Algebra (Graduate Texts in Mathematics)

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.


Worth it's weight in GOLD!   December 11, 2006
Jason Schorn (Spokane, WA)
14 out of 16 found this review helpful

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.

Well, if the previous paragraph did not convince you that buying and subsequently struggling through this text would be benificial, then let me try this. Out of the given texts who can claim the status of 'classic', this is by-far the most versatile Algebra text. That is, it offers the greatest flexibility with respect to learning about a specific sub-field of Algebra. This allows you to focus and properly chart your course. Whereas, with other texts you are given little or no insight into how to plot a course and hence you are left to assume reading the given text cover to cover is the only possible option. Furthermore, the material presented is foundational to any and every graduate student regardless of their Mathematical predilection and therefore cannot be considered out-of-date as asserted by other reviewers. Finally, and as far as notation/aesthetics goes, if this is why you dis-like the text and feel detracts from your ability to learn Algebra, then I would strongly suggest venturing into another field other than Mathematics. If you are a graduate student or someone doing research on their own, then you are required to read works written by authors from around the world and the notational differences should be the last of your worries.

In summary, this text is the best possible text that you can buy in order to adequately learn Algebra at the graduate level. Yes it is difficult and some of the problems may take you weeks to solve but that's Mathematics. Enjoy!


comprehensive and rigorous   January 12, 2002
8 out of 11 found this review helpful

I agree with others, this book isn't for those who are
unmotivated. But if you know what you want from algebra
and need a comprehensive, rigorous treatment, this book is
great. I was able to learn on my own from it, and I'm not only
a non-math major, I had no access to any instructors. That
should tell you something. Aside from that, the book has a
few minor quirks, like exercises which aren't really doable
or exceedingly difficult (i know because I've seen these
questions answered in other books). But there are few of those
so it's a minor nuisance.


Clear and compact guide to beginning graduate level Algebra.   November 14, 1998
6 out of 7 found this review helpful

This text, though not good for undergraduates, is the best text for beginning graduate students in Algebra. All the important concepts are outlined clearly and concisely. Reading through is difficult because the text is organized with a dictionary feel, but this is beneficial for later review of topics. This book is known as the Algebra "Bible" in some departments.


My all time favorite book!   March 18, 1999
6 out of 9 found this review helpful

Though the book was written in 1974, but it seems it is written in 90s. The notation, proofs and typesetting are quite update. The cross refrences are excellent. The theorems are given in quite the genearlity way, though not boring, the proves are very exact, for example mentioning where the axiom of choice is used ETC. This is a book i can not imagine how the writer started to write it. It is very consistant!!!