Michael Spivak


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Queens, New York, The United States
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Michael David Spivak is a mathematician specializing in differential geometry, an expositor of mathematics, and the founder of Publish-or-Perish Press. He is the author of the five-volume Comprehensive Introduction to Differential Geometry. He received a Ph.D. from Princeton University under the supervision of John Milnor in 1964.

His book Calculus takes a very rigorous and theoretical approach to introductory calculus. It is used in calculus courses, particularly those with a pure mathematics emphasis, at many universities.

Spivak's book Calculus on Manifolds (often referred to as little Spivak) is also rather infamous as being one of the most difficult undergraduate mathematics textbooks.

Average rating: 4.4 · 1,124 ratings · 45 reviews · 20 distinct worksSimilar authors
Calculus

4.47 avg rating — 639 ratings — published 1967 — 14 editions
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Calculus On Manifolds: A Mo...

4.28 avg rating — 254 ratings — published 1965 — 10 editions
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A Comprehensive Introductio...

4.22 avg rating — 58 ratings — published 1970 — 6 editions
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The Hitchhiker's Guide to C...

4.32 avg rating — 44 ratings — published 1995 — 2 editions
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A Comprehensive Introductio...

4.38 avg rating — 24 ratings — published 1999
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A Comprehensive Introductio...

4.43 avg rating — 21 ratings — published 2005 — 3 editions
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A Comprehensive Introductio...

4.55 avg rating — 20 ratings — published 1999 — 2 editions
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Answer Book to Calculus

4.46 avg rating — 24 ratings — published 1984 — 5 editions
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A Comprehensive Introductio...

4.35 avg rating — 17 ratings — published 1999
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Physics for Mathematicians:...

4.58 avg rating — 12 ratings — published 2010
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“For many years I have been saying that I would like to write a book (or series of books) called Physics for Mathematicians. Whenever I would tell people that, they would say, “Oh good, you're going to explain quantum mechanics, or string theory, or something like that”. And I would say, “Well that would be nice, but I can't begin to do that now; first I have to learn elementary physics, so the first thing I will be writing will be Mechanics for Mathematicians”. So then people would say, “Ah, so you're going to be writing about symplectic structures”, or something of that sort. And I would have to say, “No, I'm not trying to write a book about mathematics for mathematicians, I'm trying to write a book about physics for mathematicians”; …… it's elementary mechanics that I don't understand. … I mean, for example, that I don't understand this – lever.
... Most of us know the law of the lever, but this law is simply a quantitative statement of exactly how amazing the lever is, and doesn't give us a clue as to why it is true, how such a small force at one end can exert such a great force at the other.
Now physicists all agree that Newton's Three Laws are the basis from which all of mechanics follows, but if you ask for an explanation of the lever in terms of these three laws, you will almost certainly not get a satisfactory answer.”
Michael Spivak

“... who can forget the amazement of a child balancing an adult on a see-saw, simply by being placed at the right position. How could this be? Where did all that extra force come from!?

The only wonder nowadays is that a physics student is unlikely to produce a satisfactory answer to this question. Perhaps we will be offered a few mumblings about moments, force times distance, laws of the lever perhaps even the "principle of virtual work". But we probably won't get an answer that seems to explain where that extra force comes from; and it is highly unlikely that we will get an answer that begins by establishing principles about rigid bodies, even though the rigidity of the lever is an absolute necessity for it to work.

In fact, the whole path from Newton's Laws, which basically concern "point masses", to bodies whose shape and extent are significant, is often rather dubiously traversed, even though elementary physics courses blithely pose such problems of the most diverse sorts.”
Michael Spivak, Physics for Mathematicians: Mechanics I



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