Differential Geometry of Curves and Surfaces

Students and professors of an undergraduate course in differential geometry will appreciate the clear exposition and comprehensive exercises in this book that focuses on the geometric properties of curves and surfaces, one- and two-dimensional objects in Euclidean space. The problems generally relate to questions of local properties (the properties observed at a point on the curve or surface) or global properties (the properties of the object as a whole). Some of the more interesting theorems explore relationships between local and global properties.

A special feature is the availability of accompanying online interactive java applets coordinated with each section. The applets allow students to investigate and manipulate curves and surfaces to develop intuition and to help analyze geometric phenomena.

Thomas F. Banchoff is a geometer and has been a professor at Brown University since 1967. Banchoff was president of the MAA from 1999-2000. He is published widely and known to a broad audience as editor and commentator on Abbotts Flatland. He has been the recipient of such awards as the MAA National Award for Distinguished College or University Teaching of Mathematics and most recently the 2007 Teaching with Technology Award.

Stephen Lovett is an associate professor of mathematics at Wheaton College in Illinois. Lovett has also taught at Eastern Nazarene College and has taught introductory courses on differential geometry for many years. Lovett has traveled extensively and has given many talks over the past several years on differential and algebraic geometry, as well as cryptography.