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Title: Differential Geometry: A Geometric Introduction by David W. Henderson ISBN: 0-13-569963-0 Publisher: Prentice Hall Pub. Date: 24 July, 1997 Format: Paperback Volumes: 1 List Price(USD): $81.00

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Average Customer Rating: 3 (1 review)

Rating: 3
Summary: Fantastic concept, flawed execution
Comment: It's certainly a great concept: explain differential geometry - and and the myriad real-world applications of this subject - by appealing to our geometric intuition! (Those who have read just about any other text will realize that I am sincere, not sarcastic in this remark - the intuitive approach is quite unusual in treatments of the subject material.)

To a limited degree, the book is a success. The first chapter flows rather smoothly, and could actually be used to introduce differential geometry in an advanced high school classroom. I would consider that in and over itself to be a truimph! In places, it's fun to read, and some of the "constructions" (often using three dimensions) are both clever and helpful. And I must confess that reading this book I picked up bits and pieces of intuition that I had missed when reading other texts.

For all of these reasons, I found myself really wanting to like this book; sadly, I ultimately found that I could not. Unfortunately, the intuitive approach starts to break down as the book proceeds. In the later chapters, I could only intuitively grasp and fully understand what Henderson was trying to explain because of previous familiarity with the material; I would have pretty baffled without prior knowledge of the subject. The writing and presentation just does not compare with that in some of the better (if more traditional) texts in differential geometry, such as Manfredo P. Do Carmo's Differtial Geometry of Curves and Surfaces or Michael Spivak's excellent five-volume Comprehensive Introduction to Differential Geometry. If one is familiar with those (or other similar) texts, it might be fun to take a look at Henderson's book. If not, look there first - or at least look there as well - in your explorations of this field of mathematics.