Introductory Course on Differentiable Manifolds (Aurora: Dover Modern Math Originals)

Book Details

• Author: Siavash Shahshahani

• Publisher: Dover

• Edition: First Edition, First ed.

• Binding: Paperback

• Format: Illustrated

• Number of Pages: 352

• Release Date: 17-08-2016

• Language: English

• ISBN: 9780486807065

• Package Dimensions: 8.9 x 6.0 x 1.0 inches

About The Book
Differentiable Manifolds by Siavash Shahshahani is an in-depth, rigorous course on the theory of differentiable manifolds, offering advanced undergraduates and graduate students a thorough exploration of this crucial topic in modern mathematics. Based on the author’s extensive teaching experience, this textbook is designed for students with a solid background in undergraduate mathematics, including multivariable calculus, linear algebra, elementary abstract algebra, and point-set topology.

The book is divided into four comprehensive parts. The first chapter focuses on the tensor algebra of linear spaces and their mappings, laying the groundwork for the rest of the course. Part II delves into the integration of vector fields, the Lie bracket, the exterior derivative, and the Lie derivative, expanding the student’s understanding of the fundamentals. Part III introduces manifolds and vector bundles, providing the core material for the course. Finally, the last chapter offers a glimpse into geometric structures, introducing connections on the tangent bundle, and demonstrating their role in implementing the second derivative and the derivative of vector fields on the base manifold.

The textbook is rich with over 200 exercises, allowing students to apply their knowledge, deepen their understanding, and refine their problem-solving skills. In addition to the rigorous mathematical content, historical and philosophical insights are woven into the material, offering context to the development of the subject. Helpful appendices further enhance the learning experience by providing supplementary material to support the core text.