First Steps in Differential Geometry: Riemannian, Contact, Symplectic (Undergraduate Texts in Mathematics)

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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.

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First Steps in Differential Geometry: Riemannian, Contact, Symplectic (Undergraduate Texts in Mathematics) Review

Whether you're a professor seeking approaches to teaching these concepts, or a student encountering the foundational concepts, this book is a must have. Elegant, well written, concise and carefully organized, who could imagine a book in advanced mathematical concepts would be such a joy to encounter?

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