First Steps in Differential Geometry : Riemannian, Contact, Symplectic par Andrew McInerney

November 21, 2019

First Steps in Differential Geometry : Riemannian, Contact, Symplectic par Andrew McInerney

Titre de livre: First Steps in Differential Geometry : Riemannian, Contact, Symplectic

Auteur: Andrew McInerney

Date de sortie: July 10, 2013

Broché: 410 pages

ISBN: 146147731X

Éditeur: Springer-Verlag New York Inc.

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Differential geometry arguably offers the smoothest transition from the standard university mathematics sequence of the first four semesters in calculus, linear algebra, and differential equations to the higher levels of abstraction and proof encountered at the upper division by mathematics majors. Today it is possible to describe differential geometry as "the study of structures on the tangent space," and this text develops this point of view. This book, unlike other introductory texts in differential geometry, develops the architecture necessary to introduce symplectic and contact geometry alongside its Riemannian cousin. The main goal of this book is to bring the undergraduate student who already has a solid foundation in the standard mathematics curriculum into contact with the beauty of higher mathematics. In particular, the presentation here emphasizes the consequences of a definition and the careful use of examples and constructions in order to explore those consequences.