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Algebra: Chapter 0 (Graduate Studies in Mathematics)
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Top Customer Reviews
I've experienced Fraleigh, Artin, Dummit and Foote, and Aluffi's texts on abstract algebra. While each has it's place, I have to say that Aluffi is my favorite. His writing style is phenomenal (and humorously pretentious at times). This text is not intended to be a reference, but instead read from start to finish, and Aluffi monopolizes this to its full effect. The content is spot on for the intended audience. His exercises cover important, relevant topics to important fields I and my fellow graduate students intend to pursue. These include, but are not limited to: algebraic geometry, commutative algebra, homological algebra, and Lie theory.
This book is the best I have encountered for transitioning from an elementary understanding of abstract algebra to a mature perspective, backed by the might of category theory. That being said, I can see how the book may go more smoothly if one has had some initial exposure to algebra before Aluffi. This text does an excellent job synthesizing my understanding, but the organization could be confusing for a beginner.
My only real disappointment with the book is in the final chapter on homological algebra. By the last two or three sections, the content is almost prohibitively confusing. It could be the case that there are errata that have confused me (indeed, the listed errata on his website sharply fall in this chapter, and I believe it's because most students don't get this far).Read more ›
Homological Algebra are superb. He always provides useful comments to place topics in context. I hope Professor Aluffi will write more texts.
My only real quibbling with the book is how its main feature - the integration of category theory - is handled. I certainly agree that its use is beneficial in this context, but I think delaying the introduction of functors until the second-to-last chapter is a weakness if categories are going to come up as much as they do. He tosses them aside early for a more intuitive "working definition" of universals, which is understandable at first as it could easily be a bit much to take in at the time, but I assume that's the same reason adjoints are glossed over the way they are when introduced very shortly after functors. I think it would be helpful to just once when proving something is an adjunction prove the naturality part as well as the bijection part, because not doing so somewhat gives the idea that the naturality condition is simply auxiliary. In general, chapter VIII is a weak point in an otherwise very good book, in many ways it just seems like a preview of the following chapter with less substance than anywhere else in the book.
I'll also add as a very minor complaint: the determinant is poorly motivated upon it's introduction.Read more ›
Most Recent Customer Reviews
I'm a first year graduate student and we used this book as the core text for our algebra class. It was great, really nice to read and introduces category theory from the very... Read morePublished 2 months ago by targetdemo
This is book is awesome for a beginning graduate student. It suits its name Chapter 0 well, i.e. serves as a comprehensive review. Read morePublished 3 months ago by Gray Shin
Having attempted to read this book a number of times I have finally given up and decided to move onto Dummit and Foote which I am enjoying a lot more. Read morePublished 6 months ago by Callum Haycock
This is a nice treatment of the subject. But I found you can download this entire book as pdf, somebody has the pdf on their home page (at math DOT uic DOT edu).Published 13 months ago by Gets Around
By far, one of the best basic algebra books out there, next to Hungerford. Personally, other competing books -- like Lang and Dummit and Foote -- lack clarity, or are too verbatim. Read morePublished 13 months ago by Gabriel
Very interesting, but this book should provide more examples and be more thorough with its proofs. Simply stating that "the proof follows" is not sufficient. Read morePublished 15 months ago by Michael Carey
The book is exceptionally well-written - the text is balanced not to be too hard or too easy-going. It has lots and lots of meaningful exercises to facilitate understanding. Read morePublished 18 months ago by Bananeen