Math 419-01: Introduction to Abstract Algebra II, Spring 2015

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• Syllabus
• Homework:
  1. Due 1/28: Solve these problems; also pp. 182--184 #24, 28, 30
  2. Due Friday, January 30 The Office Visit
  3. Due 2/4: pp. 189--190 #1, 2, 27, 28, 29, 30
  4. Due 2/11:
     1. Prove that the field of fractions (as we defined it in class) is a field.
     2. Prove the uniqueness part of the division algorithm.
     3. p. 197 #12; p. 208--209 #26, 27
  5. Due 2/25:
     1. Prove that no ordered ring has a square root of -1.
     2. p. 234 #17; p. 243--245 #12, 13, 20, 22, 30, 34, 35
  6. Due 3/18:
     1. Solve all problems correctly that were on the exam.
     2. (Note Tuesday due date) Due 3/24: p. 252--254 #1, 4, 8, 24, 25, 28, 34, 35; p. 265 #20
     3. Due 4/8: Let K be a field, and h an automorphism of K. Prove that the set of elements fixed by h is a field. Also, solve p. 272--274 #29, 35.
     4. Due 4/15: p. 291-293 #6, 8, 30; p. 422--424 #8, 32, 36
     5. Due 4/22: p. 434--436 #2, 8, 17; p. 442--444 #2, 12
     6. Due 5/4: p. 454--456 #1, 11, 16, 17; p. 462--463 #4, 12; p. 475 #8
• Laboratory:
  1. Due Friday, January 30 Complete all of Chapter -1 from the lab manual, as well as Chapter 0 up to and including Exercise 0.6.
  2. Due Monday, March 30 Complete all of Chapter 14 and 16 from the lab manual.

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