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Algebra. Second Edition, by Saunders Mac Lane, Garrett Birkhoff
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This third edition examines the fundamentals of algebra.
- Sales Rank: #4043401 in Books
- Published on: 1979-06
- Ingredients: Example Ingredients
- Original language: English
- Number of items: 1
- Binding: Hardcover
- 608 pages
Most helpful customer reviews
0 of 1 people found the following review helpful.
Clear exposition. Also a very well-made book--so call me stupid.
By 3rd Day Believer
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 600 pages and worked all the problems? Fibbers!
20 of 21 people found the following review helpful.
Amazing Book
By Michael Cloud
This is a fabulous book. I have had basically one year of effectively 'algebra for non-mathematicians' at a graduate level, and have a background in Physics and Engineering. I find this book to be the perfect next step in terms of understanding things a bit more deeply than Dummit&Foote, in particular because they bring in some wider issues and connect them to the basic material of group theory, ring theory, modules vector spaces etc. In other words it covers the same or similar material as Dummit & Foote, but adds in some wider examples (more lattice theory, operator theory) as well as a higher level of sophistication because it brings in a category theory perspective for example. It seems that this book is really oriented toward seeing the big mathematical picture implicit in lots of physics. So in that sense, for me, it's a fantastic mathematical physics book, without explicitly being so.
16 of 17 people found the following review helpful.
Beautiful exposition
By Christian
Let's start off with the bad: Not having a marker for the end of each proof annoys me. Some of the terminology is a little awkward. (For example, the word "homomorphism" appears once in the entire text, to note it as an alternative to their usage of the word "morphism".) There are a few minor typos here and there. And that's it. I have nothing else really negative to say about this book.
I make no claims to being a math prodigy; I pursue it simply because I enjoy it. When I read math, it's a struggle. What I found so remarkable about this book is that I was not struggling, despite the complexity of the material. That's not to say I found nothing in here difficult, because it's all difficult to some degree by the very nature of the material, but that the moments of frustration were few and far between. I will admit that I had familiarity with probably about 30% of the material when starting, so it is possible my opinion would be different had I not known what a group was beforehand. I kind of doubt that though, the exposition seemed nearly ideal. Beyond being a smooth read, there was no overstatement. Everything said added to the content.
The book covers a lot of territory in only 600 pages, but none of it should be a surprise to see in an algebra text: groups, rings, modules, Galois theory, a little on categories, etc. I think the chapter on matrices should be pointed out in particular. This is a better explanation of how matrices and their entries can and ought to be interpreted than any other I have read, including Axler! Admittedly, Axler does a slightly better job with some of the other linear algebra topics, such as characteristic polynomials.
Prerequisites for this book are extremely slim - naïve familiarity with the real and complex number systems are the only absolute necessity. However, anyone taking this on with nothing more than the bare minimum is going to be in for quite a challenge. You should already have some comfort with reading texts filled with theorems and proofs.
This is possibly the best textbook I have encountered to date. If you want to learn algebra, I can't imagine a better single place to look to get a well-rounded exposure to the subject.
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