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A Book of Abstract Algebra: Second Edition (Dover Books on Mathematics) Paperback – Digital_copy, December 17, 2009

90 customer reviews
ISBN-13: 978-0486474175 ISBN-10: 0486474178 Edition: Second Edition

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Product Details

  • Series: Dover Books on Mathematics
  • Paperback: 400 pages
  • Publisher: Dover Publications; Second Edition edition (January 14, 2010)
  • Language: English
  • ISBN-10: 0486474178
  • ISBN-13: 978-0486474175
  • Product Dimensions: 1 x 5.5 x 8.2 inches
  • Shipping Weight: 12 ounces (View shipping rates and policies)
  • Average Customer Review: 4.5 out of 5 stars  See all reviews (90 customer reviews)
  • Amazon Best Sellers Rank: #25,287 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

343 of 354 people found the following review helpful By Kevin Urban on February 1, 2010
Format: Paperback
Each class I've taken as a grad student, I've gone a little overboard buying all sorts of books on the subject matter. I like that each author has a unique style and approach.

In abstract algebra, there are the standards (Dummit, Hungerford, etc). These are the more down-and-dirty texts. They're good. They're thorough. They're rigorous. They do the job quite well if you already have some familiarity with the subject.

Then there are the older, cheaper books, like Deskins. It's alright. Some people nay-say it, but whatever: it's cheap and is one more voice to add to the choir.

Pinter, though, reads like a novel---and not in a cheesy way. As I waited for a friend in Barnes and Noble, I half-heartedly picked it up to skim through it... The introduction hooked me--it sums up what lies ahead like a movie trailer, leaving one mad to find out the whole story. Some might shrug this book off as a lowly "undergraduate" book, but if this is the case, you're missing out on the one author who has been able to deftly convey just how inspiring this subject really is. No other book has convinced me of the power of abstract algebra like this book.

Will it be the only book you read on the subject? If it is, then it was a good choice.

Having experience with the more standard tomes out there, there is the chance that I think this reads like a novel and is "so good" because I am familiar with the material. But, seriously, this is the kind of book that you're lucky to stumble across, whoever you are: a math nerd, physics geek, bio dweeb, or chem freak. This book will, at the least, open your eyes to well-kept secrets of higher mathematics.
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173 of 180 people found the following review helpful By sp on February 22, 2010
Format: Paperback Verified Purchase
This is an excellent book on abstract algebra that makes the transition into this difficult area
as painless as possible. As a engineer who was forced to learn group theory, I read through at least 50 books
on this subject (another good choice is
Groups and Their Graphs by Grossman)
and Pinter's treatment was the most user friendly treatment I came across.

I have no doubt that most physicists and applied scientists would
also love the style of this book. However, ivory tower mathematics types might put their nose up at the
way Pinter develops the material.
Specifically, this book goes to great lengths to show the scaffolding behind the ideas and proofs. Concrete
examples and toy problems are given without apology.
As a result, the
mathematics is brought alive and not depicted as cold and detached theorem proving. This book actually
is a perfect response to the snobby elitism exuded by many
advanced math texts. Overall, this book is a model of good mathematics texbook writing. My highest recommendation.
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74 of 79 people found the following review helpful By AM on August 19, 2010
Format: Paperback Verified Purchase
I fully agree with the comments of the previous reviewers. This introductory book on abstract algebra is simply superb.
The author uses a discursive language, pretty unusual for a book of this type but extremely effective. While going through this book, you have the impression not of reading a textbook but of "listening" to the author talking to you.
I am not a professional mathematician, and therefore I don't feel entitled to judge about its mathematical rigor but I have read and studied similar textbooks on the subject (like Fraleigh and Gallian) and the clarity of this book surpasses them all.
The author provides lots of exercises and some worked out solutions.
Definitively this is my strongest recommendation for a book on this subject.
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33 of 33 people found the following review helpful By Steve on December 6, 2010
Format: Paperback
This books starts with an historical chapter which not only provides the history of abstract algebra, but also offers a perspective along the lines of "Why would anyone want to do this at all? What good is it for anything?"

The book then offers a very step-by-step, each idea carefully explained approach to the subject. Each chapter ends with multiple exercises which show applications as well as theory. The problems themselves are broken into steps or stages, for those of us who are not experienced with theoretical math. Some of the problems are solved at the back of the book (though I wish more were solved).

The level of the proofs in the book is excellent for someone like myself with a background in applied math, but not much by way of theoretical math. No steps are skipped, everything is spelled out. For a college or university that likes to really "challenge" its students with books that race through the material, or pack the material very densely, some professors might find this book too easy. But for a school that wants to make sure everyone can keep up -- and also for self-study as I'm doing -- I highly recommend this textbook.

The only thing I wish they'd add in a future edition are more solutions to the problems, and also a glossary of symbols and terms.
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31 of 33 people found the following review helpful By xpovos on October 26, 2004
Format: Hardcover
Pinter's book compares very favorably to other elementary treatments, such as Gallian or Birkhoff+Maclane. The author has intentionally deviated from the established modern writing style in mathematics texts (theorem...proof...theorem...proof...), presenting instead an eminently readable work of mathematical prose which can be understood by any conscientious ninth-grader. Pinter's straightforward proofs of "Cayley's theorem" and the so-called "Fundamental Homomorphism Theorem" alone justify the purchase.

This relaxed and readable style notwithstanding, a suitable level of rigor has been maintained throughout the text---which is fairly complete in its coverage of elementary topics. From basic group theory and ring theory to field extensions and Galois theory, many minor, auxiliary results are left as exercises to aid the student's facility in proof technique, while the important major results are explained in the most natural way possible.

Most importantly, Pinter's book would serve as an excellent second reference for those students approaching the daunting subject with another text. Once you've read Pinter, you can read just about any other text on the subject and immediately grasp. For this reason, it IS the best "first course" text, as previously stated. I consider it a masterpiece in its genre.
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