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Title: Calculus by Michael Spivak ISBN: 0914098896 Publisher: Publish or Perish Pub. Date: December, 1994 Format: Hardcover Volumes: 1 List Price(USD): $70.00 |
Average Customer Rating: 4.82353
Rating: 5
Summary: Calculus as it Should Be
Comment: In my time as a student, then later as a college professor type, I was fortunate indeed to know four excellent teachers. The kinds of teachers that make you enjoy the learning process (and when learning isn't both fun and challengingly difficult, its pretty worthless) even as they push, cajole, pull and help you through the tough spots.
Foremost among these was Mike Spivak - I encountered him in a summer math program for high school students where he put up with me (as a math student far from as good as most in the program) and gave me a love of mathematics that survives to this day (if only I were better at it).
His book "Calculus" did the same thing for me, and I still have a (battered) copy of it with his autograph - and it is one of my most treasured books - partly because of its association with him, but mostly because it is the book that brought calculus to life for me.
I suffered through freshman calculus (hated every minute of it - it took my enthusiasm for mathematics that Spivak had nurtured and made me wonder if I was really looking at the same subject) with Thomas's "Calculus and Analytic Geometry" which is, I suppose, excellent in its way - but the focus is far more on cookie cutter calculus - here is how you take a derivative and here is how you'd use it.
But while Thomas probably did manage to teach me how to evaluate a few integrals, Spivak got me to figure out why it mattered. And it was probably only the coverage of limits in this text that eventually led to my appreciation of the (oddly beautiful in its own way) epsilon-delta dance and how limits really make the calculus work.
It's not trivial going for the most part, but the patient reader will be amply rewarded, perhaps not with the worlds greatest facility for derivatives or integrals, but with a feel for what they really are under the hood.
To top it all off there are the extras : proofs that pi is irrational and that e is transcendental, a lucid and accessible construction of the real numbers, problems that teach more than just how to plug-and-chug, and humour (even in the index - check out "yellow pig").
Nobody (in any field) can be considered to be even minimally educated without at least mathematics to the level of the calculus - and this is the best text I know of that really explains what its about without being a plug-n-chug manual. It was written for an honours program at an "elite" university, but still should be acessible for someone with a good background in algebra who is willing to work and has a bit of help. (If it could only be Mike Spivak himself, you'd be among the most fortunate few.)
And - if you know talented high schoolers with an interest in math - give them this before AP Calculus or Freshman calculus can do any serious damage.
Rating: 5
Summary: Buy this book for your children. Force them to read it.
Comment: This book will give you a deep, crystal clear understanding of Calculus. It is also the perfect introduction to analysis or to rigorous math.
Every single person on the Earth should have read this book. One day, when we have vanquished poverty and cured every disease, all of our genetically engineered, supersmart kids will read this book in elementary school.
Rating: 5
Summary: A great teacher's superb introduction to calculus/analysis
Comment: If your only experience is only with run-of-the mill texts like Thomas, Spivak's Calculus will be a revelation. And if you've worked through Apostol's Calculus, either version of his Mathematical Analysis, or the first volume of Dieudonne, you'll appreciate how much of that material can be rigorously presented in an introductory course. I was taught from Apostol's two-volume Calculus in college, and it's good, but this is much better. There's certainly difficulty for the newcomer to the subject, but no grind, no rote, no mindless technical problems. I agree with the previous reviewer who said that this book ranks with the Feynman Lectures on Physics as one of the very greatest texts. And student who has completed and understood this book is probably ready for Dr.Spivak's gentle introduction to multivariate calculus through differential geometry, _Calculus on Manifolds_, and then his mammoth five volume text-cum-lecture-notes treating differential geometry in depth.
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Title: Answer Book to Calculus by Michael Spivak ISBN: 091409890X Publisher: Publish or Perish Pub. Date: January, 1996 List Price(USD): $35.00 |
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Title: Understanding Analysis by Stephen Abbott ISBN: 0387950605 Publisher: Springer Verlag Pub. Date: 12 January, 2001 List Price(USD): $39.95 |
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Title: Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus by Michael Spivak ISBN: 0805390219 Publisher: Perseus Publishing Pub. Date: June, 1965 List Price(USD): $44.00 |
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Title: Geometry Revisited by H. S. Coxeter, S. L. Greitzer, Geometry Revisted ISBN: 0883856190 Publisher: Mathematical Assn of Amer Pub. Date: 1967 List Price(USD): $19.95 |
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Title: Calculus. by Tom M. Apostol ISBN: 0471000051 Publisher: John Wiley & Sons Pub. Date: June, 1967 List Price(USD): $127.80 |
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