Calculus Made Awesome, by Silvanus P. Thompson, is available online. (Okay, so it's actually called Calculus Made Easy, but I like my alternate title better.)
Furthermore, unlike the modern calculus texts, it is nowhere near large enough to use as a weapon, even if you buy the print version, a 1998 edition fixed up by Martin Gardner Next time I teach calculus I must make sure to tell my students this book exists. And it's in the public-domain and free online, so it's not like I'd be recommending another expensive book. How much has calculus really changed in a century, anyway?
Thanks to Sam Shahfor reminding me of it. See also Ivars Peterson's review of the 1998 reissue. John Baez likes it but doesn't like that the new edition is longer than the old one.
23 April 2009
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I used to have a copy but I lent it out so many times I no longer know where it is, and I'd love to point more people to it.
It reminds me of how I taught calculus. Teaching proofs was pointless, an exercise understood by less than half the class and reproducible by maybe 10%; any of whom could easily learn it from a book. So I lectured the practical use of it and my students did rather well.
"Thirdly, among the dreadful things they will say about "So Easy" is this: that there is an utter failure on the part of the author to demonstrate with rigid and satisfactory completeness the validity of sundry methods which he has presented in simple fashion, and has even dared to use in solving problems! But why should he not? You don't forbid the use of a watch to every person who does not know how to make one? You don't object to the musician playing on a violin that he has not himself constructed. You don't teach the rules of syntax to children until they have already become fluent in the use of speech. It would be equally absurd to require general rigid demonstrations to be expounded to beginners in the calculus."
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Is there a similar book for analysis of algorithms?
I don't know of one. There's a book I vaguely remember flipping through in our library that might fit that bill but I don't remember what it is and I haven't actually read it. Perhaps I'll see if I can find it again.
But I'm not holding my breath, because analysis of algorithms really only became a big area after textbooks started to get bloated.
Thanks for the kind reply. I meant a similar book in terms of the exposition and not the size.
I think the type of exposition and the size go together; the exposition in many modern textbooks is bad because the book is bloated.
About half the terror of calculus students is the heft of that damned book. Getting them calmed down isn't easy.
Meanwhile, maybe someone can help me on a proof I've been unable to complete.
Let a matrix be "magic" if the sum over any row or column is the same. Let two matrices be "equivalent" if it is possible to obtain one from the other by the process of multiplying rows and columns by complex phases.
Then the equivalence classes of unitary (i.e. complex orthonormal) 3x3 matrices have only one representative that is magic, up to an overall multiple of a complex phase.
I think part of the reason for the heft is the tradition of including several semester's worth of material in one book. (For example, at Penn we use Stewart's text, about 1200 pages, for three semesters.)
As for that problem about unitary matrices, I'm reasonably sure I've actually seen it before. I'll try to dig up a solution.
I've found these calculus textbooks rather unpleasant to read; analysis textbooks seem much cleaner and more intuitive. Rudin is a lot more fun to read.
Courant's book is also interesting.
Michael, re the unitary matrix problem, PhilG elegantly solved it (without uniqueness, which may not be true) in a comment on my blog.
Aw, who needs a textbook to make calculus easy? Just chew gum! Chew on this -- Wrigley paid for research with findings that chewing gum in class makes teens smarter in math! Well, you get what you pay for. The "Wrigley Science Institute" funded research by Baylor University of Medicine in Houston. And guess what? Why, they found out that kids get smarter when chewing Wrigley's sugar-free gum. They studied four math classes, 108 students aged 13 to 16 years old from a Houston charter school that serves mostly low-income Hispanic students, and the gum-chewers did 3 percent better on the Texas Assessment of Knowledge and Skills achievement test. BUT they did not get smarter when they took the Woodcock Johnson III Tests of Achievement. Sounds like whether gum makes kids smarter depends upon the test, not the gum chewing.
Sponsored (read paid-for) studies invariably produce results favorable to the economic interests of the sponsor. Wrigley wants to sell more gum and end the days of gum being contraband in the class room.
Ethic Soup has a good article on this at:
Should you have a comment on this research as a teacher, please do leave a comment on the Ethic Soup blog.
Sponsored studies invariably produce results favorable to the economic interests of the sponsor.So who sponsored the study that produced this result?
Calculus, in its true guise as the toolbox of analysis, is already awesome!
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