, 6, 7, 8, 10 that we have
covered so far, i.e. the material from Homeworks 47.
Please bring a blue book! You may bring one 8 1/2 X 11 sheet (front and back) of notes if you wish.
 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 18 answers .pdf
 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 A_{4}.)
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 19 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.
