Abstract Algebra II

Here is is a textbook that I wrote for MTH 561 and 562.

Office Hours: via Zoom, Wed and Thurs at 3-4pm

Here is the syllabus.
Assignment Due Date Topics
Homework 1
Mon, Jan 29 Classical Problem of Algebra
Preview of Galois' Theorem
Field of Fractions of a Domain
Quadratic Field Extensions
Homework 2
Fri, Feb 9 Ideals and Quotient Rings
Prime and Maximal Ideals
Euclidean Domains
Unique Prime Factorization
Homework 3
Fri, Mar 1 Evaluation of Polynomials
First Isomorphism Theorem for Rings
Minimal Polynomials
Exam 1: Fri, Mar 8
Homework 4
Fri, Mar 29 Primitive Nth Roots of Unity
Cyclotomic Polynomials
Existence of Splitting Fields
Symmetric Polynomials
Homework 5
Fri, Apr 12 Fundamental Theorem of Algebra
Finite Fields
Galois Theory of Finite Fields
Homework 6
Wed, May 8 Cyclotomic Fields
Galois Theory of Cyclotomic Fields
The Gauss-Wantzel Theorem
Unsolvability of the Quintic
Sketch of Galois Theory