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Title: Elements of Abstract Algebra
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Manufacturer: Dover Publications
List Price: $12.95
Our Price: $8.57
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| Customer Reviews: |
| Elements of Abstract Algebra by Dover Publications DO NOT READ THIS PLEASE! IT COULD SAVE LIVES! |
I think I bought this book only because it had that neat Moor Methodesque presentation. And because I like to buy math books. And because it was cheap.
So far so good, though I can't say that it differs particularly from any standard text on algebra. It's not big enough to be Lang. Not terse enough to by Hungerford. And not comprehensive enough to be Dummit and Foote.
It also costs about a fifth of the price of any of those and has a neat do-it-yourself kind of methodology. |
| Elements of Abstract Algebra by Dover Publications Good Book on Algebra |
| I wanted to study Galois Theory to understand why the quintic is not solvable in radicals. I did some search on the net and ran into this book. My math background is in probability and analysis. With my background and interest this book I feel this book is perfect. It is not too difficult, plenty of exercises and I can follow the development; also I do not feel I am being talked down to by the author. I will have a good understanding of Galois and related theories after putting in the time and effort with this book. |
| Elements of Abstract Algebra by Dover Publications No answers to exercises , . |
It is inappropriate for self-study . |
| Elements of Abstract Algebra by Dover Publications One of the most insightful introductory algebra books |
I'm a math undergrad, and we're using this as our class text. While some of the criticizms in other reviews are true, Clark's treatment of algebra is thourough, rigourous, and full of many details that other books leave out. While it's true that this is a very concise text, I've found that Elements of Abstract Algebra offers deeper, richer insight into the topics it covers when compared to other intro books.
As an example - cosets. Many other texts completely leave out the fundamental concept of cosets: they are congruence classes modulo a subgroup. In at least three other intro texts I've looked at, the left coset of a subroup was simply defined as gH = {gh | h an elt of H}. 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.
For at least the first two chapters, the reader may want to consider supplementing this book with another, simpler book like Maxfield's "Abstract Algebra and Solutions by Radicals" (another great book). However, any beginner with enough time and discipline will find Clark's book to be a thorough and enlightening introduction. |
| Elements of Abstract Algebra by Dover Publications Extremely compact, not enough discussion |
| 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. |
| Elements of Abstract Algebra by Dover Publications Product Description |
Helpful illustrations and exercises included throughout this lucid coverage of group theory, Galois theory and classical ideal theory stressing proof of important theorems. Includes many historical notes. Mathematical proof is emphasized. Includes 24 tables and figures. Reprint of the 1971 edition.
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