Math 3140 Fall 16

MATH 3140: Abstract Algebra 1 (Fall 2016)

Syllabus

Final Exam:

Thursday 12/15, 1:30-4 pm, in class
Discussion of results: Friday 12/16, d10-11 am

Office hours:

Tuesday 3-4 pm Wednesday 11-12 am Friday 10-11 am

Schedule

Numbers are for orientation and refer to sections with related material in Goodman, Algebra: Abstract and Concrete.
  1. 08/22: symmetries, multiplication table (1.1-1.3)
  2. 08/24: linear maps, matrices (1.4)
  3. 08/26: permutations (1.5)
  4. 08/29: cycle notation, order of permutations (1.5)
  5. 08/31: perfect shuffle (1.5),
  6. 09/02: Z_n (1.7)
  7. 09/07: gcd, Euclidean algorithm, Bezout's coefficients (1.7)
  8. 09/09: Euler's Theorem (1.9), RSA (1.12)
  9. 09/12: groups (1.10), uniqueness of identity, 2.1.1, inverses 2.1.2, 2.1.3, 2.1.4
  10. 09/14: subgroups, homomorphisms
  11. 09/16: REVIEW
  12. 09/19: MIDTERM
  13. 09/21: isomorphisms, cyclic subgroups 2.2.9, 2.2.20, 2.2.21
  14. 09/23: 2.4.12, Cayley's Theorem
  15. 09/26: dihedral groups D_2n, generators and relations 2.3
  16. 09/28: left cosets, Lagrange's Theorem 2.5.6, index
  17. 09/30: kernel, image of homomorphisms 2.4.16
  18. 10/03: abelian groups, conjugacy, normal subgroups
  19. 10/05: center 2.5.11,
  20. 10/07: quotient groups 2.7.1
  21. 10/10: quotients
  22. 10/12: homomorphism theorem 2.7.6
  23. 10/14: correspondence theorem 2.7.13
  24. 10/17: direct products 3.1
  25. 10/19: finitely generated abelian groups 3.6
  26. 10/21: Fundamental Theorem of finitely generated abelian groups 3.6.21
  27. 10/24: REVIEW
  28. 10/26: MIDTERM
  29. 10/26: discussion of midterm
  30. 10/31: Fundamental Theorem of finitely generated abelian groups (2)
  31. 11/02: Group actions, orbits, transitivity 5.1
  32. 11/04: stabilizers, orbit size (5.1.14)
  33. 11/09: fixed points, counting orbits (5.2.2)
  34. 11/09: Burnside-Frobenius lemma (5.2.2)
  35. 11/11: conjugation (5.1.17), class equation (5.4), p-groups (5.4.2)
  36. 11/14: groups of size p^2 (5.4.3) 11/16: Sylow subgroups (5.4.7), 1st Sylow Theorem
  37. 11/18: 2nd and 3rd Sylow Theorem (5.4.10-11), groups of size pq (5.4.12)
  38. 11/28: rings (6.1)
  39. 11/30: units, fields, subrings
  40. 12/02: ring homomorphisms, ideals, principal ideals (6.2), quotient rings (6.3)
  41. 12/05: direct product, Chinese Remainder Theorem
  42. 12/07:
  43. 12/09: REVIEW

Assignments

  1. due 08/24 [pdf]
  2. due 08/31 [pdf]
  3. due 09/09 [pdf] [tex]
  4. due 09/14 [pdf] [tex]
  5. due 09/21 [pdf] [tex] [solutions]
  6. due 09/28 [pdf] [tex] [solutions]
  7. due 10/05 [pdf] [tex] [solutions]
  8. due 10/12 [pdf] [tex] [solutions]
  9. due 10/19 [pdf] [tex] [solutions]
  10. due 10/26 [pdf] [tex] [solutions]
  11. due 11/02 [pdf] [tex] [solutions]
  12. due 11/09 [pdf] [tex] [solutions]
  13. due 11/16 [pdf] [tex] [solutions]
  14. due 11/30 [pdf] [tex] [solutions]
  15. due 11/30 [pdf] [tex] [solutions]

Handouts

  1. Basic definitions in group theory [pdf]
  2. Quizzes: [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]
  3. List of topics [pdf]

Textbooks

There are many good textbooks on the topic, including the ones listed below. We will mainly follow Goodman's book. You can find the others online or at the Mathematics Library for additional reading.
  1. J. Fraleigh, A First Course in Abstract Algebra (Seventh Edition), Addison Wesley 2002.
  2. F. Goodman, Algebra: Abstract and Concrete (Edition 2.6), 2015. [pdf]
  3. T. Hungerford, Abstract Algebra: An Introduction (Second Edition), Brooks Cole 1996.
  4. I. Herstein, Abstract Algebra, John Wiley 1996.
  5. T. Judson, Abstract Algebra: Theory and Applications. [pdf]
  6. S. Lang, Undergraduate Algebra (Third Edition), Springer 2005. [pdf]