Abstract Algebra II

 Course Notes Date Details Textbook: Algebra, by M.Artin, Chapters 11-16 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