Math 3140 Spring 24

MATH 3140: Abstract Algebra 1 (Spring 2024)

Syllabus

Office hours

M 12:30 - 2:00 pm, W 10 - 11 am at Math 310

Final Exam:

Tuesday 05/07, 1:30 - 4 pm, in class

Schedule

Numbers are for orientation and refer to sections with related material in the book by Gallian.
  1. 01/17: symmetries, multiplication tables (1)
  2. 01/19: groups, basic properties (2)
  3. 01/22: subgroups, center (3)
  4. 01/24: review integers mod n (see handout)
  5. 01/26: order of elements (3), cyclic groups (4)
  6. 01/29: subgroups of cyclic groups (4)
  7. 01/31: permutation groups, Sym X, S_n (5)
  8. 02/02: homomorphisms (10), isomorphic groups (6)
  9. 02/05 automorphisms (6)
  10. 02/07: (inner) automorphism groups, Cayley's Theorem (6)
  11. 02/09: cosets, index of subgroups, Lagrange's Theorem (7)
  12. 02/12: applications of Lagrange's Theorem, groups of order p (7)
  13. 02/14: groups of order 2p (7)
  14. 02/16: orbit-stabilizer theorem, symmetry group of the cube (7)
  15. 02/19: REVIEW
  16. 02/21: MIDTERM 1
  17. 02/23: discussion of midterm, direct products of groups (8)
  18. 02/26: orders in direct products (8)
  19. 02/28: conjugacy, normal subgroups (9)
  20. 03/01: quotient groups (9), first isomorphism theorem (10)
  21. 03/04: sign of permutations, alternating groups (5)
  22. 03/06: correspondence theorem (10)
  23. 03/08: finite abelian groups, factorization into p-groups (11)
  24. 03/11: finite abelian groups, factorization of p-groups (11)
  25. 03/13: group actions (29)
  26. 03/18: orbits, fixed points, Burnside-Frobenius Lemma (29)
  27. 03/20: counting orbits
  28. 03/22: Rubik's cube in GAP, [GAP calculations], [pdf], hardness of finding shortest solutions [arxiv]
  29. 04/01: conjugation as group action, class equation, p-groups (24)
  30. 04/03: groups of size p^2, Sylow subgroups (24)
  31. 04/05: REVIEW
  32. 04/08: MIDTERM 2
  33. 04/10: Sylow Theorems (24)
  34. 04/12: discussion of midterm
  35. 04/15: groups of size pq (24)
  36. 04/17: simple groups, composition series, A_5 is simple (25)
  37. 04/19: rings (with 1), polynomials, subrings (12)
  38. 04/22: integral domains, units, fields (13), ring homomorphisms

Assignments

  1. due 01/24 [pdf] [tex] [solutions]
  2. due 01/31 [pdf] [tex] [solutions]
  3. due 02/07 [pdf] [tex] [solutions]
  4. due 02/14 [pdf] [tex] [solutions]
  5. due 02/21 [pdf] [tex] [solutions]
  6. due 02/28 [pdf] [tex] [solutions]
  7. due 03/06 [pdf] [tex] [solutions]
  8. due 03/13 [pdf] [tex] [solutions]
  9. due 03/22 (updated) [pdf] [tex] [solutions]
  10. due 04/05 [pdf] [tex] [solutions]
  11. due 04/17 [pdf] [tex] [solutions]
  12. due 04/26 [pdf] [tex]

Handouts

  1. Equivalence relations [pdf]
  2. Integers mod n [pdf]
  3. Basic definitions in group theory [pdf]

Reading