Mathematics, Its Magic and Mastery by Aaron Bakst (out of print, but used copies are available as of this review - I have the 1967 version)

It has clear writing like the Isaac Asimov books, but a little more flair. The book is packed - it could actually function as a high school text for one year for a print-oriented learner that doesn't need a lot of practice problems. Most of it is anecdotes and examples. Similar to the Harold Jacobs MAHE text, the scope is very comprehensive, but it is designed to be read, whereas the Jacobs book IS a textbook with more focus on working practice problems. All illustrations are b&w, but are very clear, there is enough white space in the book to keep it from seeming crowded.

Here are the chapter headings:

Numerals and Numeration (History and use of numerals)
Systems of Numerations (one of the best descriptions of other bases I have ever seen)
Some Remarkable Properties of Numbers
Number Giants (large nos, history including Archimedes contribution)
Number Pygmies
There's Secrecy in Numbers (cryptography, codes, etc.)
The Arithmetic of Measurement
Simple Calculating Devices (abacus, soroban, etc.)
Rapid Calculations ("human calculators", math tricks)
Problems and Puzzles (actual cases)
How the Number Magician Does It
Algebra & Its Numbers (the algebra chapters all contain many problems in real applications)
The Algebra of Number Giants and Pygmies
The Grammar of Algebra
Algebra, Boss of Arithmetic
Algebra Looks at Installment Buying
Chain Letter Algebra
Streamlining Everyday Computation (logs)
The Bankers Number - Jack of All Trades (net present value, future value, compounding in other ares such as growth and aging)
How to Have Fun with Lady Luck (probability)
The Thinking Machines
Postoffice Mathematics (relativity, probability, geometry)
New Worlds for Old (zero dimension, Flatland, geometry meets arithmetic and algebra)
Passport for Geometric Figures (geometry and movement)
Man's Servant - The Triangle
The Triangle - Man's Master
Circles, Angles & an Age Old Problem (pi)
The Mathematics of Seeing (optical illusion)
The Lost Horizon (curvature of the earth, natural illusions)
The Shape of Things (geometry beyond circles and triangles)
The Size of Things (three dimensions, area of geometric figures)
Escape from Flatland (solid geometry)
How Algebra Saves Geometry (applications of geometry & algebra)
Cork-Screw Geometry (distances between points in solid geometry)
Mathematics, Interpreter of the Universe (geometry in astronomy / geology, physics)
The Firing Squad & Mathematics (math and movement)
Of Math and Magic (more math & motion, time and distance)

The chapters encompass about 700 pages, after which there is an extensive appendix of tables, definitions, and answers to problems posed in the book.

This is a really good resource, and relatively inexpensive for now while there are copies available. I haven't seen anything comparable IN print for a while, except possibly the Birth of Numbers book I have been using for the high school math history course - but this one is less scary :o). What I really like about it is that the text is virtually all applied, rather than just talking about math in the abstract. It is also conversational - i.e., just opening up to page 389, "Let the reader imagine that he is a Flatlander, living in a two-dimensional world. As we found out when we examined this type of world, he will be able to move around only in a plane, as in the space between two plates of glass. Moreover, he cannot see what is above him or below him and could only imagine a world of three dimensions. A Flatlander may know everything about flat figures such as lines, triangles, squares, and circles, but he will have to use his imagination to picture a cube or a sphere. Suppose a sphere has suddenly descended upon Flatland. . "

It would also be an excellent refresher book for an adult that may have been good at math in high school but has not reviewed math for a long time. This may not be good for a math-phobic parent trying to overcome math anxiety - it really does assume a fairly strong high school math base, even as it explains things well, it does not treat topics as if they are being introduced to real beginners.

Hope that helps someone else, I was really surprised at finding this resource and more surprised when I found there are copies available.

Julie Brennan - Reviewed 7/24/05

Review of Mathematics: Its Magic & Mastery by Aaron Bakst