Prerequisite: permission of the instructor.

Texts: We will be using Dummit & Foote as a primary reference for the majority of the course.

• Abstract Algebra (3^rd Edition) by David S. Dummit & Richard M. Foote ISBN: 978-0-471-43334-7 (Used cost approx. $30 -- you can go to AddAll.com for prices)
• General algebra references: Abstract Algebra: The Basic Graduate Year by Robert Ash (Dover paperback), Basic Algebra I & II by Nathan Jacobson (Part I ($15) & Part II ($15)), Advanced Modern Algebra by Joseph Rotman ($80), A First Course in Abstract Algebra by John Fraleigh ($25) is a lower level but excellent text.
• Category Theory references: Category Theory by Steve Awodey ($50), Toposes, Triples, and Theories by Michael Barr and Charles Wells, Toposes and Local Set Theories: An Introduction by J. Bell ($13), Topoi: the Categorial Analysis of Logic by Robert Goldblatt ($15)
• Classification of PID Modules reference: Rings, Modules, and Linear Algebra by Hartley and Hawkes ($25)
• Galois Theory reference: Galois Theory by Harold Edwards ($30)

  Web Page: My webpage is located here: https://mathsci.appstate.edu/~cookwj and
                      our course webpage is located here: https://mathsci.appstate.edu/~cookwj/courses/math5220-spring2015.

  Meeting times: We meet Wednesdays 3-5pm in Walker 302 and Fridays 10-11am in Walker 105.

  Final Exam: Our final exam date/time/location will be arranged with each student.

  Lecturer:

  	Name:	Dr. William (Bill) Cook
  	Office:	Walker Hall 347
  	Office Hours:	Monday 12-12:30pm Tuesday 9-11am & 12-12:30pm Wednesday 10-11am & 12-12:30pm Friday 8-9am & 12-12:30pm Other times by appointment
  	Phone:	(828) 262-2367
  	Email:	cookwj@appstate.edu
  	Webpage:	https://mathsci.appstate.edu/~cookwj

  Technology: You are welcome to use any technology at your disposal to complete out of class assignments. No calculators or other computer technology will be allowed on exams or quizzes unless otherwise specified.

  Course Topics: The course catalog says, "A study of some advanced topics from abstract algebra, including splitting fields, finite fields, geometric constructions, and Galois theory."
  
  This iteration of Abstract Algebra II will be taylored to M. Kelley and N. Hughes taking into account their previous exposure to Lie algebras, representation theory (of Lie algebras and groups), and other algebra. Broadly we plan to cover the following topics:

  • Category Theory: An introduction to categories including examples, functors, natural transformations, universal properties, limits/colimits, adjoints, and the Yoneda embedding lemma.
  • Ring Theory: Some ring theory beyond the basic definitions focusing on factorizations in Euclidean domains, PIDs, and UFDs
  • Ring Modules: The main goal is to discuss the classification of finitely generated modules over a PID and applications to abelian groups and linear algebra.
  • Field Theory and Galois Theory: Field extensions, splitting fields, finite fields, Galois groups, Galois correspondence, and solvability of poylnomial equations.
  A tentative course schedule can be found at: https://mathsci.appstate.edu/~cookwj/courses/math5220-spring2015/schedule.html.

  Your term grades will be based on the results of your exams and homework. Here is more information about the individual components of your grade:

  Exams: There will be two exam. A midterm and final exam each will make up 30% of your final grade.

  Homework: I will suggest homework problems during most lectures these will be discussed (and written up and collected if necessary). This will make up 40% of your term grade.

  Here are the components of the term grade with their weights:

  Component Weight Midterm 30% Final Exam 30% Homework 40%

  Attendance: Don't miss class. If you miss class, you are responsible for the material covered during your absence. If you miss a quiz, test/exam, or workshop, you must bring in documentation proving that your absence is excusable or otherwise receive a zero. If a make-up quiz/test/exam is granted, it must be made up before the next quiz/test/exam.

  Help! If you need help, please come to my office hours. If you are in Walker Hall and my office door is open, please feel free to stop by and ask questions – even if it's not during my posted office hours.

  Fine Print: Copies of the academic integrity code, disability services information, religious observance policies can be found at https://academicaffairs.appstate.edu/syllabi.