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biblix's review
3.0
At $7.50 on Amazon now, the price is great, and the exposition is classic. But it's not that great.
First: If only someone could update the typesetting/formatting. I'm not just griping about the obvious 50's lecture-note-style straight-out-of-a-typewritter kind of typesetting. Notationally many things are suspect, such as using "a" and "α" to stand for different things in the same formula (with subscripts, used multiple times, etc. Also, unlike in TeX, "a" and "α" don't look that different). Or using "x_k" as fixed coefficients while "a_k" becomes a variable. These are nitpicks, but I believe that they prevent the exposition from being more readable.
Second: It's thin for a reason. It is not that self-contained. Perhaps back in the day knowledge of linear algebra was not that wide-spread, so Artin chooses to include it. But there are the occasional, non-trivial group theoretic results that are simply assumed (such as Cayley's theorem, which is implicitly used at least once). On the other hand, the audience of this book should have completed a first course in algebra anyway, so this is not a big problem.
Third: The book is seriously lacking in examples, and hence motivation for each lemma and theorem is not necessarily clear. It appears to me that the best way to read this book is to have a skim over the whole book to get a feel for the overall progression of the book (partly because the book lacks an index, so things may be hard to find if you don't do this). Then jump straight into Milgram's bit about "applications" (basically, Galois theory in explicit form) and read that. Only whenever things stop making sense do you go back to the main bit by Artin.
First: If only someone could update the typesetting/formatting. I'm not just griping about the obvious 50's lecture-note-style straight-out-of-a-typewritter kind of typesetting. Notationally many things are suspect, such as using "a" and "α" to stand for different things in the same formula (with subscripts, used multiple times, etc. Also, unlike in TeX, "a" and "α" don't look that different). Or using "x_k" as fixed coefficients while "a_k" becomes a variable. These are nitpicks, but I believe that they prevent the exposition from being more readable.
Second: It's thin for a reason. It is not that self-contained. Perhaps back in the day knowledge of linear algebra was not that wide-spread, so Artin chooses to include it. But there are the occasional, non-trivial group theoretic results that are simply assumed (such as Cayley's theorem, which is implicitly used at least once). On the other hand, the audience of this book should have completed a first course in algebra anyway, so this is not a big problem.
Third: The book is seriously lacking in examples, and hence motivation for each lemma and theorem is not necessarily clear. It appears to me that the best way to read this book is to have a skim over the whole book to get a feel for the overall progression of the book (partly because the book lacks an index, so things may be hard to find if you don't do this). Then jump straight into Milgram's bit about "applications" (basically, Galois theory in explicit form) and read that. Only whenever things stop making sense do you go back to the main bit by Artin.