Calculus

by Paul Abbott, Hugh Neill

Book by Abbott, P., Neill, Hugh

Genres: Mathematics, Science, Nonfiction, Textbooks, Reference

Paperback

First published January 1, 1970

Reviews

[Manny · Rating 5 out of 5]

Reading Jesse Kraai's novel Lisa a couple of weeks ago, I was once again reminded of the dreadful state that school math teaching has somehow got itself into. Lisa, a gifted young Aspie chessplayer, is failing most of her classes. Her mentor decides that she should at least be able to handle math, and takes her off to visit a research mathematician he knows.

"I need to know how to do the ninety degree triangle theorem," says Lisa sullenly. "What's that?" asks the mathematician, surprised. After a while, he figures out that Lisa means Pythagoras's theorem. She has a bunch of exercises she's supposed to complete, but they make no sense to her. The mathematician isn't interested in teaching her the rules for passing the test; instead, he shows her how you prove Pythagoras's theorem. This is a novel experience for Lisa, who has never seen a mathematical proof. Kraai, unfortunately, isn't making it up. A mathematician friend, who's an expert on geometry, says the situation is beyond belief. After complex negotiations involving mergers between various more or less incompatible courses, US geometry textbooks present an absurd parody of the subject: some of them include as many as a hundred "axioms", while Euclid's original treatment only used five axioms and five postulates. Obviously, this vast superfluity of so-called axioms would not be necessary if kids were taught to prove theorems, but the idea of proof has gone out of style.

If you're curious to see how things used to be done, you might want to check out Teach Yourself Calculus, a book I read when I was a geeky pre-teen in the early 70s. It was the closest thing I'd yet seen to a real math text; I absolutely loved it, and I can still remember the content quite well. Instead of forcing you to learn the dumb rules that are driving Lisa and her generation crazy, the author starts off by explaining fundamental principles: rates of change, limits, differentiation, the notion of an integral. He proves everything from first principles, assuming just basic algebra and trig, so you can see where all the mysterious formulas come from. By the time I'd got to the end, I could solve simple differential equations, and I understood what I was doing. I hadn't just picked up some useful skills; I could start to see what math was actually about.

Well, these things are always cyclic, and no doubt some cutting-edge educational theorist is at this moment telling people that logical proof is the way to go. It'll probably be back on the syllabus by the time today's pre-teens are sending their own kids to school. But if you're a geeky pre-teen who wants to find out now what real math looks like, do yourself a favor and buy a used copy of Teach Yourself Calculus from biblio.com. It could be the best $2 you ever spend.

[Dave · Rating 4 out of 5]

Teach Yourself Calculus is a self-instructional mathematics novel that aims to give an complete knowledge of beginning to intermediate calculus. With clear and workable definitions and precise examples even on the most complex concepts of the topic that can be applied to the exercises that follow, the book is thoroughly a good example of how an instructional book should be like.

[Andrew · Rating 3 out of 5]

I'm still teased for this one. Whatever. I like math. Calculus isn't all that superadvanced and esoterical with a good explanation. It was a great refresher.