MATH 421: Abstract Algebra I
James Cook's Abstract Algebra I Homepage:

Welcome. This webpage contains some resources I have created for Abstract Algebra I. The current semester work is found in Blackboard, thanks!
  1. You Tube Playlist for Math 421 of Fall 2017
  2. Course Plan for Math 421 of Fall 2017
  3. I'm here to help. Please make wise use of my office hours when you get stuck. Also, in lecture, if I write something obviously wrong. Please politely interupt me before I burn 5 minutes of class on a bogus calculation. I have no patience for corrections! I want them immediately.
  4. Someone will be unable to make it to my office hours. It's inevitable in a given semester. Therefore, if you are such a person, it especially important for you to work with a study group which has at least one person who can make it to office hours.
General Advice: When confronting many "proof" problems in this course (and in more advanced abstract math courses) as a starting point you ought to ask yourself:
  1. What am I asked to prove ?
  2. Can I define the words used ?
It is not usually the case that you will find the same proof in my notes or the text. Definitions are key, I cannot emphasize this enough. Past this, you should consider using theorems, propositions etc. which we have developed. However, beware of proof by synonym. A common beginners mistake is to simply restate the claim in slightly different words as to prove the claim by invoking an entirely equivalent theorem. I usually write an arrow pointing back to itself to warn you of the circularity of such logic. Anyway, enough about what not to do, you can learn what is a good method of proof simply by following lectures and paying mind to study the structure of our arguments in each lecture. We do solve problems in this course, but, our more over-arching goal is to understand the structure of abstract algebra.

Useful Abstract Algebra Materials and Links from Past Years:
Keep in mind the structure of this course differs a bit from the current course. So, beware, definitions may not exactly align. This was based on Gallian's classic friendly text. Here are links to 2016's Lecture Notes and Lectures: Tests and some Solutions from Fall 2016:
Homework Solutions from Fall 2016:
Linear Algebra Background:
Here's what I covered in the Prerequisite to Math 421 most recently. On occasion I mention a topic which you don't recall, if you are curious, the details are probably in here:
Spring 2017 Linear Algebra Lectures:
Spring 2015 Linear Algebra Lectures:
These are the lectures from Math 321 I taught in Spring of 2015.


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The background picture was taken from Wikipedia's E8 article
Last Modified: 8-8-2017