Abstract Algebra II
| Textbook: Algebra, by M.Artin, Chapters 11-16 | ||
| Course Notes | Date | Details |
|---|---|---|
| Homework 1 Solutions | Tues, Feb 4 |
Course Notes Review of Z Unique Factorization (Who Cares?) The Ring Concept Examples of Rings Z/nZ and (Z/nZ)^X Chinese Remainder Theorem |
| Homework 2 Solutions | Thurs, Feb 20 |
Course Notes Ring Homomorphisms Image is a subring; Kernel is not. Kernel is an Ideal Quotient Rings and Isomorphisms Fundamental Theorem of Cyclic Groups Preview of Galois Theory |
|
Exam 1 Review Notes |
Thurs, Feb 27 |
Total = 20 Average = 15 Median = 19 Deviation = 7 |
| Homework 3 Solutions | Thurs, Mar 20 |
Prime Ideals and Domains Field of Fractions Maximal => Prime Prime => Maximal in a PID; not in general. |
| Homework 4 Solutions | Tues, Apr 1 |
Course Notes Euclidean => PID PID => Noetherian Noetherian => Factorization Exists PID => Euclid's Lemma Euclid's Lemma => Factorization is Unique Therefore PID => UFD |
|
Exam 2 Review Notes |
Thurs, Apr 3 |
Total = 24 Average = 20 Median = 22 Deviation = 5 |
| Homework 5 Solutions | Tues, Apr 22 |
Course Notes Field Extensions The Evaluation Homomorphism The Minimal Polynomial Algebraic vs. Transcendental The Tower Law Kronecker's Theorem Classification of Finite Fields |
|
Exam 3 Review Notes |
Thurs, Apr 24 | In Class |
| Algebra Prelim |
Fri, May 30 |
Review Session 1 Review Session 2 Review Session 3 Review Session 4 |