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Title: Algebra by Michael Artin ISBN: 0-13-004763-5 Publisher: Pearson Education Pub. Date: 24 April, 1991 Format: Hardcover Volumes: 1 List Price(USD): $101.33 |
Average Customer Rating: 4.11 (18 reviews)
Rating: 2
Summary: A Bad Text Book
Comment: I must read everything from any other text book to understand clearly what Artin is saying in his book. can you believe it? Few definition is described clearly, few theorem is proved in a logic-clear, easy-to-undersatnd way. The most important is that many useful properties of Ring , field are not included in his book, but in the problems you have to find all these totally by yourself in order to solve the problems. Also, the textbook is NOT well- orginized. A typical exmaple, Artin has not yet tell the reader basic informations and properties of Ring Of Polynomial in one variable , but he starts to describe the structure of Ring Of Polynomial in 2 or more variables. The reader's minds would be completely mixed up if he doesn't not have an extremely high IQ. I believe , your knowlege of Ring and Filed will be very limited and very unclear if you use Artin's book only. Abstract Algebra is a hard topic. You should not use a book which is definitely not a help for you but rather a trouble for you!.Artin may be a famous mathematician, but he is not a good educator. He doesn't not know to teach students in a good manner.
Rating: 5
Summary: good, solid treatment of algebra
Comment: I bought this book for a class that I ended up dropping. In the beginning, I hated this book. I found Herstein's "topics in algebra" much better, and more to the point. It was only when I was getting bored with Herstein that I bothered to pick this up again. I was pleasantly surprised. A lot of the material flowed very smoothly - exactly as if Artin was teaching the material to you. It must however be noted that people tend to love or hate this book. This is predominantly due to the author's writing style. Given how expensive this book is, you might perhaps want to peruse it somewhere before deciding to buy it. But if you do, you'll get a solid exposition on most of the introductory topics in algebra as well as some insight on groups and symmetry, lie groups, representation theory, galois theory and quadratic number fields. And a whole lot of intuition as well, for the more regular topics. Give this book a chance - it's worth the effort and money.
Rating: 5
Summary: Great book for challanging you to think with clarity
Comment: Artin's book is probably one of the better books, more because of the way you have to read it to learn it. Artin's book is extremely nonstandard, in the sense that it isn't so "encyclopedic" as you usually encounter with the whole theorem, corollary, proof, proof, proof, example, example sequence. What I think a lot of readers miss is that Artin's book makes you fill in the details he leaves out by using the hints he mentions in words within the text. For example, I was able to expand the two pages of notes on Ch 2, section 5, in Artin into about 8 pages of original notes and theorems, just by digging for the main points. If you want a sample of my notes, please email me and I'll email you a brief PDF sample for you to compare. That being said, assume that you will have to dig a lot in this book, and should you choose to study from it, I suggest the following:
How to read it:
With a cup of coffee, or tea, and a notepad of paper for you to make comments on. Do not take notes; anyone knows that simply rewriting things doesn't do anything for learning. You should do the proofs in different ways, if you can see how, and try to make some of the aside remarks he makes into theorems or more precise ideas (this is not to say that Artin lacks rigor; this is just talking about the general commentary. When he makes commentary, it always seems to be enough to actually dig out exactly what to do after a little scratching). He also leaves a lot of easier proofs to the reader, so do them.
Is non-standard a less-rigorous approach?
No. Artin is definitely doing his own thing here, but I think it works really well. Getting through that book FORCES you to take responsibility for your math education by making you get your hands dirty while also developing an intuitive understanding of algebra.
What about his personal flavor of algebra?
Well, it's fairly clear to all of us that texts seem to have different flavors (being a function of the author's research area, and what was fashionable during the time the book was authored). Artin's book is algebra with light strong hints of geometry throughout, as he is in algebraic geometry. You will find that unlike most authors, Artin loves structures made of matrices when working with examples, as opposed to permutation groups or the ``symmetries of the square group,'' known also as the ``octic group.'' While these things have their place in his book, he changes the emphasis here. That's why I suggest using a companion book so as to have two sharply contrasting flavors of presentation, and Herstein seems to write in such a way that would do this. Artin covers a lot of material extremely quickly, but focuses on the bigger picture in several key areas. For example, the sections 7 and 8 in chapter 2 deal almost exclusively with how one would go about investigating a particular group structure to learn about it, teaching a student how to dig into something they might barely understand.
Advice to make a wondeful course:
Use another book which IS encyclopedic as a reference, since Artin doesn't label theorems and definitions so explicitly. I suggest Herstein's Abstract Algebra, or his book Topics in Algebra.
Personal Charracterization:
I place this book as one of my favorites on the bookshelf, and it sits among others like Rudin, Ahlfors, Sarason's notes, Herstein, though it's obvious to me that Artin is on a very very different path than all those books, very nonstandard (Artin DOES DO all that a usual algebra course does, and more, if you were wondering), but as a result, very very very thorough and very clearly presented. I love this book very much.
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Title: Topology (2nd Edition) by James Munkres ISBN: 0131816292 Publisher: Pearson Education Pub. Date: 28 December, 1999 List Price(USD): $101.33 |
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Title: Principles of Mathematical Analysis (International Series in Pure & Applied Mathematics) by Walter Rudin ISBN: 007054235X Publisher: McGraw-Hill Science/Engineering/Math Pub. Date: 01 January, 1976 List Price(USD): $147.70 |
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Title: Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus by Michael Spivak ISBN: 0805390219 Publisher: Westview Press Pub. Date: 01 June, 1965 List Price(USD): $44.00 |
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Title: Counterexamples in Topology by Lynn Arthur Steen, J. Arthur Seebach ISBN: 048668735X Publisher: Dover Publications Pub. Date: 01 October, 1995 List Price(USD): $11.95 |
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Title: Counterexamples in Analysis (Dover Books on Mathematics) by Bernard R. Gelbaum, John M. H. Olmsted ISBN: 0486428753 Publisher: Dover Publications Pub. Date: 01 June, 2003 List Price(USD): $14.95 |
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