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• Title : Geometry from a Differentiable Viewpoint
• Author : John McCleary
• Rating : 4.96 (382 Vote)
• Publish : 2016-7-1
• Format : Paperback
• Pages : 368 Pages
• Asin : 0521133114
• Language : English

Beginning with the ancient sources, the author first explores synthetic methods in Euclidean and non-Euclidean geometry and then introduces differential geometry in its classical formulation, leading to the modern formulation on manifolds such as space-time. New topics include Clairaut's relation for geodesics, Euclid's geometry of space, further properties of cycloids and ma

Beginning with the ancient sources, the author first explores synthetic methods in Euclidean and non-Euclidean geometry and then introduces differential geometry in its classical formulation, leading to the modern formulation on manifolds such as space-time. New topics include Clairaut's relation for geodesics, Euclid's geometry of space, further properties of cycloids and map projections, and the use of transformations such as the reflections of the Beltrami disk.. The presentation is enlivened by historical diversions such as Hugyens's clock and the mathematics of cartography. The intertwined approaches will help undergraduates understand the role of elementary ideas in the more general, differential setting. This thoroughly revised second edition includes numerous new exercises and a new solution key. The development of geometry from Euclid to Euler to Lobachevsky, Bolyai, Gauss, and Riemann is a story that is often broken into parts - axiomatic geometry, non-Euclidean geometry, and differential geometry. This poses a problem for undergraduates: Which part is geometry? What is the big picture to which these parts belong? In this introduction to diff

Review of the first edition: ' an unusual and interesting account of two subjects and their close historical interrelation.' The Mathematical Gazette' the author has succeeded in making differential geometry an approachable subject for advanced undergraduates.' Andrej Bucki, Mathematical Reviews

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His research interests lie at the boundary between geometry and topology, especially where algebraic topology plays a role. 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.

. John McCleary is Professor of Mathematics at Vassar College on the Elizabeth Stillman Williams Chair. He has been a visitor to the mathematics institutes in Goettingen, Strasbourg and Cambridge, and to MSRI in Berkeley. His papers on topology have appeared in Inventiones Mathematicae, the American Journal of Mathematics and other journals, and he has written expository papers tha