Preface. Birkhoff & Mac Lane’s Algebra is a brilliant book. I should probably spend some time with it again, actually. Also, I apologize for such a. This book presents modern algebra from first principles and is accessible to undergraduates or graduates. It combines standard materials and necessary. Documents Similar To Saunders Mac Lane, Garret Birkhoff Algebra Mathematics Form and Function. Uploaded by. jacinto [Charles C. Pinter] a Book.
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The main advantage of the authors had been the introduction of thoroughly categorical concepts into algebra. Would you like to tell us about a lower price? If you are a seller for this product, would you like to suggest updates through seller support?
This book presents modern algebra from first principles and is accessible to undergraduates or graduates. It combines standard materials and necessary algebraic manipulations with general concepts that clarify meaning and importance.
The present book presents the developments from that time to the first birkjoff of this book. This third edition includes corrections made by the authors. Read more Read less. Discover Prime Book Box for Kids. Add both to Cart Add both to List.
Algebra – Saunders Mac Lane, Garrett Birkhoff – Google Books
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Write a customer review. Read reviews that mention category theory maclane and birkhoff affine and projective galois theory abstract algebra third edition birkhorf on galois multilinear algebra learn algebra algebra and affine big book algebra book exposition categories topics basic modern math lang algebraic. Showing of 18 reviews. Top Reviews Most recent Top Reviews. There was a problem filtering reviews right now. Please try again later.
MacLane was, according to wikipedia, one of the two founders of category theory in This algebra book by MacLane and Birkhoff applies the category theory perspective throughout, for better or worse. I’ll be marked down for saying this, but in my opinion, category theory is not necessarily a good idea. It algebbra now the orthodox way to do algebra, and no university will let you do advanced algebra without it nowadays, although in the s it was not universally taught as the standard framework.
I didn’t encounter category theory until my early burkhoff years, and that was only very specifically in the context of algebraic topology. But if you want to be in the modern mainstream, you need the category theory perspective, and ,aclane book is probably the best way to get it. Now there’s a little oddity about what is really meant by “category maclzne. Someone informed me a couple of months ago that I had made a grave error in my own definition of ring epimorphisms.
Apparently the really modern definition of an epimorphism in madlane theory requires the right cancellative property. And monomorphisms require the left cancellative property. See wikipedia for details. But this book by MacLane and Birkhoff page 38 uses the old-fashioned definition, which only requires surjectivity. In the case of the ring category, it makes a big difference. The old-fashioned epimorphism definition is also given by Seth Warner “Modern algebra”, page 82; Lang “Algebra”, page ; Grove “Algebra”, pages 8, 49, ; Ash “Basic abstract algebra”, pages 19, 37, So if you want to use MacLane and Birkhoff for category theory, beware of this difference.
It seems to me as a non-algebraist that category theory was introduced as a kind of “grand unified theory” to implement bulk handling of algebraic categories.
In conclusion, if you don’t have this book, you’re not an algebraist. And if you’re some other kind of mathematician, it is the best all-round reference for all of the basic categories of modern abstract algebra. This book has pretty much everything a non-algebraist would want to know about the broad sweep of algebra.
It even has chapters on multilinear and exterior algebra and affine spaces. It’s a tidy, carefully-written reader-friendly book which tries to help the reader, not show off the superior genius of the authors as some frustrating books do. By the way, as I understand it, MacLane only introduced the space between Mac and Algbera because his wife couldn’t type a capital letter in the middle of a word. I think that’s maclaen silly reason to change the spelling of one’s name.
So I spell it in the traditional way as “MacLane”. Honi soit qui mal y pense! Contains some good algebra. I enjoyed Mac Lane’s exposition.
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It is clear, with nice examples. It only has a few small line diagrams I haven’t read all the way through, it gets to some advanced graduate-level material. There is so much heart poured in this book, just beautifully written and intended for all things good. I ended up buying a second copy just to have a new one. Arrived early and as advertised. Also a very well-made book–so call me stupid.
Herewith, the dumbest preliminary, in the sense of I just got it in the mail today review of MacLane and Birkhoff, 3rd Edition that you’ll read. This book is very well made, with quality paper, and a buckram binding Smyth-sewn in signatures.
Also from a more substantive POV: The exposition seems clear. More to come as I work through the text.
I guess some reviewers have read all pages and worked all the problems? One person found this helpful. See all 18 reviews. Maclabe Giveaway allows you to run promotional giveaways in order to create buzz, reward your audience, and attract new followers and customers.
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