By Richard Evan Schwartz

This publication provides a couple of issues regarding surfaces, akin to Euclidean, round and hyperbolic geometry, the basic team, common masking surfaces, Riemannian manifolds, the Gauss-Bonnet Theorem, and the Riemann mapping theorem. the most proposal is to get to a couple attention-grabbing arithmetic with no an excessive amount of formality. The booklet additionally contains a few fabric simply tangentially relating to surfaces, akin to the Cauchy tension Theorem, the Dehn Dissection Theorem, and the Banach-Tarski Theorem. The target of the ebook is to provide a tapestry of principles from a number of components of arithmetic in a transparent and rigorous but casual and pleasant manner. necessities comprise undergraduate classes in actual research and in linear algebra, and a few wisdom of complicated research.

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