| Date | Topic |
|---|---|
| Lecture 1 (February 2): | Binary operations, groups, group tables |
| Lectures 2, 3 (February 4, 9): | Cyclic groups, applications to number theory |
| Lectures 4, 5 (February 11, 16): | Groups of permutations, braid groups, dihedral groups |
| Lecture 6 (February 23): | Lagrange's theorem and its applications |
| Lecture 7 (February 25): | Homomorphisms and isomorphisms |
| Lectures 8, 9 (March 2, 4): | Normal subgroups and conjugacy classes, factor groups. Classication of nitely generated abelian groups |
| Lectures 10, 11 (March 9, 11): | Group action, Birnside formula and applications to combinatorics |
| Lecture 12 (March 16): | Sylow theorems |
| Lecture 13 (March 18): | Test 1 |
| Lecture 14 (March 30): | Rings and fields |
| Lecture 15 (April 1): | Integral domains and applications |
| Lecture 16 (April 6): | Rings of polynomials, Eisenstein criterion |
| Lecture 17 (April 8): | Quaternions |
| Lectures 18, 19 (April 13, 15): | Ideals, principal ideal domains, and applications |
| Lecture 20 (April 22): | Euclidean domains |
| Lecture 21 (April 24): | Unique factorization domain and Gauss lemma |
| Lectures 22, 23 (April 29, May 4): | Elements of Galois theory, applications to planar geometry |
| Lecture 24 (May 6): | Test 2 |
| Lectures 25, 26 (May 11, 13): | Discussion |
18.703 - Modern Algebra (Spring 2010)
