Geometry from a Differentiable Viewpoint

出版者:Cambridge University Press

作者:John McCleary

页数:324

出版时间:1995-01-27

价格:USD 44.99

装帧:Paperback

isbn号码:9780521424806

图书标签:数学计算机科学Geometry

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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