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on 16 May 2017
This is a brilliant book for someone in my position who is learning this material be self-study.

Pinter gives loads of practical examples before going on to the rigorous proofs.

My only detrimental comment is that I would like to have more answers to the problems - maybe on an external web site.
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on 9 November 2013
Almost two decades ago, I got my applied math PhD, and it's been that long that I have been looking for a good book to refresh my abstract math skills in particular in algebra, of which I only had a vague memory of really having loved the lectures as an undergrad. (I should also note that I don't do much really advanced maths in my jobs).

This is literally the first book I found that goes right into the subject matter, clearly, concisely, and -- most of all -- comprehensively and in full generality. For example, not only are number theory, vector spaces, and Galois theory covered (as one should really expect), but even things like cellular automata, information theory, singalling, coding, and anthropology (!).

It is hard going, but it is also more instructive than most books. It really hammers home the fundamental reason why we do abstract algebra in the first place: because once we have defined THE algebra, the nature of the objects we describe with it doesn't matter any more and this generality is extremely powerful. It hammers home the full generality of algebra once you set it free from the constraint of dealing with numbers only. "Let's take things that behave like this, then what can we say about them?" That's the abstract question, and the book does not, like so many others, forget to open your eyes at the end of every section how various the applications of each of the abstract algebras are.

If you only get one book on abstract algebra, get this one.
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on 3 November 2012
This little book is truly excellent for self-study or to brush up on your abstract algebra. The material is well laid-out and there are answers/hints to questions at the back. The good thing is there are an abundance of questions to help reinforce the topics. If you know a little algebra, linear algebra and a little about sets you will not have problems with this book. Truly a good book for self study.
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on 16 January 2015
It has taken me nearly 6 months to work my way through this book. I have tackled all the problems, which are many. I worked independently and only rarely did I need to dig deeper into topics. What was spooky was when I occasionally needed some inspiration to tackle one of the problems, there was a hint in the back (Mr Pinter is selective with his hints!).

I was taken on a journey from groups to rings to number theory to field extensions and finally Galois Theory. The author has a very readable style but I was not aware of any loss of rigour.

If you wish to deeply understand abstract algebra you must spend most of your learning time with pen and paper. Mr Pinter's approach forces you down this path.

When you consider how cheap this book is compared to other books that occupy the same space I have to describe it as great value for money.

It has been an exhilarating experience and I highly recommend the book and the approach.
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on 13 January 2014
This book is without a doubt one of the best introductory maths books that I have ever read. The author does not shy away from the necessary formalism but he explains the reason for it and makes the proofs almost comforting. Reading this book doesn't feel like work but almost like a gentle conversation with a more knowledgeable, older friend. I think this has to be the easiest and least painful way of learning abstract algebra, particularly for those like me studying it on our own.
If you work your way through the exercises and rely on Pinter's hints he will take you from essentially zero knowledge to a pretty decent understanding of Galois Theory.
If you get only one book on algebra make sure it is this one.
The only minor cavil is I would have liked to see more problems with solutions to test my understanding.
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on 5 December 2014
I now love books published by Dover, they're cheap and brilliant.

This book is no exception, it is short and light and will go up to (and slightly beyond) any second year undergraduate maths course. After that you're looking at the thicker "Springer Graduate Series" hardbacks really.

I like this book because it has some great pictures, it's easy to just pick up and read and also the questions. Most of the book is questions. I wouldn't recommend this as your only abstract algebra book though.

As always with books the first 1 or 2 chapters are mind-numbingly boring and tedious but after that it gets good.

I would recommend another "hand-holding" book (write me a comment if you want to know what it is, I think it's called "essentials of abstract algebra" - ask and I will confirm) along side this, for if you are like me and at first lack confidence all those questions (DIY theorems if you will) can be daunting. However this book will both develop your confidence and provide you plenty of practice.

I have absolutely no hesitation in recommending this book.
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on 7 November 2016
This book makes abstract algebra as easy as it gets. The author really takes good care of his readers by taking the time to explain difficult concepts in clear, simple language. If you are interested in any of the topics covered by this book, just buy it - you will not be disappointed. Also, if you want to see how to write a truly great mathematics text, buy it and use it as an example. I am an author myself, and I was blown away by the clarity and precision of the writing.
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on 6 May 2016
We used this book as the textbook for both semesters of Abstract Algebra, and worked through the entire book (skipped the chapter "Topics in Number Theory" and "Ruler and Compass"). I enjoyed reading through the book. The entire book acts as an introduction to the Abstract Algebra you need to know for Galois Theory, ultimately culminating in a brief introduction to the important bits of it in the last couple chapters.

The things I didn't like about the book:
- Important concepts taught in the exercises. If you're self-studying or particularly dedicated in school, you will likely go over these, but there was enough content introduced in the exercises that could have been brought into the chapters that it bothered me a bit.
- Formatting wise, sometimes theorems and proofs were just randomly thrown in without much warning of when you're starting/ending. They read exactly like the rest of the page. More than once I found myself wondering why he's bringing up some new definition in a proof, when I realized that I finished the proof of the theorem half a page ago.
- Some chapters feel "incomplete" because they're just a few pages long and end abruptly. (Though, this is somewhat "good", see below)

The things I liked about the book:
- Super readable. Only a couple times did I think that the writing was terse at all.
- Proofs were solid and explained well
- Chapters were short and engaging, which is a breath of fresh air in the world of mathematics textbooks
- Cool applications of the topics in the exercises
- Good exercises
- Well suited for self-study, and works well in tandem with more rigorous books
- Cheap

Who shouldn't buy this book?
- Those with more than a little exposure to group theory. You'll find it a little too easy and lacking in rigor found in Lang, etc.
- Those looking for a really thorough look at Group/Ring/Field theory. There's a lot of info in the book, but it fits Groups, Rings, Fields, and Galois Theory into just a couple hundred pages. Field Theory is taught as an "aside", mainly to introduce polynomials.
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on 27 February 2017
Accessible book that serves as a good introduction to Abstract Algebra. It takes the reader on a journey and feels more interactive than a lot of texts. This helped me in my undergrad studies as the material given to us by the lecturer was rather impenetrable.
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on 21 September 2014
Do not hesitate; buy this book. A wonderful introductory text, clear expositions and a great style. Not a single complaint, and the topics covered are wide enough and detailed enough to serve as a perfect introduction to Abstract Algebra.
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