Ebook: First Steps in Differential Geometry: Riemannian, Contact, Symplectic
Author: Andrew McInerney (auth.)
- Tags: Differential Geometry, Global Analysis and Analysis on Manifolds, Manifolds and Cell Complexes (incl. Diff.Topology)
- Series: Undergraduate Texts in Mathematics
- Year: 2013
- Publisher: Springer-Verlag New York
- Edition: 1
- Language: English
- pdf
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.
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.
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.
Content:
Front Matter....Pages i-xiii
Basic Objects and Notation....Pages 1-7
Linear Algebra Essentials....Pages 9-66
Advanced Calculus....Pages 67-133
Differential Forms and Tensors....Pages 135-193
Riemannian Geometry....Pages 195-270
Contact Geometry....Pages 271-337
Symplectic Geometry....Pages 339-404
Back Matter....Pages 405-410
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.
Content:
Front Matter....Pages i-xiii
Basic Objects and Notation....Pages 1-7
Linear Algebra Essentials....Pages 9-66
Advanced Calculus....Pages 67-133
Differential Forms and Tensors....Pages 135-193
Riemannian Geometry....Pages 195-270
Contact Geometry....Pages 271-337
Symplectic Geometry....Pages 339-404
Back Matter....Pages 405-410
....