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A Book of Abstract Algebra: Second Edition (Dover Books on Mathematics) [Paperback]

Charles C Pinter
4.4 out of 5 stars  See all reviews (63 customer reviews)

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Book Description

December 17, 2009 0486474178 978-0486474175 Second Edition
Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. Intended for undergraduate courses in abstract algebra, it is suitable for junior- and senior-level math majors and future math teachers. This second edition features additional exercises to improve student familiarity with applications.
An introductory chapter traces concepts of abstract algebra from their historical roots. Succeeding chapters avoid the conventional format of definition-theorem-proof-corollary-example; instead, they take the form of a discussion with students, focusing on explanations and offering motivation. Each chapter rests upon a central theme, usually a specific application or use. The author provides elementary background as needed and discusses standard topics in their usual order. He introduces many advanced and peripheral subjects in the plentiful exercises, which are accompanied by ample instruction and commentary and offer a wide range of experiences to students at different levels of ability.

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A Book of Abstract Algebra: Second Edition (Dover Books on Mathematics) + Introduction to Topology: Third Edition (Dover Books on Mathematics) + Introduction to Graph Theory (Dover Books on Mathematics)
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Product Details

  • Series: Dover Books on Mathematics
  • Paperback: 400 pages
  • Publisher: Dover Publications; Second Edition edition (December 17, 2009)
  • Language: English
  • ISBN-10: 0486474178
  • ISBN-13: 978-0486474175
  • Product Dimensions: 8.4 x 5.3 x 0.9 inches
  • Shipping Weight: 12 ounces (View shipping rates and policies)
  • Average Customer Review: 4.4 out of 5 stars  See all reviews (63 customer reviews)
  • Amazon Best Sellers Rank: #16,261 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews
305 of 315 people found the following review helpful
5.0 out of 5 stars Don't let this book be the one that got away... 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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164 of 171 people found the following review helpful
By sp
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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70 of 74 people found the following review helpful
5.0 out of 5 stars Superb introduction to abstract algebra 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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25 of 25 people found the following review helpful
5.0 out of 5 stars Excellent for self study December 6, 2010
By Steve
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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26 of 27 people found the following review helpful
By deluger
Format:Paperback
When I first learned that the general quintic polynomial equation was insolvable by radicals, such a counter-intuitive idea, I wanted to learn Abstract Algebra primarily to understand it, and when I took Abstract Algebra in college they bombarded me with a "completist" agenda whereby it seemed they tried to teach everything there was to know about group theory, instead of just what was relevant to prove truly remarkable results. So, I was disappointed. That's also my complaint with most Abstract Algebra textbooks. Then, when I found this book, I was excited, because I was able to learn all the essentials I needed to understand the insolvability of the quintic. After this book proves that remarkable result, it ends, and that's what I love about this book. If you're looking for a completist treatment of Abstract Algebra, consider Dummit and Foote, what I used in college. But, if you're primarily interested in a very lucid, accessible, yet intricate proof of the insolvability of the quintic, then by all means buy this book! Sure, there are other tangential topics in exercises, an optional chapter, and _sprinkled_ throughout but these are usually indicated as such and don't obtrude the main inquiry. Other remarkable results treated in this book are the impossibility of certain compass and straight-edge constructions that tormented geometers for over two thousand years. There are a few typos in this book, but you'll always be able to figure out what the author means.
So, definitely pick up this wonderful book! I can't reccomend it more! I've been re-reading it for months now!
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Most Recent Customer Reviews
3.0 out of 5 stars Terribly mediocre, though you get what you pay for.
Honestly, its alright. I commend it for being very cheap, and my professor studied under Pinter so it came with the highest praise. But really, its just okay. Read more
Published 7 days ago by T. Duffy
5.0 out of 5 stars A Waitin' For Read
Read takes one where everything before accumulated and wasn't used! It's absolutely delightful with sense never before known. A required delight.
Published 28 days ago by Jude
5.0 out of 5 stars Great Intro
If you have never taken an abstract algebra course, this book will be very informative yet not too harsh. Read more
Published 1 month ago by Allie Burkhardt
4.0 out of 5 stars Good reference book.
This book has it all for Abstract Algebra and is a good reference book if you have already taken at least a semester of basic Abstract Algebra or are looking for just a quick... Read more
Published 4 months ago by CG
5.0 out of 5 stars Algebra book
Clear and concise instructions
Would recommend if the reader is a college grad who understands higher level math and is familiar with set theory
Published 4 months ago by D. Henderson
1.0 out of 5 stars WORST. BOOK. EVER.
Do not buy. Even the author himself said this book contains many errors. There are no solutions to check your work and the homework problems do not match the 2 page chapter... Read more
Published 6 months ago by Preston stock
5.0 out of 5 stars Great Undergrad Book!
This is the best undergrad mathematics book I've ever read- as someone interested in math and engineering, it really appealed to me through its clear proofs and interesting,... Read more
Published 6 months ago by George Abraham 2017
5.0 out of 5 stars An elegant introduction to an elegant field of study
As a physics major, I find this book to be incredibly helpful. The formalism of abstract algebra is all but necessary in the modern treatment of theoretical physics (whether we are... Read more
Published 7 months ago by Tony
5.0 out of 5 stars I'm impressed.
Extremely well written text. Easy to follow and well paced. I would recommend this for an introduction to group theory in a heartbeat.
Published 8 months ago by Alex Betty
1.0 out of 5 stars Great Textbook Kindle Version Is terrible
Actual book is fine but the Spelling errors in the kindle version actually make some of the problems impossible to solve had to buy the book because I got fed up with having to... Read more
Published 9 months ago by MathMajor
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Topic From this Discussion
Good second book on group theory (after Pinter)
I'm no expert, but some recommend Dummit and Foote: http://www.amazon.com/Abstract-Algebra-Edition-David-Dummit/dp/0471433349
Feb 11, 2014 by Matthew H. Adams |  See all 2 posts
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