Geometry from a Differentiable Viewpoint
By (author) John McCleary
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Geometry from a Differentiable Viewpoint by John McCleary
Book DescriptionDifferential geometry has developed in many directions since its beginnings with Euler and Gauss. This often poses a problem for undergraduates: which direction should be followed? What do these ideas have to do with geometry? This book is designed to make differential geometry an approachable subject for advanced undergraduates. The text serves as both an introduction to the classical differential geometry of curves and surfaces and as a history of the non-Euclidean plane. The book begins with the theorems of non-Euclidean geometry, then introduces the methods of differential geometry and develops them towards the goal of constructing models of the hyperbolic plane. Interesting diversions are offered, such as Huygens' pendulum clock and mathematical cartography; however, the focus of the book is on the models of non-Euclidean geometry and the modern ideas of abstract surfaces and manifolds. Although the main use of this text is as an advanced undergraduate course book, the historical aspect of the text should appeal to most mathematicians.
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Book DetailsISBN: 9780521424806
(247mm x 174mm x 17mm)
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 27-Jan-1995
Country of Publication: United Kingdom
Books By Author John McCleary
Geometry from a Differentiable Viewpoint, Paperback (October 2012)
A thoroughly revised second edition of a textbook for a first course in differential/modern geometry that introduces methods within a historical context.
Hippie Dictionary, Paperback (November 2003)
Whether you lived through the sixties and seventies or just wish you had, this revised and expanded edition of the "Hippie Dictionary" entertains as much as it educates. And it wasn't just about sex, drugs and rock 'n' roll. These were the early years of pro-ecology and anti-capitalist beliefs.
User's Guide to Spectral Sequences, Hardback (December 2000)» View all books by John McCleary
This book describes some of the most important examples of spectral sequences and some of their most spectacular applications.
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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.
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