Manifolds, Vector Fields, and Differential Forms: An Introduction to Differential Geometry (Springer Undergraduate Mathematics Series)

Book Details

• Publisher: Springer

• Author: Gal Gross

• Language: English

• Edition: 1st Edition (2023)

• ISBN: 9783031254086

• Pages: 343

• Cover: Paperback (Import Edition)

• Dimensions: 9.3 x 6.1 x 0.6 inches

About The Book

Introduction to Modern Differential Geometry by Gal Gross is a carefully crafted textbook designed to introduce advanced undergraduate and master's students to the world of differential geometry. The book emphasizes intuitive understanding and motivation, making the complex subject matter accessible without requiring a deep background in abstract mathematics.

This first edition focuses on developing a solid intuition for differential geometry, using minimal prerequisites—just linear algebra, multivariable calculus, and, ideally, a course in ordinary differential equations. The book begins with the introduction of manifolds, explaining them intrinsically through coordinate patches and transition functions, making the concepts easy to grasp. The text presents the material as a natural extension of multivariable calculus, keeping point-set topology to a minimum.

A key feature of the book is its interactive approach to learning. Throughout the text, questions are sprinkled to engage students actively, encouraging participation and helping them solidify their understanding. Detailed answers are provided at the end of the book, making it ideal for independent study. Additionally, the book contains homework problems ranging from basic to challenging, allowing students to practice and deepen their knowledge. The material is comprehensive enough to extend beyond a single semester, with detailed suggestions for instructors provided in the Preface.

Whether you're learning on your own or using the book in a classroom setting, Introduction to Modern Differential Geometry offers a structured and engaging path to mastering this fascinating area of mathematics.