Saturday, 23 November 2013

Strogatz's Joy of x

I bought a book recently called, The Joy of x: A Guided Tour of Math, from One to Infinity, by Steven Strogatz (First Mariner Books, edition 2013). I think it's a great introduction to mathematical ideas and I highly recommend it.

It is a very visual treatment of mathematics (if I may use the term, "visual"). It is very much in the tradition of Riemann, whom, it is said, believed that geometric demonstrations were key to understanding the equations and their implications (Riemann helped create differential geometry whose ideas Einstein used heavily in his relativity theories - Einstein, himself was a highly visual person).

Strogatz is masterful in his historical development pedagogy and his demonstrations are intuitive precisely because he marries equations so well with illustrations. I've never quite thought about the method of exhaustion tied to the name of Archimedes as Strogatz has done it: he lays out quarter sections of a circle into a scalloped shape, first into four, then 8ths, 16ths, etc., 'til he finally achieves a regular rectangle with r height and πr base - brilliant.

And this is not the only instance where he makes mathematical demonstrations come alive. He does a similar thing with a demonstration that all angles of a triangle equal 180 degrees by appealing to the existence of a parallel line. Everything is logically laid out so when he comes to calculus the ideas he speaks about earlier are recalled and retooled for other purposes.

Where I'd take issue is his treatment of "closed rings" (ie, how different types of numbers are called into existence by the requirements of arithmetical operations: natural numbers, integers, algebraic numbers, transcendental numbers, imaginary numbers) though he adumbrates how these types of numbers arise in talking about the fundamental operations of arithmetic and the rise of imaginary numbers. There are other books like this available so I'd grant him this.

I have always wished that Nunavut schools would use the narrative (historical development pedagogy) as a basic teaching tool. This book is another important case why we need such a thing for this type of teaching and learning introduces the notion of mortals discovering and creating mathematics from a problem-solving perspective rather than suggesting this seemingly otherworldly subject as having come from heaven already fully formed and without the need for human contribution.


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