Description - Geometry from a Differentiable Viewpoint by John McCleary
This book offers a new treatment of the topic, one which is designed to make differential geometry an approachable subject for advanced undergraduates. Professor McCleary considers the historical development of non-Euclidean geometry, placing differential geometry in the context of geometry students will be familiar with from high school. The text serves as both an introduction to the classical differential geometry of curves and surfaces and as a history of a particular surface, the non-Euclidean or hyperbolic plane. The main theorems of non-Euclidean geometry are presented along with their historical development. The author then introduces the methods of differential geometry and develops them toward the goal of constructing models of the hyperbolic plane. While interesting diversions are offered, such as Huygen's pendulum clock and mathematical cartography, the book thoroughly treats the models of non-Euclidean geometry and the modern ideas of abstract surfaces and manifolds.
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(247mm x 174mm x 17mm)
Cambridge University Press
Publisher: Cambridge University Press
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Author Biography - John McCleary
John McCleary is Professor of Mathematics at Vassar College on the Elizabeth Stillman Williams Chair. His research interests lie at the boundary between geometry and topology, especially where algebraic topology plays a role. His papers on topology have appeared in Inventiones Mathematicae, the American Journal of Mathematics and other journals, and he has written expository papers that have appeared in American Mathematical Monthly. He is also interested in the history of mathematics, especially the history of geometry in the nineteenth century and of topology in the twentieth century. He is the author of A User's Guide to Spectral Sequences and A First Course in Topology: Continuity and Dimension and he has edited proceedings in topology and in history, as well as a volume of the collected works of John Milnor. He has been a visitor to the mathematics institutes in Goettingen, Strasbourg and Cambridge, and to MSRI in Berkeley.