First Steps in Differential Geometry
McInerney, Andrew.
First Steps in Differential Geometry Riemannian, Contact, Symplectic / [electronic resource] : by Andrew McInerney. - XIII, 410 p. 54 illus., 25 illus. in color. online resource. - Undergraduate Texts in Mathematics, 0172-6056 . - Undergraduate Texts in Mathematics, .
Basic Objects and Notation -- Linear Algebra Essentials -- Advanced Calculus -- Differential Forms and Tensors -- Riemannian Geometry -- Contact Geometry -- Symplectic Geometry -- References -- Index.
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.
9781461477327
10.1007/978-1-4614-7732-7 doi
Mathematics.
Global analysis (Mathematics).
Manifolds (Mathematics).
Differential geometry.
Complex manifolds.
Mathematics.
Differential Geometry.
Global Analysis and Analysis on Manifolds.
Manifolds and Cell Complexes (incl. Diff.Topology).
QA641-670
516.36
First Steps in Differential Geometry Riemannian, Contact, Symplectic / [electronic resource] : by Andrew McInerney. - XIII, 410 p. 54 illus., 25 illus. in color. online resource. - Undergraduate Texts in Mathematics, 0172-6056 . - Undergraduate Texts in Mathematics, .
Basic Objects and Notation -- Linear Algebra Essentials -- Advanced Calculus -- Differential Forms and Tensors -- Riemannian Geometry -- Contact Geometry -- Symplectic Geometry -- References -- Index.
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.
9781461477327
10.1007/978-1-4614-7732-7 doi
Mathematics.
Global analysis (Mathematics).
Manifolds (Mathematics).
Differential geometry.
Complex manifolds.
Mathematics.
Differential Geometry.
Global Analysis and Analysis on Manifolds.
Manifolds and Cell Complexes (incl. Diff.Topology).
QA641-670
516.36