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Algebra (Graduate Texts in Mathematics) (v. 73) 8th Edition

4.4 out of 5 stars 29 customer reviews
ISBN-13: 978-0387905181
ISBN-10: 0387905189
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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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Product Details

  • Series: Graduate Texts in Mathematics (Book 73)
  • Hardcover: 504 pages
  • Publisher: Springer; 8 edition (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: 1.6 pounds (View shipping rates and policies)
  • Average Customer Review: 4.4 out of 5 stars  See all reviews (29 customer reviews)
  • Amazon Best Sellers Rank: #129,847 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

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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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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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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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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Format: Hardcover Verified Purchase
Hungerford is definitely not the place to start in algebra. It is too terse and assumes the reader is a competent, graduate level mathematician. If you are an undergraduate look to Abstract Algebra or Contemporary Abstract Algebra; both of those leave the kid gloves on and have some fun bits along the way. Hungerford doesn't pull any punches. Proofs are concise and have no unnecessary explication. Initially, I thought the proofs were too brief. The proofs are in fact fine, I just needed to read with more care. I used this book as the primary source of review material for algebra comprehensive exams and was pleased with it. There are ample exercises and they have a nice range in difficulty; trying to work most of them was good practice and fun. This book is certainly not the last algebra book you will ever need. It has a very brief treatment of categories and that is certainly an issue should you go forward. Algebra (Graduate Texts in Mathematics) is a good book to follow Hungerford and nail down the category theory. Still despite that omission, Hungerford is a good midpoint in learning algebra. I am constantly pulling it off the shelf as a reference or trying to keep it from being stolen by people needing to look things up. Buy it and start studying, you'll learn things!
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