This is the second part of the Modern Algebra sequence. The main topics are rings, especially polynomial rings, and Galois theory.
Provisional syllabus: Each of the topics listed below will occupy roughly onetwo weeks of course time.

Rings and ideals, basic notions

Polynomial rings

Modules (basic notions)

Fields of fractions

Principal ideal domains, polynomials over a field

Irreducible polynomials and factorization, Eisenstein polynomials

Field extensions and splitting fields

Galois groups and the main theorems of Galois theory

Applications: finite fields, cyclotomic fields

Applications: solution by radicals, ruler and compass constructions
If time permits, we will cover noetherian rings and modules over a PID.
Prerequisites: Modern Algebra I.
Textbook: Joseph Rotman, Galois Theory.
The book Abstract Algebra by Dummit and Foote (on reserve in the math library) can be used as a reference.
Online resources:
Abstract Algebra: Theory and Applications, by Thomas W. Judson
Notes on Modern Algebra II by Patrick Gallagher
Lecture notes by Robert Friedman
Modern Algebra II review notes by Robert Friedman in three parts: Part 1 Part 2 Part 3
Midterms: October 13, November 12 (in class)
Final: to be announced
Practice exams and notes in various languages (as requested)