J.A. Thorpe Boeken

This introductory text explores the geometry of n-dimensional oriented surfaces in Rn+1, using vector field calculus as the main tool. It emphasizes global concepts early on, introducing differential forms and coordinate patches as needed. Designed for junior/senior level students, it builds on prior knowledge from linear algebra and multivariate calculus.

This book addresses the compartmentalization of undergraduate mathematics, focusing on the interconnections between topology, geometry, and algebra. It introduces key results like De Rham's theorem and the Gauss-Bonnet theorem, aiming to integrate concepts from various fields and enhance understanding for students.