Abstract Algebra Resources


This page points to resources still in a high level of developement, but even at this state may prove useful to some.

The Abstract Algebra Refresher (last modified: March 10, 2023) is intended for those who have previously taken a first course in abstract algebra, and who are looking to take a second course or simply one for which one term of abstract algebra is needed.

It is available both as html and pdf, though the html is more compact to read.

Not all first courses are equal. At Dartmouth, Math 31 is rather different than Math 71, and not always an adequate preparation for Math 81/111 which is a graduate course covering field theory and other topics. So this refresher goes over most of the material in a first course like Math 71, assuming that this is the second time students have seeen most of the material.

It endeavors to take a slightly more sophisticated perspective taking advantage that students already know the basics about groups, rings, quotients, etc. Its aim it to really focus on the ring theory, in particular polynomial rings, facility with which is crucial to a successful study of field and Galois theory.

Caveat: This project remains under development, and these resources are simply the current draft. Comments and suggestions are welcome, well some more than others.