How to Think About Abstract Algebra

This is a great book to read for anyone who has been away from the subject for a number of years and wants a refresher; also great for anyone coming to the subject for the first time. Written in engaging coversational style, the author guides the reader through basic group theory and ring theory as well as a number of other related topics. The importance of proofs is also stressed. The book is in a handy printed format, with excellent diagrams.

I love this book so far! It’s exactly what I needed for my self study. Its been helpful and I like it’s approach (as opposed to facing a bunch of definitions off the bat)

I am currently taking a second semester course in abstract algebra. Unfortunately, my first semester course was over a year ago and I forgot much of the material. My class began with the isomorphism theorems and I was getting completely lost in the terminology of homomorphisms, quotient groups, etc.This book not only caught me up, but helped me understand things I don't think I really grasped in my first semester. I think I will get an A in my course partly because of this book giving me a good foundation with lots of concrete examples. Speaking of which, the examples are extremely helpful. My current textbook rarely gives useful examples following the definitions and theorems, which makes the subject really hard to follow.One weakness of the book is motivation. I still read about groups, rings, and fields and keep asking myself "ok, but who cares?" In calculus, linear algebra, and even number theory classes you will learn about interesting and important applications of those subjects. I have yet to learn a single application of abstract algebra, nor has it answered any questions I had that were swept under the rug in my prior math classes. I know there are applications to things like geometric constructions and the insolvability of the quintic, but it seems like you have to learn an immense amount of mathematical machinery to get to those points. But maybe that is just an issue with the subject itself, and not the Author's fault.I also highly recommend her book on Analysis. I wish she would write some full textbooks in her chatty, example-driven style. I know I would read them.

I used it to gain a basic understanding of Abstract Algebra.

The book lives up to its title. If more students knew what she has to teach them, there’d be more students in mathematics, and more laypersons reading mathematics. Also, the Kindle version, which appears to be a pdf, is a step forward in integrating mathematical material with the surrounding text. No more that cut-and-paste look. But there isn’t the same ease of highlighting, bookmarking, searching, moving to distant pages, and seeing one’s notes. All these operations usually freeze movement, once they’re carried out. I hope the Kindle programmers are working on this problem.

I have an engineering degree with no heavy background on pure mathematics. I started with other books, and got stuck here and there. This book solves. It is fore sure one of a kind. Sometimes it can get a bit chatty but it is for good.