Enhanced descriptions from Syndetics:

Focusing Your Attention The purpose of this book is Cat least) twofold. First, we want to show you what mathematics is, what it is about, and how it is done-by those who do it successfully. We are, in fact, trying to give effect to what we call, in Section 9.3, our basic principle of mathematical instruction, asserting that "mathematics must be taught so that students comprehend how and why mathematics is qone by those who do it successfully./I However, our second purpose is quite as important. We want to attract you-and, through you, future readers-to mathematics. There is general agreement in the (so-called) civilized world that mathematics is important, but only a very small minority of those who make contact with mathematics in their early education would describe it as delightful. We want to correct the false impression of mathematics as a combination of skill and drudgery, and to re­ inforce for our readers a picture of mathematics as an exciting, stimulating and engrossing activity; as a world of accessible ideas rather than a world of incomprehensible techniques; as an area of continued interest and investigation and not a set of procedures set in stone.

Table of contents provided by Syndetics

• 1 Going Down the Drain
• 2 A Far Nicer Arithmetic
• 3 Fibonacci and Lucas Numbers
• 4 Paper Folding and Number Theory
• 5 Quilts and Other Decorative Geometries
• 6 Pascal, Euler, Triangles, and Windmills
• 7 Hair and Beyond
• 8 An Introduction to the Mathematics of Fractal Geometry
• 9 Some of Our Reflections

Reviews provided by Syndetics

CHOICE Review

Two distinct, established genres might have a claim to this book: the wide-ranging, popular account of mathematics for the general reader, e.g., G. Gamow's One, Two, Three, Infinity (1947), J. Casti's Five Golden Rules (CH, May'96), J. P. Davis and W.G. Chinn's 3.1416 and All That (CH, Apr'70), or any number of books by Ian Stewart; versus the "transition to higher mathematics" textbook aimed at future serious students of mathematics, e.g., G. Polya's How to Solve It (1945), D.J. Velleman's How to Prove It (CH, Jun'95), and A. Cupillari's The Nuts and Bolts of Proofs (1989). Like the former group, this book presents a number of loosely related topics (spirals, modular arithmetic, Fibonacci numbers, paper-folded regular polygons, wallpaper symmetry, binomial coefficient identities, orders of infinity, and fractals), emphasizing aesthetics throughout. Like the latter group, the authors focus on the process of discovery and the use of rigorous proof, and so make fair demands on the reader. The final chapter contains a pedagogical polemic explicitly setting forth the principles of communication presumably exemplified in the main body of the text; its presence suggests that teachers of mathematics might represent the book's true intended audience. Actually, one might wonder if the transition from classroom to printed page has not made this material more seemingly complex, more daunting, so that the book will demand a higher caliber of reader than the students with whom the authors tested their materials. A modest portion of the mathematics appears in print here for the first time. For all undergraduates and talented high school students. D. V. Feldman; University of New Hampshire