Differential Topology: A New Approach

Author: Zhang Zhusheng
Publisher:
Publish Date: 2002-07-01
Features: Differential topology is one of the most significant and influential branches of mathematics in the 20th century, with extensive and important applications in many disciplines. The winner of the 1983 Nobel Prize in Economics vividly described how differential topology methods helped him achieve a breakthrough. World-renowned universities have included differential topology in the curriculum for both undergraduate and graduate students and have designated it as an important subject for doctoral entrance examinations. This book is based on the lecture notes of the author's multiple presentations of differential topology courses at Peking University in recent years. The book is divided into twelve chapters, with the first two chapters and the appendix providing a detailed introduction to the necessary prerequisites. Chapters 3 to 12 cover the fundamental concepts and methods of differential topology, accompanied by examples of important applications. The book emphasizes inspirational teaching, with selected material having broad applicability, reflecting the modernization trend of the discipline and meeting the needs of students, researchers, and professionals in mathematics, computer science, mechanics, physics, economics, and other fields. The predecessor of this book, "Lectures on Differential Topology," was awarded the Second Prize of the National Science and Technology Progress Award by the Ministry of Education of the People's Republic of China in 2000.