Differential Topology: First Steps (Dover Books on Mathematics)

Book Details

• Publisher: Not Specified

• Author: Wallace, Andrew H.

• Language: English

• Edition: Not Specified

• ISBN: 9780486453170

• Pages: 149

• Cover: Paperback

• Release Date: 24-05-2012

About The Book

Differential Topology: First Steps by Andrew H. Wallace is a concise and approachable introduction to differential topology, tailored specifically for undergraduate students. Requiring only a minimal mathematical background, this 149-page paperback guides readers through key concepts while emphasizing intuitive understanding over technical complexity.

The text begins with fundamental topics such as open and closed sets and continuous maps, making it ideal for those with no prior exposure to topology. It then progresses into the study of differentiable manifolds and maps, focusing on the critical points of functions—a core theme in differential topology. Wallace introduces the concept of spherical modifications and offers a clear treatment of level manifolds and their roles in manifold theory.

Designed to build a strong conceptual foundation, the book culminates in the classification of surfaces and encourages further exploration through suggested readings. This volume is an excellent starting point for students interested in topology, geometry, or the broader applications of mathematical analysis.