- Tuesday 05/07, 1:30 - 4 pm, in class
- Topics
- Practice problems
- Discussion of results: Wednesday 05/08, 3-4 pm in Math 310

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

- due 01/24 [pdf] [tex] [solutions]
- due 01/31 [pdf] [tex] [solutions]
- due 02/07 [pdf] [tex] [solutions]
- due 02/14 [pdf] [tex] [solutions]
- due 02/21 [pdf] [tex] [solutions]
- due 02/28 [pdf] [tex] [solutions]
- due 03/06 [pdf] [tex] [solutions]
- due 03/13 [pdf] [tex] [solutions]
- due 03/22 (updated) [pdf] [tex] [solutions]
- due 04/05 [pdf] [tex] [solutions]
- due 04/17 [pdf] [tex] [solutions]
- due 04/29 [pdf] [tex] [solutions]

- Joseph A. Gallian. Contemporary Abstract Algebra. (any edition, available electronically via the CU library)