Customer Reviews

Professor Stewart's Hoard of Mathematical Treasures

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Ian Stewart has amassed an extremely diverse collection here, with topics ranging from bad jokes ("Q: What's a polar bear? A: A Cartesian bear after a change of coordinates.") to biographical snippets (especially about forgetful mathematicians, like the one who failed to recognize his own daughter) to math-based puzzles to discussions of advanced topics like topology and some advanced number theory.

For the high school student, much of the material in the book will probably be hard going, but the great thing about the book is that it is so full of fascinating problems and diversions that it is necessary only to turn a page or two to get to something more congenial to the reader. For the more advanced college math major, there is much here to educate and delight.

To give but a single example of the mathematical puzzles the book deals with, I will refer to Professor Stewart's treatment of the sequence "1, 11, 21, 1211, 111221, . . ." In this sequence each term after the first is constructed by "reading" the previous term. Thus, the fourth term reads "one 1, one 2, two 1s" and thus generates the fifth term. At first glance, there seems to be little mathematical about this sequence. It's more of a cute brain teaser that really has little to do with math. But what if we asked how many digits the nth term has? Professor Stewart presents that response and an approximation. (In this case, he does not explain the derivation of the approximation, but the point is that he does go well beyond the standard treatment of the sequence.)

Highly recommended.

A few months ago I saw the book "Prof Stewart's cabinet..." in a book store. Only the price kept me from buying it then (thinking I would get it cheaper through Amazon). A few days later, at Amazon's, I found this 2nd book (which was even cheaper 'used'), so I decided to buy this 2nd book of "Prof Stewart" first. And indeed it was first class, money worth! Ian Stewart writes in a clear and attractive way, you would not expect from a professional mathematician. Fun with all kinds of different math problems and games, not just the 'useless' (but mind-triggering) stuff, but with many problems a link to 'real math' is given as well. Hyperlinks to sites with more information make it really complete.

I am still reading the book (as many topics tease me to do further 'research' myself, I proceed only slowly), but it is really great fun for all who like math puzzles and the like. My kids now do find me a real math geek even more - though I am not (I think...) - but the book surely will get a prominent place on my bookshelves. If I will finish the book, I might buy some other books of Ian Stewart as well.

Worthy successor to Professor Stewart's Cabinet of Mathematical Curiosities -- it is a compilation of recreational mathematics, puzzles, trivia, short notes on theory and introduction to mathematical personalities. Think of it as a scrapbook + notebook + most interesting blog articles anthology.

My favorite parts from 'Hoard' -

* Byron on Newton

* Egyptian Fraction / Greedy Algorithm

* Fermat's poser (Euler's solution which was not mentioned; stopped after 3 hrs of furtive trying)

* Short article on ancient Indian mathematician Lilavati

* Proof techniques. e.g., Proof by vague authority -- 'Ortho-equilibrium in Cauchy-Mandelbrot set disavows Deric fallacy' -- made it up, but you get a gist!

* Invention of '=' (equals to) sign

* and..the parlor trick of three inverted cups (could make one mad just trying in frustration)