Math 30810 Honors Algebra III (Fall 2016)
Groups and Rings
| Date | Lecture | Topics |
| Wed 08/24 | 1 | Overview |
| Fri 08/26 | 2 | Groups and subgroups |
| Mon 08/29 | 3 | Subgroups of the integers, gcd, lcm |
| Wed 08/31 | 4 | Cyclic groups and orders |
| Fri 09/02 | 5 | Orders and homomorphisms |
| Mon 09/05 | 6 | Kernels and images, normal subgroups |
| Wed 09/07 | 7 | Permutations |
| Fri 09/09 | 8 | Center of S_n, structure of S_3 |
| Mon 09/12 | 9 | Determinants |
| Wed 09/14 | 10 | Equivalence relations |
| Fri 09/16 | 11 | Cosets and the index of a subgroup |
| Mon 09/19 | 12 | Quotients of groups by normal subgroups |
| Wed 09/21 | 13 | Modular arithmetic |
| Fri 09/23 | 14 | The Chinese Remainder Theorem. The isomorphism theorems. |
| Mon 09/26 | 15 | The isomorphism theorems. |
| Wed 09/28 | 16 | Primitive roots mod p. A little public key cryptography. |
| Fri 09/30 | 17 | First exam |
| Mon 10/03 | 18 | Automorphisms of groups |
| Wed 10/05 | 19 | Direct and semidirect products. |
| Fri 10/07 | 20 | Semidirect products. |
| Mon 10/10 | 21 | Generators for groups |
| Wed 10/12 | 22 | Abelianizations |
| Fri 10/14 | 23 | Group actions |
| Mon 10/24 | 24 | Size of GL(n, F_p), stabilizers |
| Wed 10/26 | 25 | Stabilizers and orbits |
| Fri 10/28 | 26 | Conjugacy classes |
| Mon 10/31 | 27 | Simplicity of A_n and Sylow 1 with applications |
| Wed 11/02 | 28 | Applications of Sylow 1,2, 3 |
| Fri 11/04 | 29 | Proof of Sylow 1 |
| Mon 11/07 | 30 | Normalizers and the proofs of Sylow 2 and 3 |
| Wed 11/09 | 31 | Rings, fields, polynomials, power series, Laurent series, division with remainder |
| Fri 11/11 | 32 | Second exam |
| Mon 11/14 | 33 | Fraction fields and ring homomorphisms |
| Wed 11/16 | 34 | Ring homomorphisms and ideals |
| Fri 11/18 | 35 | Isomorphism theorems |
| Mon 11/21 | 36 | Maximal and prime ideals |
| Mon 11/28 | 37 | Euclidean domains |
| Wed 11/30 | 38 | ED implies PID |
| Fri 12/02 | 39 | PID implies UFD |
| Mon 12/05 | 40 | Gaussian integers |
| Wed 12/07 | 41 |
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