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A Book of Abstract Algebra: Second Edition (Dover Books on Mathematics)
Download Ebook A Book of Abstract Algebra: Second Edition (Dover Books on Mathematics)
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About the Author
Charles C. Pinter is Professor Emeritus of Mathematics at Bucknell University.
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Product details
Series: Dover Books on Mathematics
Paperback: 400 pages
Publisher: Dover Publications; Second edition (January 14, 2010)
Language: English
ISBN-10: 0486474178
ISBN-13: 978-0486474175
Product Dimensions:
5.5 x 0.9 x 8.4 inches
Shipping Weight: 1.1 pounds (View shipping rates and policies)
Average Customer Review:
4.2 out of 5 stars
155 customer reviews
Amazon Best Sellers Rank:
#87,881 in Books (See Top 100 in Books)
This is quite a good book for a first introduction to abstract algebra. The only other algebra book I’ve read in any detail is Fraleigh’s, and Pinter’s is written at a slightly lower level, both in the style of presentation and the mathematical content. The first 30 or so chapters are great and what could have been a major problem with the book—the relatively limited material covered in the chapters themselves—is made up for in the exercise sets, which add greatly to the theoretical material covered in the book. Don’t worry if you don’t think you’re up to proving them yourself; they’re broken down into manageable chunks, sometimes even excessively so that some might call it hand holding. Just about anything covered in a typical first course is included one way or another in this book, and with help available anytime online now, relegating material to the exercises isn’t especially troublesome. There are the usual typos and very minor errors that make their way into just about every math book (one such minor error made the cover!) but nothing too serious. Until...I was prepared to give it five stars until I got to the later chapters on Galois theory, which seem rushed and a bit sloppy compared to the rest of the book. I did some detective work and checked this edition against the first and I know what happened. In the first edition there were some minor errors in some of the material, for example for one theorem to work he needs to assume that two field extensions are contained in a common extension but he never does, so the theorem he states implies that all splitting fields are equal instead of just isomorphic. Worse, he states a fundamentally incorrect theorem—there’s even an obvious error in the proof—and it looks like he implicitly relies on it a few chapters later. He tries to fix these in the second edition but patching up proofs and inserting some sentences here and there in the chapters instead of redoing them entirely is hard; the result is a hybrid of the old incorrect presentation and the corrected one. This is confusing and results in one theorem that is still technically incorrect (but at least easily fixable) and a VERY confusing proof about polynomials solvable by radicals having solvable Galois groups. The hardest exercise in the book for me was cross-checking with Fraleigh and trying to figure out what Pinter was talking about. I’ll provide the details and some more errata in a comment for anyone interested, which should be everyone planning to go through the entire book.I view this as a fantastic 30 chapter book with a decent 3 chapter appendix on Galois theory.
I am a math teacher (teaching lower-level math at a university) who is reviewing abstract algebra after 20 years of not thinking much about it. I have amassed quite a number of abstract algebra books over the past few months and have been jumping around between them as I work through this stuff. I have decided to review several of them. So here's what I think of this one:I suppose this is about as good as it gets for what's available. It's one of my favorites so far. I think the text and meat of the book is quite well done. Pinter explains the concepts very well, although more worked out examples would be even better.However, I'm not at all a fan of the form he used for the exercises, thus the deducted star. I really don't like the way Pinter sort of buries half the material within the exercises. As well as he explains things, he should have just put all the important concepts and material in the chapter presentations. Yes, that would have reduced the brevity of the chapters, but it would have been much clearer and more convenient. Also, there just aren't enough problems of all difficulty levels. What's there is fine, but there needs to be way more of them.Also, as I've griped elsewhere, for Pete's sakes, put the solutions in the back of the book already! It's not supposed to be some kind of secret. The idea is, student thinks about problem, student does problem, student checks answer immediately, student either moves on after gaining command, or repeats as many times as needed until he/she has it. Let's bag the games and ivory tower elitism. A math course is not some kind of competition. It's a place to learn mathematics. Secrecy is not an efficient mode of learning. Neither is wandering through a lost forest. Okay... enough! Off the soapbox.Anyway, decent book. Worth having, especially considering the price.
I'm really enjoying studing for the first time Abstract Algebra with this book. I like how the chapters are quite small, to the point and, in the same time, rigorous and really easy to understand. The author explains really well all the concepts! Don't be fooled by the 4-6 pages chapters, the content is explained really well. But be warned: take you time and do the exercices in the end of the chapter, all of them. A review down below complains that he didn't like that a part of the content of the chapter is 'hidden' in the exercices, but I'm quite digging it! All the tools that you need are really well explained in the chapter, so when you do the exercices you feel like you're exploring the subject and making discoveries on your own, so you have this really nice feeling of satisfaction and accomplishment! And the way the exercices are layed down is great to: they are well leveled in terms of a difficult curve and there is plenty of help, insights and hints by the author alongside them. So you don't feel like the author just gave some exercices and a "good luck, see you in the next chapter", you feel his presence there and his orientation throughout them.I'm really impressed by the way this book was build and recommend to anyone who wants to learn Abstract Algebra for the first time. But remember, do the exercices, more than half the book is there (and like I explained, it's not a bad thing).
This is a decent book, especially given the price. However, there are mistakes and general sloppiness throughout the book.For example, on page 127 the following theorem is introduced:If a element of Hb, then Ha = Hb.This theorem is presented as a single sided implication. Only the singled sided implication is ever proved. However, forever afterwards this theorem is used as if it's a bidirectional implication (if and only if, iff). Other books present this theorem as an iff and prove both implications.There are mistakes like that all over the book. As a result, one cannot rely on this book as his/her only reference on abstract algebra.
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