It goes on to serve as an excellent study of a small business struggling to survive and then coping with its own success. I found it hard to put down. Even though I knew the outcome, I found myself carried along with the story. Enough "insider detail" is provided to reveal character and move the "plot," but not enough to bog the book down. The book also serves as the best biography of Leo Fender that I have read. He is revealed as an inspired man with significant flaws. Importantly, "revealed" is the operative word here. Smith generally does not preach or make pronouncements. He describes actions and quotes interviews. The reader is left to his own conclusions.
The only book like this one in brevity and scope is Reid UNDERGRADUATE ALGEBRAIC GEOMETRY--with its highly informed, highly polemical, final chapter on the state of the art. Both are very good. This one is more advanced. Beyond what Reid covers, Smith sketches Hilbert polynomials, Hironaka's (and very briefly even De Jong's) approach to removing singularities, and ample line bundles. You do need a bit of topology and analysis to follow it. Smith has very many fewer concrete examples than Reid. They are beautifully chosen classics, like Veronese maps and Segre maps, so they teach a lot. And the more you know to start with, the more you will see in each.
The book does geometry over the complex numbers. It is good old conservative material, with terrific graphics of curves and surfaces. The proofs and partial proofs are very clear, intuitive and to the point. But, in fact, just because the proofs are so clear and to the point they usually work in a much broader setting. Long stretches of the book apply just as well over any field or any algebraically complete field. This generality is only mentioned a few times, in passing, but is there if you want it. Smith describes schemes very briefly, and mentions them at each point where they naturally arise. You will not know what schemes "are" at the end of this book. You will know some things they DO. She has no time for fights between "concretely complex" and "abstractly scheming" approaches--for her it is all geometry.
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Conrad Ekstrom WB1GXM/KB1CCA(GEARS) ADVISOR GOSHEN-LEMPSTER EDUCATIONAL AMATEUR RADIO SOCIETY EST 1989
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--LLOYD BOSTON, author of MEN OF COLOR
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This is a very un-biased book and it's very nice to read. The pictures in this book are awesome, and this is only one of the books I have that I trust the facts on. Kudos to Mr. Smith!