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Abstract Algebra, 3rd Edition
 
 
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Abstract Algebra, 3rd Edition [Hardcover]

David S. Dummit (Author), Richard M. Foote (Author)
4.2 out of 5 stars  See all reviews (50 customer reviews) |
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Book Description

Publication Date: July 14, 2003 | ISBN-10: 0471433349 | ISBN-13: 978-0471433347 | Edition: 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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Editorial Reviews

From the Publisher

This text is designed to give students insight into the main themes in abstract algebra. Early introduction to recurring notions such as homomorphisms, isomorphisms, actions, and classifications provides a natural flow for the development of basic abstract algebra. Students are immediately exposed to concepts the way an algebraist (or mathematician) envisions and works with them. --This text refers to an alternate Hardcover edition.

From the Back Cover

Key Benefit: The book carefully develops the theory of different algebraic structures, beginning from basic definitions to some in-depth results, using numerous examples and exercises throughout to aid the reader's understanding. Key Topics: This edition includes substantial new material in areas that include: tensor products, commutative rings, algebraic number theory and introductory algebraic geometry. Also, includes rings of algebraic integers, semidirect products and splitting of extensions, criteria for the solvability of a quintic, and Dedekind Domains. --This text refers to an alternate Hardcover edition.

Product Details

  • Hardcover: 944 pages
  • Publisher: Wiley; 3 edition (July 14, 2003)
  • Language: English
  • ISBN-10: 0471433349
  • ISBN-13: 978-0471433347
  • Product Dimensions: 7.8 x 1.6 x 9.2 inches
  • Shipping Weight: 3.6 pounds (View shipping rates and policies)
  • Average Customer Review: 4.2 out of 5 stars  See all reviews (50 customer reviews)
  • Amazon Best Sellers Rank: #65,462 in Books (See Top 100 in Books)

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More About the Authors

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Richard M. Foote
David Steven Dummit

Customer Reviews

Most Helpful Customer Reviews
100 of 101 people found the following review helpful
Format:Hardcover
Most of the reviews have been positive, and basically explain the strengths of the book, but I thought some would appreciate hearing what someone, like me, who has gone through most of the material in the book over the last three and half years, would say.

This is the only book I bought as an undergraduate that I still look at today. All my other undergrad texts are either stored away somewhere or gather dust on my bookshelf. The reason is simple: Dummit and Foote has stocked in one book almost all the basic algebra that is required for my study of 3-manifold theory. I suspect this is true of other fields also. By "basic algebra" I mean the key ideas and examples that are used in many different areas of mathematics.

Just recently, I needed to pick up some algebraic geometry in order to understand SL(2, C) character varieties. As usual, I went to my Dummit and Foote and found what I needed (for the most part). And also as usual, I will need to supplement that knowledge with some more advanced books.

A couple things about this book annoy me though: 1) the price -- however, I have certainly gotten my money's worth out of it over the years, so I can't really complain 2) Initially when I first got the book, the wealth of material in the book appeared intimidating and esoteric to me; however, nowadays I would say there isn't *enough* in this book. Oftentimes it seems that I get just a taste before the discussion of a topic ends. On the other hand, I am realistic, so I realize that this book is not meant to be encyclopedic but to introduce the reader to the more advanced topics.

I've yet to see another book that carries all the topics of this one, and remains fairly reader-friendly (as this one does).

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42 of 46 people found the following review helpful
The book after Herstein December 11, 2004
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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16 of 16 people found the following review helpful
Format:Hardcover
This book arose from the lecture notes of Dave Dummit and Richard Foote, both at the University of Vermont. I first encountered this book in Dummit's own graduate algebra I-II class and was swept away by the clarity in contrast with my previous classes. Both authors are excellent teachers, and their text is equally good. Really slick development of group and ring theory, in an intuitive manner, constantly working through examples with symmetric and dihedral groups. Also includes high-level algebra suited for topics courses. I highly recommend this text.
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Most Recent Customer Reviews
The best on the market
Extremely good explanation, structure of the book. Lots of examples makes it a pleasure to read.
Among my peers - graduate students - this book is considered the best... Read more
Published 17 days ago by Snohvit
RIGOROUS AND CHALLENGING
This book can be used in both graduate and undergraduate modern algebra courses. I bought it to self study algebra for number theory and advanced geometry. Read more
Published 2 months ago by PersonReviewing
Not the best place to learn
It was a happy day when I sold this back and got Artin instead. If you want to "learn" abstract algebra, it might be better to use a book like Artin, since it develops the subject... Read more
Published 6 months ago by aps
A must have for any math student
I am taking a graduate level algebra course, and I've found many of my previous texts to be insufficient as a reference when I need to bail myself out of a jam. Read more
Published 8 months ago by From Detroit
good graduate text
This is a good graduate text in Abstract Algeba. The authors offer many good examples to explain or to motivated discussions. Read more
Published 14 months ago by phys_math
My favorite algebra book so far
I really like (and would recommend) Dummit and Foote for those wanting to learn abstract algebra
I've used others (Lang, Jacobson, and Herstein). Read more
Published 14 months ago by M. Fore
Great textbook... if you already know everything in it
This book is great if you already know the material. I was taking a first class in Abstract Algebra with this as a textbook, though, and it was completely unenlightening. Read more
Published 20 months ago by Maxim Vengerov
Goodbook for a class
It's a good book with a lot of exercises.
Very good for a graduate class.
Being read with Hungerford is a good combination to prepare for the qual.
Published 20 months ago by Xuwen Chen
The Best Abstract Algebra Textbook!
This textbook is amazing. If you're looking for something more applied, this isn't it. But if you're ready to really dig into abstract algebra, this book will give you a strong... Read more
Published 23 months ago by M. Dosseva
The Wordiness is overwhelming
Dummit and Foote's Abstract Algebra book, in terms of content, is one of the best. It should be easily read by any decent student at the advanced undergraduate or early graduate... Read more
Published on April 26, 2010 by Georg Cantor
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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First Sentence:
Some results and notation that are used throughout the text are collected in this chapter for convenience. Read the first page
Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
nonprincipal irreducible character, nonpivotal columns, modules whose annihilators, same free rank, grevlex monomial, invariant factor decomposition, simple radical extensions, universal side divisor, taking homomorphisms, map aug, largest invariant factor, minimal primary decomposition, constructible elements, divisor decomposition, ring under componentwise addition, rational canonical form, left group action, inequivalent extensions, affine algebraic sets, nonisomorphic groups, compatible homomorphisms, known subfields, distinct irreducible characters, complete preimage, localization commutes
Key Phrases - Capitalized Phrases (CAPs): (learn more)
Euclidean Domain, Unique Factorization Domain, Fundamental Theorem, Principal Ideal Domain, Sylow's Theorem, Lagrange's Theorem, Zorn's Lemma, Chinese Remainder Theorem, Wedderburn's Theorem, Lattice Isomorphism Theorem, Cauchy's Theorem, Eisenstein's Criterion, Hilbert's Basis Theorem, Burnside's Theorem, Hilbert's Nullstellensatz, Hilbert's Theorem, Maschke's Theorem, Second Isomorphism Theorem, Nakayama's Lemma, Schur's Lemma, Bezout Domain, Shapiro's Lemma, Feit-Thompson Theorem, Frattini's Argument, Noether's Normalization Lemma
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