An Introduction to Homological Algebra (Cambridge Studies in Advanced Mathematics, Series Number 38) by Charles A. Weibel (PDF)

Description

The landscape of homological algebra has evolved over the past half-century into a fundamental tool for the working mathematician. This book provides a unified account of homological algebra as it exists today. The historical connection with topology, regular local rings, and semi-simple Lie algebras is also described. The first half of the book takes as its subject the canonical topics in homological algebra: derived functors, Tor and Ext, projective dimensions and spectral sequences. Homology of group and Lie algebras illustrate these topics. Intermingled are less canonical topics, such as the derived inverse limit functor lim1, local cohomology, Galois cohomology, and affine Lie algebras. The last part of the book covers less traditional topics that are a vital part of the modern homological toolkit: simplicial methods, Hochschild and cyclic homology, derived categories and total derived functors.

User’s Reviews

Editorial Reviews: Review “It is…the ideal text for the working mathematician need- ing a detailed description of the fundamentals of the subject as it exists and is used today; the author has succeeded brilliantly in his avowed intention to break down ‘the technological barriers between casual users and experts’.” Kenneth A. Brown, Mathematical Reviews”By collecting, organizing, and presenting both the old and the new in homological algebra, Weibel has performed a valuable service. He has written a book that I am happy to have in my library.” Joseph Rotman, Bulletin of the American Mathematical Society Book Description A portrait of the subject of homological algebra as it exists today.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Now Homological Algebra is not a simple subject that can be picked up with only a minimal background. The subject is deep and permeates many different braches of mathematics. If you are thinking of buying this text, then I have two suggestions. First, just buy it. For the price, you will not find another book that is as up to date or as rich in content. Second, ask yourself if you are really ready for this text? What I would do is use Amazon’s “Search Inside” in order to check out the first two or three pages of chapter one. If you feel at home with the material presented there, then just buy it. You will not be upset. Well, you may get upset-this book covers a lot of material and at times can be rather overwhelming. Let me stress that the level of comfort with the preliminary material is analogous to a tenured professors level of comfort with, say, Calculus. That is, very comfortable. With respect to the actual text, I am hard pressed to find any negative words. Weibel has set the modern standard and this text is fast becoming the standard from which all other texts will have to model themselves after. The material is presented in small palatable chunks that can be consumed at any time. Just make sure you have a new pencil and couple notebooks handy when you read this text.

⭐Great book

⭐What are these bad reviews talking about? Every professor I’ve had has punted on quite a few of the topics explained with great clarity in this book. It has increased my awareness and understanding of homological algebra a great deal, and I keep refering back to it. Someone looking for a geometric intuition should be aware though that homological algebra, if I’m not mistaken, grows out of algebraic topology. My impression (as a student of algebra) is that topology studies questions where geometry doesn’t really exist or is irrelevant. So, maybe that’s why the picture isn’t clear?

⭐This is by far the most accessible and well-written Homological Algebra book I’ve dealt with. I’m an analyst at heart, so the subject does not in any way come easy to me. However, the exposition in this book greatly shortened the learning curve, and Dr. Weibel provided a plethora of understandable examples and accessible exercises, all of which greatly aided my understanding of the subject.

⭐This is an excellent book on Homological Algebra. I am surprised at how often I find myself turning to it.

⭐This book was absolutely priceless for me while I was doing my qualifying exams and dissertation. Excellently written, with modern notation and applications and a clearly-exposited writing style. I wish all “hard” math books were written like this. Thanks Prof. Weibel

⭐This is one of the worst books I have read. I am reviewing it because I have seen the other reviews and think they are entirely misleading. The book makes endless definitions without explaining motivation, use or history of any of the subjects. There is no context and the book makes the subject pointless. For example the definition of Tor gives no clues as to why it is named Tor. As the root is Torsion and is clearly explained in MacLane (a fantastic start, forget comments about it being dated) which immediately gives a great insight why not let the reader know. Then there is no motivation for it’s use and the definition gives a definition from a projective resolution which is great if you already know all about Tor and projective resolutions. The whole book goes on in this style. There is a list of references at the back but as you go through nothing, no comments on derivation, motivation, application or anything. The book is great as a reference on how not to write notes and how to demotivate readers. I would sell mine secondhand but I couldn’t live with the guilt.

⭐I agree with the one star rating; if someone runs a query on each term (in this book), say in mathematica/wiki etc., and then concatenates the defintions together – the outcome will resemble this book very closely. Well, may be that is an overstatement, but you get the point!Horrible book for someone who looks for some intuition/motivation. It may be a great book for a hardcore mathematician who can gather inspiration from absolute abstraction. Not for a geometric-intuition-searching soul.

⭐The four stars are for the content. But the book has too many typos: the errata sheet on the author’s site is six pages long. Such an influential text deserves a corrected reprint.

⭐È un libro chiaro e conciso; naturalmente richiede delle conoscenze basilari di Algebra.

⭐Not found.

⭐The Book!!!!

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