- 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)
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Abstract Algebra, 3rd Edition 3rd Edition
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Top Customer Reviews
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.
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.
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.Read more ›
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.Read more ›
Most Recent Customer Reviews
excellent book especially if you combine it with the solutions posted at [...], whose correctness is cited by several other seemingly credible online commentators.Published 1 month ago by mda77
While not the most high-level algebra text (Hungerford is perhaps the gold standard), this comes with many well crafted examples and wonderful explanatory prose when other texts... Read morePublished 1 month ago by mw
I thought this book was better than some of the other advanced undergraduate/graduate books out there. However, I wouldn't recommend it for you're first course in abstract algebra.Published 2 months ago by Schwarz
As a student I enjoyed this book. I had it for a class, but I think one could self study from it. There are lots of problems in every chapter of varying difficulty.Published 11 months ago by F.F.
Just what I needed to fill-in my knowledge of mathematics.Published 11 months ago by Driftwin Books