By Richard Evan Schwartz
This booklet offers a couple of subject matters regarding surfaces, corresponding to 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 booklet additionally contains a few fabric purely tangentially relating to surfaces, reminiscent of the Cauchy stress Theorem, the Dehn Dissection Theorem, and the Banach-Tarski Theorem. The aim of the publication is to offer a tapestry of principles from a variety of components of arithmetic in a transparent and rigorous but casual and pleasant approach. must haves contain undergraduate classes in actual research and in linear algebra, and a few wisdom of advanced research.
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