By Richard Evan Schwartz

This booklet provides a few subject matters concerning surfaces, resembling Euclidean, round and hyperbolic geometry, the basic workforce, common protecting surfaces, Riemannian manifolds, the Gauss-Bonnet Theorem, and the Riemann mapping theorem. the most proposal is to get to a few fascinating arithmetic with out an excessive amount of formality. The ebook additionally contains a few fabric in basic terms tangentially relating to surfaces, corresponding to the Cauchy pressure Theorem, the Dehn Dissection Theorem, and the Banach-Tarski Theorem. The objective of the booklet is to provide a tapestry of rules from quite a few components of arithmetic in a transparent and rigorous but casual and pleasant manner. must haves comprise undergraduate classes in genuine research and in linear algebra, and a few wisdom of advanced research.

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