"Worked Problems in Modern Differential Geometry" is a textbook written by Michael Spivak that covers the foundations of modern differential geometry, including topics such as smooth manifolds, Riemannian geometry, and Lie groups.
This book is primarily intended for advanced undergraduate and graduate students in mathematics or physics who have a solid understanding of linear algebra, multivariable calculus, and basic topology.
Some of the key topics covered in this book include smooth manifolds, vector fields, differential forms, Riemannian metrics, connections, curvature, and Lie groups.
Yes, a strong background in linear algebra, multivariable calculus, and basic topology is necessary for understanding the material in this book. Additionally, some familiarity with abstract algebra and analysis may be helpful.
Yes, there is a solutions manual available for instructors, as well as a supplementary text, "A Comprehensive Introduction to Differential Geometry" by Michael Spivak, which provides more in-depth explanations and proofs for the concepts covered in this book.