Differential Geometry of Curves and Surfaces

Kristopher Tapp is Professor of Mathematics at Saint Joseph's University. He has been awarded two National Science Foundation research grants to support research in differential geometry, and several teaching awards. He is the author of Symmetry: A Mathematical Exploration (Springer, 2012) and over twenty research papers featured in top journals.

“This is the first textbook on mathematics that I see printed in color. … This book is not a usual textbook, but a very well written introduction to differential geometry, and the colors really help the reader in understanding the figures and navigating through the text. … this book will surely serve very well for students who want to learn differential geometry from the ground up no matter what their main learning goal is.” (Árpád Kurusa, Acta Scientiarum Mathematicarum, Vol. 84 (1-2), 2018)“This book is perfect for undergraduate students. ... There is also plenty of figures, examples, exercises and applications which make the differential geometry of curves and surfaces so interesting andintuitive. The author uses a rich variety of colours and techniques that help to clarify difficult abstract concepts.” (Teresa Arias-Marco, zbMATH 1375.53001, 2018)“This is a visually appealing book, replete with many diagrams, lots of them in full color. … the author’s writing style is extremely clear and well-motivated. … this is still the book I would use as a text for a beginning course on this subject. It would not surprise me if it quickly becomes the market leader.” (Mark Hunacek, MAA Reviews, July, 2017)

• Introduction.- Curves.- Additional topics in curves.- Surfaces.- The curvature of a surface.- Geodesics.- The Gauss–Bonnet theorem.- Appendix A: The topology of subsets of Rn.- Recommended excursions.- Index.