Discussion of results: Friday 12/16, d10-11 am

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

- due 08/24 [pdf]
- due 08/31 [pdf]
- due 09/09 [pdf] [tex]
- due 09/14 [pdf] [tex]
- due 09/21 [pdf] [tex] [solutions]
- due 09/28 [pdf] [tex] [solutions]
- due 10/05 [pdf] [tex] [solutions]
- due 10/12 [pdf] [tex] [solutions]
- due 10/19 [pdf] [tex] [solutions]
- due 10/26 [pdf] [tex] [solutions]
- due 11/02 [pdf] [tex] [solutions]
- due 11/09 [pdf] [tex] [solutions]
- due 11/16 [pdf] [tex] [solutions]
- due 11/30 [pdf] [tex] [solutions]
- due 11/30 [pdf] [tex] [solutions]

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

- J. Fraleigh, A First Course in Abstract Algebra (Seventh Edition), Addison Wesley 2002.
- F. Goodman, Algebra: Abstract and Concrete (Edition 2.6), 2015. [pdf]
- T. Hungerford, Abstract Algebra: An Introduction (Second Edition), Brooks Cole 1996.
- I. Herstein, Abstract Algebra, John Wiley 1996.
- T. Judson, Abstract Algebra: Theory and Applications. [pdf]
- S. Lang, Undergraduate Algebra (Third Edition), Springer 2005. [pdf]