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Abstract Algebra [Hardcover]

David S. Dummit , Richard M. Foote
5.0 out of 5 stars  See all reviews (2 customer reviews)
List Price: CDN$ 120.95
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Book Description

July 14 2003 0471433349 978-0471433347 3
Widely acclaimed algebra text. This book is designed to give the reader insight into the power and beauty that accrues from a rich interplay between different areas of mathematics. The book carefully develops the theory of different algebraic structures, beginning from basic definitions to some in-depth results, using numerous examples and exercises to aid the reader's understanding. In this way, readers gain an appreciation for how mathematical structures and their interplay lead to powerful results and insights in a number of different settings.
* The emphasis throughout has been to motivate the introduction and development of important algebraic concepts using as many examples as possible.

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Most helpful customer reviews
3 of 3 people found the following review helpful
5.0 out of 5 stars Comprehensive book July 9 2004
By A Customer
Format:Hardcover
I'm a graduate student in math. We used this book for the basic year-long abstract algebra sequence: group theory, chapters 1-4 and some of chapter 5; ring/field/galois theory chapters 7-9, 13-14. Some of my fellow students took a module theory course which was at least partially based off chapters 10 and (I think) 11. I'm sure more advanced courses could easily be based off chapters 15-end. Considering the cost of university books, I consider it very nice to buy one book for essentially 3+ courses.
The exercises in some sections are very diverse. My group theory professor made us do a huge number of them, and now I am amazed at how often I see questions similar to those from Dummit-Foote show up on past qualifier exams from many different universities. Regarding lack of answers in the back...well, you shouldn't need too many, and if you get really stuck, that's what the professor is for. And if you're learning it on your own then I'm thinking you should be brainy enough not to need answers!
The text itself is very readable and complete.
I don't think I'd recommend this as an undergrad textbook, although I've no doubt that there are some clever undergrads who could learn from it. I used Herstein's "Topics in Algebra" for my intro-to-abstract course as an undergrad. Herstein is designed to be introductory in nature, though still a wonderful book, while DF is more encyclopedic.
I do have one complaint though: the binding in DF started to crack and pages started to fall out near the end of its first semester of use. It did see some moderate backpack use but not too much, certainly less than many other books I've had in the past. So take care of it!
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0 of 1 people found the following review helpful
5.0 out of 5 stars Best Algebra Book Ever Jan. 17 2006
Format:Hardcover
This is the best abstract algebra I have ever read.
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Most Helpful Customer Reviews on Amazon.com (beta)
Amazon.com: 4.3 out of 5 stars  41 reviews
59 of 65 people found the following review helpful
3.0 out of 5 stars Excellent Problems, Mediocre Exposition, Overpriced May 18 2008
By Justin Hilburn - Published on Amazon.com
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.
54 of 60 people found the following review helpful
5.0 out of 5 stars The book after Herstein Dec 11 2004
By Michael B Williams - Published on Amazon.com
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).
19 of 20 people found the following review helpful
5.0 out of 5 stars Comprehensive book July 9 2004
By A Customer - Published on Amazon.com
Format:Hardcover
I'm a graduate student in math. We used this book for the basic year-long abstract algebra sequence: group theory, chapters 1-4 and some of chapter 5; ring/field/galois theory chapters 7-9, 13-14. Some of my fellow students took a module theory course which was at least partially based off chapters 10 and (I think) 11. I'm sure more advanced courses could easily be based off chapters 15-end. Considering the cost of university books, I consider it very nice to buy one book for essentially 3+ courses.
The exercises in some sections are very diverse. My group theory professor made us do a huge number of them, and now I am amazed at how often I see questions similar to those from Dummit-Foote show up on past qualifier exams from many different universities. Regarding lack of answers in the back...well, you shouldn't need too many, and if you get really stuck, that's what the professor is for. And if you're learning it on your own then I'm thinking you should be brainy enough not to need answers!
The text itself is very readable and complete.
I don't think I'd recommend this as an undergrad textbook, although I've no doubt that there are some clever undergrads who could learn from it. I used Herstein's "Topics in Algebra" for my intro-to-abstract course as an undergrad. Herstein is designed to be introductory in nature, though still a wonderful book, while DF is more encyclopedic.
I do have one complaint though: the binding in DF started to crack and pages started to fall out near the end of its first semester of use. It did see some moderate backpack use but not too much, certainly less than many other books I've had in the past. So take care of it!
22 of 24 people found the following review helpful
5.0 out of 5 stars Excellent book Sept. 2 2004
By Amazon Customer - Published on Amazon.com
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.
12 of 12 people found the following review helpful
5.0 out of 5 stars Were love meets lust. Aug. 18 2008
By Jimmy Salvatore - Published on Amazon.com
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.

Overall, wonderful book. One of my favorites of all time. DEFINITELY have it, and if you study from it, you may feel more comfortable supplimenting it with Herstein's Algebra, Artin's Algebra (which are just as hard) or Fraleigh's Abstract Algebra, Gallian's Abstract Algebra, or Rotman's Abstract Algebra (which are much, much easier).
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