Table of Contents

Curves in the Plane and in Space.- How Much Does a Curve Curve?- Global Properties of Curves.- Surfaces in Three Dimensions.- The First Fundamental Form.- Curvature of Surfaces.- Gaussian Curvature and the Gauss Map.- Geodesics.- Minimal Surfaces.- Gauss's Theorema Egregium.- The Gauss-Bonnet Theorem.- Solutions.- Index

Reviews

From the reviews:
"By the inclusion of 200 exercises with full solutions, this book has become a helpful tool for everyone teaching in its field. Summing up, it is a very good first book on the topic." (Internationale Mathematische Nachrichten, 187, August 2001) "a ]Pressley takes the simplest route with respect to all the technical setup: avoid it all. Instead of covariant derivatives, use derivatives with respect to local coordinates. Use moving frames without mentioning connections. Mention the Christoffel symbols very quickly, but dona (TM)t do very much with them. For the most part, it worksa ]the book does include several versions of the Gauss-Bonnett theorem, allowing the professor to end the course with a bang. All in all, I was quite happy with the book." (MAA Online)

From the reviews: INTERNATIONALE MATHEMATISCHE NACHRICHTEN"By the inclusion of 200 exercises with full solutions, this book has become a helpful tool for everyone teaching in its field. Summing up, it is a very good first book on the topic."
Internationale Mathematische Nachrichten, Nr. 187, August 2001MAA ONLINE"¨Pressley takes the simplest route with respect to all the technical setup: avoid it all. Instead of covariant derivatives, use derivatives with respect to local coordinates. Use moving frames without mentioning connections. Mention the Christoffel symbols very quickly, but dont do very much with them. For the most part, it works¨the book does include several versions of the Gauss-Bonnett theorem, allowing the professor to end the course with a bang. All in all, I was quite happy with the book."