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ASSIGNMENTS
PROBLEM SET 
ASSIGNMENT 
Problem Set #1
Due Wed, Jan 11 
Read:
Appendices A,B,C
Do:
Individual:
Appendix A:
2, 9, 17, 21
Appendix B: 4, 6, 8, 9
Group:
Appendix A: 12, 16, 24
Appendix B: 5, 13

Problem Set #2
Due Thurs, Jan 19 at 2:50 in my office.

Read:
Appendix C, Chapters 14
Do:
Individual:
Appendix C: 1,5, extra (below)
Chapter 2: B1, C (all)
Extra: Show using strong induction that if a set S has an associative and commutative operation * then a string of operations may be
recommuted in any way, that is, it doesn't matter what order
you write the product in, so eg a*b*c*d=a*d*b*c=b*d*a*c, etc. (you may use the result from class that the string may be reassociated in any way)
Group:
Appendix C: 4, 6
Chapter 2: B3, B7

Problem Set #3
Due FRI, Jan 27 
Read: Chapter
46
Do:
Individual:
Chapter 3:
A2, B4,5
Chapter 4: B3, C2, D1, F2, H2
Chapter 5: A4, C2, D1, F3
Group:
Chapter 3: A3, F (all)
Chapter 4: B4, F4, G1,2, H1
Chapter 5: B2, C6, D3, E3

Problem Set #4
Due Wed, Feb. 8 
Read: Chapters
610
Do:
Individual:
Chapter 6: A2, C4, E3, F3,4
Chapter 7: A1, B2, F3,4, H1
Chapter 8:
A1a,2a,3a,4a, F2, G4
Group:
Chapter 6: C5, F1,2
Chapter 7: B1, F1,2
Chapter 8:
A1b,2b,3b,4b, C2 
Problem Set #5
Due Wed, Feb 15 
Read: Chapters 913
Do:
Individual:
Chapter 9: A3, B1,2, D3, E3, G4, H1
Group:
Chapter 9: A1,2, B3, C2, D1, E4, I3

Problem Set #6
Due Thurs, Feb 23 
Read:
Chapters 1215
Do:
Individual:
Chapter 10: B2, C5, D3
Chapter 11: B4, C1
Chapter 12: A6, B2, C2, D2
Chapter 13: A2, C1, D3, E2, I1
Group:
Chapter 10: B6, D1
Chapter 11: B3
Chapter 12: A5, B6, D3
Chapter 13: B6, C2, D1, I2

Problem Set #7
Due THURS, Mar 2 
Read:
Do:
Individual:
Chapter 14: A1, B3, C9, D6, G1
Chapter 15: A1, B2, C1, E2
Chapter 16: A1, I
Group:
Chapter 14: A3, B6, C4, D1, G2
Chapter 15: A3, C2, B1
Chapter 16: E

Problem Set #8
Due Fri, Mar 10 
Read:
Do:
Individual:
Chapter 17: A1,5, C, H1, I1, J3,4
Chapter 18: A6, B4, D5,F4
Chapter 19: A1, Prove that the ideal nZ in Z is prime iff n is prime
Group:
Chapter 17: D, G1, H3, I5, J6
Chapter 18: B1, D3, E4, F5
Chapter 19: B1, Prove that the ideal nZ in Z is maximal iff n is prime. Prove that Z_n is isomorphic to Z/nZ. Conclude that
Z_n is a field iff n is prime

