FROM THE BOOKSHELF

ANDREW RUPPEL, Feature Editor, McIntire School of Commerce,
University of Virginia

For Math Whizzes, Wizards, and Wannabes

by Andrew Ruppel, Feature Editor

It is certainly encouraging to see publishers issuing more titles in mathematics aimed at non- specialist audiences and otherwise taking a fresh look at mathematical topics. Here are five books that merit the attention of specialists and non-specialists alike.

Ten years in the making, this volume has been carefully put together by a Scandinavian physician and his engineer son, who made the technical illustrations. In 34 chapters, it covers the details of mathematics from numbers systems through the classical topics in the geometries, the calculus, analysis, as well as the "contemporary" topic of fractals. Discrete math topics, such as graph theory are omitted , however.

The scope is astonishing. Yet it is not done in a dry manner. Cartoons and limericks are scattered throughout. Typically, a chapter begins with a history of the field it covers, with key contributors identified, and sample pages from landmark texts included. Worked-out examples are provided to make definitions and concepts clear. Practical applications are discussed. Separate name, subject, and symbol indices are provided, as well as a list of references used and a bibliography. Page layouts are not crowded and bold- faced type is used effectively.

An excellent reference book to both have on the shelf and to read. If you like mathematics, you will absolutely love Gullberg's book.

More than five years in development, and with NSF support, this text aims at setting a new benchmark for the beginning two-semester sequence in mathematics for math and science majors. Its reference point is the typical first-course format used in the sciences to both develop important prerequisite knowledge and to reveal the scope of the field-with the aim of encouraging students to pursue it. The authors (eight in all) of Principles and Practices thus wanted to go beyond the usual treatment of calculus and continuous functions. Instructors of the decision sciences will therefore appreciate the topic coverage in the nine chapters of this text, which in sequence are: Change; Geometry; Linear Algebra; Basic Counting Techniques; Graph Theory; Algorithms; Logic and Design of Intelligent Machines; Chance; and Modern Algebra.

Based on the McGraw-Hill Dictionary of Scientific and Technical Terms, Fifth Edition, this paperback contains 4,000 entries covering the fields of pure and applied mathematics, including arithmetic, algebra, geometry, trigonometry, calculus, logic, and topology. Includes synonyms, acronyms, abbreviations, pronunciations, and tables of useful data and information. It does not contain biographies of key figures. The entries are attractively laid out, but there are no accompanying figures. Statistics is not fully covered; for example, there is no entry for the log-normal distribution. Still, if one wanted to have a desk-drawer reference on mathematical terms, then this would be a good choice.

If you like your mathematics more in prose form, then these two previously published accounts may appeal to you.

Guillen focuses more on the personalities than on the mathematics in examining key equations in physics. The people and the equations discussed are:

• Newton and the Law of Gravitational Attraction
• Daniel Bernoulli and the Law of Hydrodynamic Pressure
• Faraday and the Law of Electromagnetic Induction
• Clausius and the Second Law of Thermodynamics
• Einstein and the Theory of Special Relativity.

One is struck in these historical accounts by the trials and tribulations faced by these pioneering thinkers and the jealousies that others often harbored of them. Admittedly though, it makes for fascinating reading. Guillen uses a five-part structure within each chapter. The opening part provides some dramatic event in the life of the scientist, followed by sections on how he encountered the subject addressed by the equation, why it is important, how he finally formulated it, and how the outcome has shaped our world today. Guillen appears to exercise considerable author's license in re- constructing historical events and, at times, there seems to be more filler than informative detail about the equations themselves.

John Casti is a frequent "repackager" of technical subjects-his most recent book (Would-Be Worlds) deals with computer simulation. In Five Golden Rules he discusses:

• The Minimax Theorem
• Brouwer's Fixed-Point Theorem
• Morse's Theorem on Singularity
• Turing and the Halting Theorem
• The Simplex Method.

Unlike the Guillen book, Casti's is aimed at a reader who is comfortable in math. He recreates the reasoning behind the each rule and how they work, but doesn't neglect describing the people involved and the history of math at the time. And clearly, Casti's choice of rules is more aligned with decision science interests than Guillen's selection is. The criteria employed by Casti in making his five rule choices included: fostered new thinking, yielded wide application, had philosophical import, and demonstrated "beauty."

Were I pressed to identify the five most important equations to contemporary business, then I might identify the following (without any ranking implied):

• The equation for compound interest growth (the whole financial world spins around variants of this one)
• The Central Limit Theorem from statistics (where would market research and opinion polling be?)
• The Harris/Wilson EOQ formula (though to some extent now obsolete in an era of computerized, continuous inventory management)
• Dantzig's linear programming formulation (it helped energize the field of logistics)
• Gauss's regression equation (for forecasters and would- be explainers everywhere).

Surely there must be readers who disagree with my choices. Let me hear from you.