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Algebra 1st Edition

3.9 out of 5 stars 43 customer reviews
ISBN-13: 978-0130047632
ISBN-10: 0130047635
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From the Publisher

This introduction to modern algebra emphasizes concrete mathematics and features a strong linear algebra approach.
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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 (43 customer reviews)
  • Amazon Best Sellers Rank: #421,178 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

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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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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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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Format: Hardcover Verified Purchase
I wish to first point out that several positive reviewers argue that the strength of the book is what it forces you to look for and that if you cannot find the missing puzzle pieces you must be mathematically weak or studying poorly. The argument seems to be that the book's strength lies in that which is omitted.

This is a silly argument, but it is telling of the pedagogical philosophy and communication bias in the book. The purpose of a text book is to communicate, but Artin's lazy stream-of-consciousness style will leave many out in the cold.

Indeed, the book does seem to be written for those who do not need it, an enormous sequence of casual asides to a lost conversation between students already versed in the field and a professor intent on communicating in fits and starts, short growls and nods.

As one reviewer noted, the text derives from Artin's lecture notes. This is not uncommon, but the book shows little evidence of any thought put into making the book useful as a reference. Rather it has many gaps both large and small. It is what one might expect from putting in the least amount of editorial work and hastily typesetting the notes for publication.

In terms of original content, Artin provides important insights. Still, while I can imagine thinking "what does Artin have to say about (blank)", I cannot imagine bothering to search a book so deliberately and thoroughly written to make the reader ask and answer their own questions.
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