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Algebra Hardcover – April 24, 1991

ISBN-13: 978-0130047632 ISBN-10: 0130047635 Edition: 1st

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Product Details

  • Hardcover: 672 pages
  • Publisher: Pearson; 1 edition (April 24, 1991)
  • Language: English
  • ISBN-10: 0130047635
  • ISBN-13: 978-0130047632
  • Product Dimensions: 7.1 x 1.5 x 9.4 inches
  • Shipping Weight: 8.6 ounces
  • Average Customer Review: 3.9 out of 5 stars  See all reviews (42 customer reviews)
  • Amazon Best Sellers Rank: #126,479 in Books (See Top 100 in Books)

Editorial Reviews

From the Publisher

This introduction to modern algebra emphasizes concrete mathematics and features a strong linear algebra approach.

Customer Reviews

Frankly, if you use this book, it will be slow going.
David
This text provides a very nice treatment of abstract algebra; most proofs are in the book and the ones that aren't are straightforward.
Anonymous
Artin's book is probably one of the better books, more because of the way you have to read it to learn it.
Ellipsic

Most Helpful Customer Reviews

103 of 113 people found the following review helpful By Ellipsic on June 23, 2004
Format: Hardcover
Artin's book is probably one of the better books, more because of the way you have to read it to learn it. Artin's book is extremely nonstandard, in the sense that it isn't so "encyclopedic" as you usually encounter with the whole theorem, corollary, proof, proof, proof, example, example sequence. What I think a lot of readers miss is that Artin's book makes you fill in the details he leaves out by using the hints he mentions in words within the text. For example, I was able to expand the two pages of notes on Ch 2, section 5, in Artin into about 8 pages of original notes and theorems, just by digging for the main points. If you want a sample of my notes, please email me and I'll email you a brief PDF sample for you to compare. That being said, assume that you will have to dig a lot in this book, and should you choose to study from it, I suggest the following:

How to read it:

With a cup of coffee, or tea, and a notepad of paper for you to make comments on. Do not take notes; anyone knows that simply rewriting things doesn't do anything for learning. You should do the proofs in different ways, if you can see how, and try to make some of the aside remarks he makes into theorems or more precise ideas (this is not to say that Artin lacks rigor; this is just talking about the general commentary. When he makes commentary, it always seems to be enough to actually dig out exactly what to do after a little scratching). He also leaves a lot of easier proofs to the reader, so do them.

Is non-standard a less-rigorous approach?

No. Artin is definitely doing his own thing here, but I think it works really well.
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43 of 46 people found the following review helpful By Dr. Joseph R. DELLAQUILA on September 26, 2004
Format: Hardcover
By treating the concrete before the abstract, Artin has produced the clearest and easiest to understand expositon I have seen. He delves quite deeply into groups, rings, field theory and Galois theory. It is NOT true, as one reviewer claims, that Artin does not treat fields: an entire chapter is devoted to the topic.

If Bourbaki is your god and you believe axiomatization is the only way to present this material, then you won't like this book. But remember that this work is written by the son of the great Emil Artin, and Michael is a first-rate mathematician as well.

The ordering of topics and the approach are non-standard but this emphasis on the concrete before the abstract and the use of a function motivated development make this book stand apart from the competition. It is not only the best undergraduate abstract algebra text that I have seen but it can be very useful for graduate students. My undergraduate major was not in math, I HAD NO UNDERGRADUATE COURSE IN ABSTRACT ALGEBRA but I jumped into a really heavy-duty graduate level abstract algebra course with Hungerford as the text. Now, I feel that Dummit and Foote is much better than Hungerford and Artin is even better than the aforementioned and much better - and more thoughtful -than Gallian. I wish I had Artin to give me enlightenment and perspective when I was struggling with this material having had no prior exposure to it.
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44 of 50 people found the following review helpful By "mikeu3" on May 7, 2000
Format: Hardcover
Pretty much any introductory abstract algebra book on the market does a perfectly competent job of introducing the basic definitions and proving the basic theorems that any math student has to know. Artin's book is no exception, and I find his writing style to be very appropriate for this purpose. What sets this book apart is its treatment of topics beyond the basics--things like matrix groups and group representations. I suppose many introductory books shy away from much of the material on matrix groups in Artin's book because it involves a little analysis (and likewise for the section on Riemann surfaces in the chapter on field theory). However, Artin correctly realizes that a reasonably mathematically mature student--even one who doesn't know much analysis--will be able to profit from and enjoy the relatively informal treatments he gives these slightly more advanced topics. Of course these topics can also be found in graduate-level texts, but I for one would much rather be introduced to them via an example-based approach such as that in Artin than through the diagram-chasing obscurantism in more advanced books. I happened upon this book a little late--in fact, only after I'd taken a semester of graduate-level algebra and already felt like analysis was the path I wanted to take--but I'm beginning to think I would have been more keen on going into algebra if I'd first learned it from a book like this one.
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14 of 16 people found the following review helpful By longhorn24 on December 12, 2006
Format: Hardcover
One of the chapters in Artin's book has a quote from Hermann Weyl: "In these days the angel of topology and the devil of abstract algebra fight for the soul of every individual discipline of mathematics." If you've studied undergraduate algebra with any other book and then encountered this wonderful book, you'll understand what he meant.

While Artin provides a comprehensive treatment of introductory algebra, starting with the most basic concepts, he covers a tremendous range of topics including matrix (Lie) groups and representation theory and Riemann surfaces. This does come at the expense of the usually comprehensive treatment of the standard topics of undergraduate algebra - readers hoping for ample opportunity to apply the Sylow classification theorems to describe all groups of order less than 100 or to describe the Galois groups of fourth-order polynomials will be sorely disappointed.

Nonetheless, the reader mathematically mature enough to view these exercises as annoying as factoring polynomials was in high school algebra will appreciate this book. Artin's clear biases towards representation theory and algebraic geometry are obvious, but considering modern research in these fields is more active than in, say, the classification of finite groups or in Galois theory, this treatment makes sense.

While some of the topics are more advanced than normally taught at the undergraduate level, the purpose of the book isn't to teach the method of mathematical proof but to provide a flavor of algebra and more importantly, its applications to other fields.
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