First steps in differential geometry Riemannian, contact, symplectic Andrew McInerney

Format:

Book

Author/Creator:

McInerney, Andrew, 1966-

Series:

Undergraduate texts in mathematics

Undergraduate texts in mathematics 0172-6056

Language:

English

Subjects (All):

Geometry, Differential.

Mathematics.

Medical Subjects:

Mathematics.

Physical Description:

1 online resource

Place of Publication:

New York, NY Springer ©2013

System Details:

text file

PDF

Summary:

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

Contents:

Basic Objects and Notation

Linear Algebra Essentials

Advanced Calculus

Differential Forms and Tensors

Riemannian Geometry

Contact Geometry

Symplectic Geometry

References

Index

Notes:

Includes bibliographical references and index

Online resource; title from PDF title page (SpringerLink, viewed July 22, 2013)

Other Format:

Printed edition:

ISBN:

9781461477327

1461477328

146147731X

9781461477310

OCLC:

853450078

Access Restriction:

Restricted for use by site license