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Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd Ed.

Alfred Gray, 1998, CRC Press. 1053pp, hardbound.

The second edition of Modern Differential Geometry of Curves and Surfaces with Mathematica was published five years after the inaugural edition and just before Alfred Gray's untimely death in October of last year. Containing nearly twice as many pages as the original, the new edition is well appointed with more encyclopedic information about the mathematics of curves and surfaces. Included in this edition are new chapters on plane curves, the construction and inversion of space curves and surfaces, and several chapters on minimal surfaces of all varieties. The overall design of the book remains similar to the previous edition, essentially a very large notebook converted to [Graphics:Images/reviews_gr_3.gif]. Most illustrations are greyscale with a brief center section of color images.

Even though it is designed as an advanced undergraduate or introductory graduate textbook, this book is still quite readable without the benefit of human tutelage. (Furthermore, I wish I could have used this book as my introduction to differential geometry instead of the here-unnamed horror-flick-of-a-book required by my early professors on the subject!) This work succeeds with symmetrical objectives: it is both a good introduction to differential geometry and a good introduction of how to use Mathematica to do differential geometry.

Of all the new material, my favorite new feature in this edition is the inclusion of short biographical sketches, most with photographs, of the mathematicians for whom so many of the theorems, surfaces, and methods are named. I never knew what Gaspard Monge looked like (a traditional French profile now gives me an idea) nor the fact that there is a statue of Teixeira in Oportp (I do hope they preserved his moustache and goatee). In the high-turnover market of textbooks, this much improved second edition is truly deserving and an excellent tribute to its author.

-- Flip Phillips

This book is available from the Mathematica Bookstore.

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