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Abstract Algebra, 3rd Edition 3rd Edition

4.4 out of 5 stars 58 customer reviews
ISBN-13: 978-0471433347
ISBN-10: 0471433349
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  • Abstract Algebra, 3rd Edition
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Product Details

  • Hardcover: 944 pages
  • Publisher: Wiley; 3 edition (July 14, 2003)
  • Language: English
  • ISBN-10: 0471433349
  • ISBN-13: 978-0471433347
  • Product Dimensions: 7.6 x 1.3 x 9.3 inches
  • Shipping Weight: 3.4 pounds (View shipping rates and policies)
  • Average Customer Review: 4.4 out of 5 stars  See all reviews (58 customer reviews)
  • Amazon Best Sellers Rank: #118,353 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

By Justin Hilburn on May 18, 2008
Format: Hardcover
(When I wrote this review D+F was almost one hundred and fifty dollars. It seems to have dropped in price significantly since then)

D+F tries to straddle the line between being a book for advanced undergraduates and a book for graduate students and does a decent job. It is fairly readable, with many excellent exercises and lots of examples. The book also covers all the material in the standard graduate algebra sequence. The section on group theory is particularly good.

I think the biggest problem with D+F is that it is bland. The exposition isn't a joy to read and full of motivation like that of Halmos, Stillwell, or Eisenbud and it isn't full of deep insights like that of MacLane, Lang, or Artin. In addition Category Theory is pushed off to an appendix at the end of the book rather than integrated through the text. Finally the book is expensive and the binding is terrible.

If you want to learn algebra I would recommend purchasing some of these cheaper more focused texts since almost everything in D+F is treated better elsewhere:

Basic Algebra - Mac Lane + Birkhoff - Algebra 3rd Edition
Galois Theory: Stillwell - Elements of Algebra, Artin - Galois Theory
Commutative Algebra: Eisenbud - Commutative Algebra With a View Towards Algebraic Geometry
Homological Algebra: Weibel - An Introduction to Homological Algebra, Mac Lane - Homology
Representation Theory - Fulton + Harris - Representation Theory

If on the other hand you are already fairly comfortable with algebra and are looking for a one volume reference I would just buy Lang. It is less than half the price, more advanced, and has more material.
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Format: Hardcover
I think I would only recommend this book to someone who has already had some exposure to algebra (or one especially gifted in mathematics). The beginning of the book is not too bad, but towards the end of Part I the pace quickens quite a bit. If you are willing to read over the text many times, and do all of the non-trivial exercises (there is an impressive olla podrida of algebra in them, most of which are the beginnings of some very deep ideas), then it should be a very rewarding experience. Namely because this is one of the most readable textbooks which covers everything from groups, rings, and fields to homological algebra and algebraic geometry. It is very rare to see this much material covered in one book, and for it to remain so structured (Rotman is an example of a book that covers a lot of material, but loses its structure somewhere).
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Format: Hardcover
I am surprised that this book has not got the 5 stars. It is very suitable for advanced undergraduates/first-year graduates. The book is full of examples; and the proofs are amazingly clear and succinct. The book introduces new concepts in the excercises long before the student encounters them in the sections.

This is a beautiful way to teach mathemtatics,--and indeed to learn it. The book is replete with examples that connect concepts from toplogy and real analysis with Algebra.

This book definitely deserves the 5 STARS.
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Format: Hardcover Verified Purchase
Dummit and Foote contains just about everything an undergraduate ought to know about abstract algebra. In addition, it is written in a more user-friendly, down-to-earth fashion than, say, Lang's Algebra is.

The pro's have been discussed in other reviews and include: clear development of group, ring, and field theory; tons of exercises at the end of every chapter; numerous examples scattered around the text; sylow theorems (for group theory, imo, it's important, and not every algebra book does sylow stuff!); great introduction to exact sequences (useful if the reader is going into algebraic topology anytime soon. ugh!); galois theory is pretty clearly laid out; and, the third section of the book has some neat topics the reader can check out (which are, I think, commutative algebra, homological algebra, and representation theory introductions, as well as a small section on category theory at the very end).

The con's of D+F are the price (it's very expensive!), the binding (it's horrible!), and some of the sections are much harder than others and D+F doesn't do as well a job at explaining them as in many of the other sections (the tensors section sticks out in my head, and they wait something like 100 pages to explain "tricks" for figuring out the structure of finite groups after explaining some of the sylow stuff (eg., they wait to tell the reader about how to "pin small groups against one-another" and to make use of the sylow n! trick). Also, D+F introduce modules before vector spaces which I have mixed feelings about --- as a student who's already taken an algebra class, I love the "flow" of the lessons; as a student who remembers what it was like to try to imagine what modules "looked like", it makes me cringe to think that they didn't introduce vector spaces first.
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Format: Hardcover Verified Purchase
This is a superb textbook on algebra that is notable for its extremely clear and well-organized presentation. Development of different sections carefully builds on what went for, and running examples that gradually become more developed (for example, the quaternions as group, then as a ring, then various structural aspects) throughout. The terminology is completely standard, avoiding the temptation that some authors - or perhaps older texts - fall into of using bizarre terminology that is its author's favorite. The whole text has a very uniform, clear, well-architected feel to it: the sections stand on their own to the extent that they can, but also fit solidly into the rest of the presentation.

The presentation itself covers many topics which, taken together, make this an invaluable reference, for example group theory includes Burnside's theorem on solvability of certain finite groups (and at least mentions Feit-Thompson); ring theory includes a discussion of Gröbner bases; linear algebra includes symmetric and exterior algebras. A good introduction to algebraic geometry (the Nullstellensatz, localization, and some basic framework) is included. There is a solid introduction to representation theory via group rings and Wedderburn's theorem - an approach which is really more useful for applications than a pure group-theoretic introduction might have been.

Despite its broad coverage of topics, the book's development is extremely clear and easy-to-read. Because of the many examples and easy exercises, it is one of the most easy-to-understand texts I have seen. Every new idea is carefully defined and illustrated with multiple examples, proofs are very clear and painstaking.
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