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Algebra: Chapter 0 (Graduate Studies in Mathematics), by Paolo Aluffi
Free Ebook Algebra: Chapter 0 (Graduate Studies in Mathematics), by Paolo Aluffi
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Algebra: Chapter 0 is a self-contained introduction to the main topics of algebra, suitable for a first sequence on the subject at the beginning graduate or upper undergraduate level. The primary distinguishing feature of the book, compared to standard textbooks in algebra, is the early introduction of categories, used as a unifying theme in the presentation of the main topics. A second feature consists of an emphasis on homological algebra: basic notions on complexes are presented as soon as modules have been introduced, and an extensive last chapter on homological algebra can form the basis for a follow-up introductory course on the subject. Approximately 1,000 exercises both provide adequate practice to consolidate the understanding of the main body of the text and offer the opportunity to explore many other topics, including applications to number theory and algebraic geometry. This will allow instructors to adapt the textbook to their specific choice of topics and provide the independent reader with a richer exposure to algebra. Many exercises include substantial hints, and navigation of the topics is facilitated by an extensive index and by hundreds of cross-references.
- Sales Rank: #513233 in Books
- Brand: Brand: American Mathematical Society
- Published on: 2009-08-02
- Original language: English
- Dimensions: 10.25" h x 7.00" w x 1.75" l, 3.20 pounds
- Binding: Hardcover
- 728 pages
Features
- Used Book in Good Condition
Review
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
Most helpful customer reviews
22 of 23 people found the following review helpful.
The Perfect Synthesizing Text for a Graduate Student
By Jeremy Kun
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). But more likely this last chapter could use some reorganization and more basic exercises early on. Of course, this is the newest and most mature topic covered in the book, it was my first time encountering the material, and it is probably intended to be a test of the reader's maturity developed throughout the book. In any event, it didn't click for me as well as the rest of the book.
All in all, I'll definitely be purchasing the second edition, and I'm eagerly awaiting Chapter 1 :)
24 of 28 people found the following review helpful.
great book
By math major
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.
19 of 22 people found the following review helpful.
Calgebra
By Eivind Evenstad Dahl
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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