First Steps in Differential Geometry

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

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

From the book reviews:

"This books presents an alternative route, aiming to provide the student with an introduction not only to Riemannian geometry, but also to contact and symplectic geometry. ... the book is leavened with an excellent collection of illustrative examples, and a wealth of exercises on which students can hone their skills. Each chapter also includes a short guide to further reading on the topic with a helpful brief commentary on the suggestions." (Robert J. Low, Mathematical Reviews, May, 2014)

"This book is a distinctive and ambitious effort to bring modern notions of differential geometry to undergraduates. ... Mclnerney's writing is well constructed and very clear ... . Summing Up: Recommended. Upper-division undergraduates and graduate students." (S. J. Colley, Choice, Vol. 51 (8), April, 2014)

"The author does make a considerable effort to keep things as accessible as possible, with fairly detailed explanations, extensive motivational discussions and homework problems ... . this book provides a different way of looking at the subject of differential geometry, one that is more modern and sophisticated than is provided by many of the standard undergraduate texts and which will certainly do a good job of preparing the student for additional work in this area down the road." (Mark Hunacek, MAA Reviews, January, 2014)

"This text provides an early and broad view of geometry to mathematical students ... . Altogether, this book is easy to read because there are plenty of figures, examples and exercises which make it intuitive and perfect for undergraduate students." (Teresa Arias-Marco, zbMATH, Vol. 1283, 2014)