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ISBN: 9780821853689

Publication Date: Jul 2011

Format: Paperback

Presents a number of topics related to surfaces, such as Euclidean, spherical and hyperbolic geometry, the fundamental group, universal covering surfaces, Riemannian manifolds, the Gauss-Bonnet Theorem, and the Riemann mapping theorem. It also includes some material only tangentially related to surfaces, such as the Cauchy Rigidity Theorem, the Dehn Dissection Theorem, and the Banach-Tarski Theorem. The goal is to present a tapestry of ideas in a clear and rigorous yet informal way.
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This book presents a number of topics related to surfaces, such as Euclidean, spherical and hyperbolic geometry, the fundamental group, universal covering surfaces, Riemannian manifolds, the Gauss-Bonnet Theorem, and the Riemann mapping theorem. The main idea is to get to some interesting mathematics without too much formality. The book also includes some material only tangentially related to surfaces, such as the Cauchy Rigidity Theorem, the Dehn Dissection Theorem, and the Banach-Tarski Theorem.

The goal of the book is to present a tapestry of ideas from various areas of mathematics in a clear and rigourous yet informal and friendly way. Prerequisites include undergraduate courses in real analysis and in linear algebra, and some knowledge of complex analysis.

Pages 312
Date Published 30 Jul 2011
Publisher American Mathematical Society
Series Student Mathematical Library
Series Part No. 60
Subject/s Geometry  
Richard Evan Schwartz is at Brown University, Providence, RI, USA.

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