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Algebra (Graduate Texts in Mathematics) (v. 73) Hardcover – February 14, 2003

ISBN-13: 978-0387905181 ISBN-10: 0387905189

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Algebra (Graduate Texts in Mathematics) (v. 73) + Real Analysis: Modern Techniques and Their Applications + Abstract Algebra, 3rd Edition
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Product Details

  • Series: Graduate Texts in Mathematics (Book 73)
  • Hardcover: 504 pages
  • Publisher: Springer (February 14, 2003)
  • Language: English
  • ISBN-10: 0387905189
  • ISBN-13: 978-0387905181
  • Product Dimensions: 6.1 x 1.1 x 9.2 inches
  • Shipping Weight: 1.8 pounds (View shipping rates and policies)
  • Average Customer Review: 4.4 out of 5 stars  See all reviews (25 customer reviews)
  • Amazon Best Sellers Rank: #245,645 in Books (See Top 100 in Books)

Editorial Reviews

Review

From the book reviews:

“This is a text for a first-year graduate course in abstract algebra. It covers all the standard topics and has more than enough material for a year course.” (Allen Stenger, MAA Reviews, September, 2014)

Thomas W. Hungerford

Algebra

"An excellent text from which to teach the beginning graduate survey course in algebra and I would recommend it to anyone considering a text for such a course."—LINEAR AND MULTILINEAR ALGEBRA


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Customer Reviews

One of the best comprehensive algebra books available to grad students.
Ash
Sure there are plenty of '...left as an exercise for the reader' but, like in his undergraduate text, Hungerford clearly illustrates how to prove a theorem.
Jason Schorn
I used this book as the primary source of review material for algebra comprehensive exams and was pleased with it.
Samuel B. Cole

Most Helpful Customer Reviews

48 of 52 people found the following review helpful By Todd Ebert on July 12, 2004
Format: Hardcover
I've been acquainted with several introductory graduate algebra
books over the years, and prefer this one for its coverage of all the fundamental areas (groups, modules, rings, linear algebra, fields, and category theory), being concise, and providing great care when outlining each proof.
If one compare's the amount of material in this book to Jacobson's "Basic Algebra Vol 1", Grove's "Algebra", or Herstein's "Abstract Algebra", Hungerford's book gets the nod.
Moreover, I much more prefer the concise definition, example, theorem, proof format over the more colloquial approach, as can be found in Jacobson's text. For me at least, the payoff for reading an algebra text is the beauty found in the logic and reasoning from which very profound results arise from the complex interaction and use of more straightforward ones. And this is exactly where Hungerford's book shines through in tremendous glory. When outlining a proof he does an outstanding job in citating the results from previous Chapters that are used. For me this is the strength of algebra (In geometry I cringe when I get a picture for proof, and in analysis it is often quite complicated to verify that a given situation possesses the appropriate conditions needed to invoke some famous lemma or theorem).
One last good word about this book: I found the exercises both in abundance (after each section) and quite reasonable for a first year grad. student. Happy reading.
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24 of 24 people found the following review helpful By David Rudel on September 8, 2000
Format: Hardcover
This tome is probably the best single-volume REFERENCE for basic abstract algebra at the graduate level. It touches on almost every important subject. However, the style is very much in the way of an efficient, concise, statement of fact rather than a lucid expository of subject-matter.
This is an excellent reference, but for the task of learning the material (especially if without a lecture), I would recommend Dummit and Foote or Steinbeck (the former for advanced undergraduate, the latter for purely graduate study).
Also, while this is very comprehensive, it simply cannot fully treat everything in all subjects. For example, very little is given in the way of group (co)homology. For the specialist, you should instead invest in more specific books (e.g. Robinson).
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20 of 20 people found the following review helpful By Amazon Customer on April 26, 2000
Format: Hardcover Verified Purchase
As a reference, this is simply an amazing book; tons of information are crammed into this book. The flip side is that if you are seeing this information for the first time, the presentation can be a little daunting. I started using this book in a class last year and hated it at first, because the presentation of material here is very densely packed together and not written for maximum clarity. For example, the chapter on category theory was the first time I'd seen the subject, and I found it frustrating, unlike the presentation given by, say, Rotman in his Algebraic Topology text. All of that said, though, I appreciate the book more now looking back on the material. Overall, if you haven't seen the material before, this is a fine book as long as you've got someone to help you through the rough spots. As a reference, though, this book is extraordinary.
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23 of 25 people found the following review helpful By Jason Schorn on December 11, 2006
Format: Hardcover
Having read the texts of Lang and Jacobson, I would defintely recommend this text to anyone who desires a very solid and rigorous mathematical base with respect to the basics of Algebra. Not as simple as Jacobson I or as terse and dry as Jacobson II or as lifeless as Lang's Algebra, this text is by far the best 'classic' that exists and can be adequately utilized by satifactorially trained first year graduate students or highly motivated undergraduates.

So what seperates this text from the myriad of other Alegra texts that exist? The simple answer is that Hungerford actually proves the essential theorems in detail. Sure there are plenty of '...left as an exercise for the reader' but, like in his undergraduate text, Hungerford clearly illustrates how to prove a theorem. Compare this with Jacobson who takes a less than rigorous tone and, in almost a one-on-one conversation with the reader, explains/proves an idea in the matter of, say, a paragraph. Then at the end of the paragraph Jacobson will state the theorem, leaving you to re-read the paragraph in order to assure yourself this in fact was the case. Further, compare Hungerford's style with that of Lang. Lang is notorious for stating a theorem in its most abstract case and then giving what Hungerford, or most of use mere mortals, would call a sketch of a proof. This high level of rigor and commitment to the reader pays off and, in fact, rubs off when turns around and attempts to prove the various exercises. It's like the saying 'if you want to be successful, then surround yourself with sucessful people'. If you want to learn Algebra and, in particular, see how to construct rock-solid proofs, then you should surround yourself with teachers or texts written by the Hungerford's out there.
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4 of 4 people found the following review helpful By Mayer A. Landau on March 4, 2012
Format: Hardcover
This is that very rare technical book that is solidly organized at the section, chapter, and book level. The author can also write. The exercises are mostly straightforward, and most of the sections are short and saturated with examples. Every result is set aside as some sort of theorem, lemma, proposition, or corollary. If you like the "definition--example--theorem" format, you will absolutely LOVE this book. I very much prefer that format. However, the most alluring aspect of the book for me is that the writing is clear and the book organization is so lovely that you can easily trace back every result. If you are studying for your PhD qualifying exam, or moving on to commutative algebra, this book is an easy to use reference. The book is also deceptively simple to read, avoiding the extreme and unnecessary (for a junior grad student) abstraction one finds in Lang's book. An undergraduate course in abstract algebra is sufficient to get you through Hungerford's book without much hangup. But, ... it is a LONG read. On the other hand, most appropriate graduate level texts are long reads.
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