First Steps in Differential Geometry

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

Andrew McInerney is a mathematics professor at Bronx Community College of the City University of New York.

Zusammenfassung

Introduces symplectic and contact geometry alongside Riemannian geometry, unlike other texts in differential geometry

Develops tools from linear algebra and advanced calculus, including differential forms and tensors, that are necessary in differential geometry

Introduces the reader to higher mathematics, including proofs of most of the main statements and results

Aimed as a text for undergraduate students who have finished two years of standard mathematics curriculum, including courses in calculus, linear algebra, and differential equations

Includes supplementary material: [...]

Inhaltsverzeichnis

Basic Objects and Notation.- Linear Algebra Essentials.- Advanced Calculus.- Differential Forms and Tensors.- Riemannian Geometry.- Contact Geometry.- Symplectic Geometry.- References.- Index.

Details

Erscheinungsjahr:	2015
Fachbereich:	Geometrie
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Seiten:	428
Reihe:	Undergraduate Texts in Mathematics
Inhalt:	xiii 410 S. 29 s/w Illustr. 25 farbige Illustr. 410 p. 54 illus. 25 illus. in color.
ISBN-13:	9781489990464
ISBN-10:	1489990461
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Mcinerney, Andrew
Auflage:	Softcover reprint of the original 1st ed. 2013
Hersteller:	Springer US Springer New York Undergraduate Texts in Mathematics
Maße:	235 x 155 x 24 mm
Von/Mit:	Andrew Mcinerney
Erscheinungsdatum:	05.08.2015
Gewicht:	0,645 kg

preigu-id: 104288777