Math 233: An Introduction to Modern Algebra
This syllabus is incomplete and tentative, and will be superseded by later versions as the course evolves. Details on assignments can be found on the assignments webpage.
| Week and Date |
Topic | Notes |
| 1: 1/27 |
F: The Questions of the course |
|
| 2: 1/30-2/3 |
M: Division and Euclid's algorithm W: Applications: finding gcds F: Fundamental Theorem of Arithmetic |
Tu: HW due F: HW due |
| 3: 2/6-2/10 |
M: Base n W: Mod n F: Finding a solution mod n |
Tu: HW due F: HW due |
| 4: 2/13-2/17 |
M: Finding all solutions mod n W: Solving simultaneous systems mod n F: Permutations |
Tu: HW due F: HW due |
| 5: 2/20-2/24 |
M: Groups W: Properties of groups F: Subgroups and cyclic groups |
F: HW due |
| 6: 2/27-3/2 |
M: Cosets W: Lagrange's theorem F: RSA |
Tu: HW due F: HW due |
| 7: 3/5-3/9 |
M: Homomorphisms W: Kernels and images F: Normal and quotient groups |
Tu: HW due F: HW due |
| 8: 3/12-3/16 |
M: Group actions W: The Counting Formula F: Burnside's Lemma |
Tu: HW due F: HW due |
| 3/19-3/23 | Spring break | |
| 9: 3/26-3/30 |
M: Rings W: Units/zero-divisors/fields/domains F: Ring homomorphisms |
Tu: HW due |
-->
| 10: 4/2-4/6 |
M: Polynomial rings W: Polynomials versus functions F: Dividing polynomials |
F: HW due |
| 11: 4/9-4/13 |
M: Ideals and principal ideals W: Quotient rings F: The First Isomorphism Theorem |
Tu: HW due F: HW due |
| 12: 4/16-4/20 |
M: Polynomial rings and division W: Polynomial rings and factorization F: Factoring polys into irreducibles |
Tu: HW due F: HW due |
| 13: 4/23-4/27 |
M: Factoring polys into irreducibles W: Principal ideals and division F: PIDs |
Tu: HW due F: HW due |
| 14: 4/30-5/2 |
M: What makes Z like Z? W: Review/catch-up |
W: HW due |