By Richard Evan Schwartz
This ebook provides a few issues on the topic of surfaces, resembling Euclidean, round and hyperbolic geometry, the elemental crew, common protecting surfaces, Riemannian manifolds, the Gauss-Bonnet Theorem, and the Riemann mapping theorem. the most suggestion is to get to a couple attention-grabbing arithmetic with out an excessive amount of formality. The ebook additionally contains a few fabric purely tangentially concerning surfaces, corresponding to the Cauchy tension Theorem, the Dehn Dissection Theorem, and the Banach-Tarski Theorem. The objective of the ebook is to offer a tapestry of rules from quite a few parts of arithmetic in a transparent and rigorous but casual and pleasant manner. necessities contain undergraduate classes in actual research and in linear algebra, and a few wisdom of complicated research.
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