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Math 300: Foundations of Algebra
Eugénie Hunsicker, Associate Professor of Mathematics

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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 1-4
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 4-6
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 6-10
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 9-13
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 12-15
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

 

 

 

 

Last updated Jan. 3, 2005

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