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Elements of Abstract Algebra (Dover Books on Mathematics) Paperback – October 1, 1984

ISBN-13: 978-0486647258 ISBN-10: 0486647250

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Product Details

  • Series: Dover Books on Mathematics
  • Paperback: 224 pages
  • Publisher: Dover Publications (October 1, 1984)
  • Language: English
  • ISBN-10: 0486647250
  • ISBN-13: 978-0486647258
  • Product Dimensions: 8.4 x 5.3 x 0.5 inches
  • Shipping Weight: 8.8 ounces (View shipping rates and policies)
  • Average Customer Review: 4.1 out of 5 stars  See all reviews (18 customer reviews)
  • Amazon Best Sellers Rank: #439,730 in Books (See Top 100 in Books)

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Customer Reviews

I recommend this book for all who are taking undergraduate Abstract Algebra.
Ariel Alcaide
While this is true and easier to cope with at first, Clark offers full discussion and suggests where the reader needs to fill in the gaps with proof.
Adam Nordloh
Just because you can begin with a set of definitions and use them to prove very complicated theorems doesn't mean doing so is worthwhile.
Ryan Malloy

Most Helpful Customer Reviews

47 of 47 people found the following review helpful By Allan H. Clark VINE VOICE on October 24, 2012
Format: Kindle Edition Verified Purchase
As the author it would be immodest to comment on the outstanding quality of my book in its original form, but whatever process was used for converting from print to Kindle, it allows misprints to creep in. For example in the statement of the First Sylow Theorem in section 56, the exponent n on the p has been replaced by ". This makes the statement nonsense. The error is not in the print version.

The problem of translation from print to Kindle becomes acute in the final chapter. In the print edition ideals of a ring are always in a fraktur font, but in the Kindle edition, they are given in ordinary letters, not even bold-face. This makes for much more difficult reading. In some equations extra symbols are introduced making complete hash of them. As a final insult the article reference numbers are omitted from the Index and the indentations for subentries removed, making it completely useless.

Having textbooks on Kindle is a wonderful thing, but some proof-reading is necessary--especially for mathematics texts--along with a reasonable effort to reproduce the text accurately. It is not enough to run it through OCR and hope for the best. If Kindle is to have a chance in the textbook market--as it should--much greater care needs to be taken with technical books.
This is a poor example of conversion to Kindle.

BUY THE PRINT EDITION AND SKIP THE KINDLE VERSION.
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40 of 41 people found the following review helpful By A Customer on July 11, 2002
Format: Paperback
This is a book whose level is between an undergraduate (e.g. Herstein) and a graduate algebra book (e.g. Hungerford,Jacobson). I am a graduate student and I used it for a quick review and i really liked it. It is a little book of 200 pages. One interesting feature is that it first covers field & Galois theory and then ring theory.
Contents (w.o. subsections):
1. Set Theory
2. Group Theory
3. Field Theory
4. Galois Theory
5. Ring Theory
6. Classical Ideal Theory.
One thing I also liked is that the exercised are scattered throughout the text rather then collected at the chapter ends. You read something and immediately work on a couple (or more) of questions. You understand at the spot rather than waiting the chapter end.
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30 of 31 people found the following review helpful By David B. Massey on August 13, 2001
Format: Paperback
I used the previous version of this book while I was a mathematics graduate student at Duke University in 1982. I have never seen a better book for LEARNING field and Galois theory; however, this book is not intended as a reference source. The exercises lead one incrementally through the theory, and this is certainly the best way to learn abstract algebra. I lost my copy of the previous version, but have replaced it with the new one - to have a copy to lend to my own graduate students who want to learn this material.
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32 of 35 people found the following review helpful By George E. Hrabovsky on October 16, 2001
Format: Paperback
This book is certainly not for everyone. If you prefer a book where you are held by the hand through the material, where you are fed the interpretation, and where all of the work is done for you then do not buy this book. This book is for people who not only want to memorize facts about algebra, but also want to learn to do algebra. The only way to learn to do algebra (or anything else for that matter) is to do it. For example, the first section is (reasonably enough) on sets and has nine subsections. Within these nine sections you are expected to perform nine tasks. This is done in three and a half pages. The section on symmetric groups has ten sections and eighteen tasks in eight pages. This averages to a fraction more than three tasks per page for a 196 page book. This is a lot of problems to work through! It is not so many that the task is impossible in a reasonable period of time. Will you solve every problem the first time? No. Many of these are quite challenging. If you at least study each problem and spend at least five minutes trying to understand it, by the time you are done with the book you will have a good understanding of abstract algebra, and you will be prepared to grapple with more elegant treatments of the subject.
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27 of 29 people found the following review helpful By Ryan Malloy on January 2, 2004
Format: Paperback
Since the reviews have been generally positive, I'll start with the major negative. Clark does a poor job of motivating the material being developed. As a reader with no background in modern algebra, I found the group theory chapter tedious and uninteresting. Just because you can begin with a set of definitions and use them to prove very complicated theorems doesn't mean doing so is worthwhile. It wasn't until I read the fourth chapter on Galois Theory that everything clicked and I realized the importance of seemingly arbitrary definitions and correspondingly ponderous theorems. But even then I had to do considerable introspection. The proof that polynomials are solvable by radicals iff the Galois group of transformations is solvable is presented as just another theorem, whereas that proof is the principal purpose of most of the book to that point. I basically had to figure out Galois's original idea for myself and then go back and reread Clark's chapters 2-4 for the complete analysis. To be fair, this book has an introduction that sort of hints at Galois's idea, but I feel it is very poorly done. Perhaps a more thorough, more motivational introduction would make this a 5-star book.
Sometimes Clark appears needlessly complex. In one part, he defines the normalizer of a subgroup as the group of all elements in which the subgroup is normal. Then he proves, in a bizarre and tedious way, that the normalizer is the largest group in which the subgroup is normal. While I'm not a mathematician, it seems to me that this is obviously true by definition.
On the other hand, you can learn a lot from this book quickly precisely because of its compactness. I am fond of concise writing, but the whole purpose for a book is to guide the reader's thought. I almost recommend beginning this book with chapter 4 unless you have already expended considerable thought on equations.
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