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Algebra: Chapter 0 (Graduate Studies in Mathematics)

14 customer reviews
ISBN-13: 978-0821847817
ISBN-10: 0821847813
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Editorial Reviews


This self-contained introduction is suitable for a first sequence at the beginning graduate or upper undergraduate level. A distinguishing feature of the book is the early introduction of categories, used as a unifying theme. ---- SciTech Book News

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Product Details

  • Series: Graduate Studies in Mathematics
  • Hardcover: 728 pages
  • Publisher: American Mathematical Society (August 2, 2009)
  • Language: English
  • ISBN-10: 0821847813
  • ISBN-13: 978-0821847817
  • Product Dimensions: 1.8 x 7 x 10.2 inches
  • Shipping Weight: 3.2 pounds (View shipping rates and policies)
  • Average Customer Review: 4.7 out of 5 stars  See all reviews (14 customer reviews)
  • Amazon Best Sellers Rank: #486,360 in Books (See Top 100 in Books)

More About the Author

Paolo Aluffi was born in Italy, and studied mathematics in Torino under the direction of Alberto Collino, and then at Brown University, obtaining a Ph.D. with a dissertation in algebraic geometry under the supervision of William Fulton. He has held postdoctoral positions at the University of Chicago and Oklahoma State University, and joined the department of mathematics at Florida State University in 1991. He is currently professor of mathematics at FSU. Paolo Aluffi has visited many universities and mathematics institutes for extended periods of time. Among these are the Max-Planck-Institut in Bonn, Germany; Harvard University; the Institut des Mathématiques in Luminy, France; the Mittag-Leffler Institut in Stockholm, Sweden; the Mathematical Sciences Research Institute in Berkeley, California; and the California Institute of Technology.

Beside `Algebra: Chapter 0', he has published more than 40 research papers in algebraic geometry. He has also published a book of mathematics for the `general public' in Italian, `Fare Matematica'.

Customer Reviews

Most Helpful Customer Reviews

16 of 17 people found the following review helpful By Jeremy Kun on June 23, 2012
Format: Hardcover Verified Purchase
I should first mention that I, along with about twenty of my fellow first-year mathematics graduate students, scoured this book from beginning to end. We completed nearly every exercise, and discovered a number of errata (there is quite a large list available on the author's website, but this book shines in spite of it all).

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).
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24 of 28 people found the following review helpful By math major on December 1, 2009
Format: Hardcover Verified Purchase
This is a well organized and clearly written book. Professor Aluffi must be an excellent teacher. He guides the reader through the material and shows the beauty of the subject. His use of category theory- particularly universal properties- reveals the underlying unity of seemingly disparate notions.The chapters on Field Theory and
Homological Algebra are superb. He always provides useful comments to place topics in context. I hope Professor Aluffi will write more texts.
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16 of 19 people found the following review helpful By Eivind Evenstad Dahl on July 9, 2010
Format: Hardcover Verified Purchase
I attended a course in abstract algebra using Fraleigh's book. Then I sorta just stumbled across this one (which I should add covers a lot more than Fraleigh). With experience from Fraleigh's book (which is good) I can say this one is absolutely brilliant. It is well organized, covers a lot of ground in a (not too) leisurly pace, and the exercises are interesting. The best part about this book, however, is the way it seamlessly and naturally uses and demystifies category theory -- a subject I thought I'd not be able to understand for years -- to unify a great deal of the topic that is undergraduate/graduate algebra.
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6 of 7 people found the following review helpful By Christian on August 14, 2012
Format: Hardcover
This is a very good book overall, the author is a great expositor. Most of the book is very elegant in a way that does not sacrifice readability, and he will not hesitate to help parse when it does. My personal opinion is that it is outclassed by Mac Lane and Birkhoff's "Algebra", but I still wouldn't have many qualms about recommending the text to someone with suitable maturity wanting to learn the subject.

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.
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1 of 1 people found the following review helpful By David on June 23, 2015
Format: Hardcover Verified Purchase
I find this book extraordinarily helpful for my self-study on derived categories. My motivation was to eventually understand algebraic analysis (D-modules) or algebraic geometry better. Before starting on more comprehensive textbooks on homological algebra by Gelfand-Manin, Kashiwara-Schapira, or even the appendix of Eisenbud, I found this book to be an ideal preparation. The style of the writing is as if listening to the author talk. He emphasizes the same important points repeatedly throughout the book and I benefited a lot from these repetitions. I had previously read parts of Lang's Algebra or Hormander's book on several complex variables, or Morimoto's Introduction to Hyperfunctions, and therefore had some modest exposure to sheaf cohomology theory or spectral sequences. But going through parts of Aluffi's book improved my understanding on homological algebra fundamentally. I would recommend the book also to mature mathematicians whose graduate education did not include much categorial viewpoints, but now curious engough to learn these viewpoints.
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