Computational Topology: An Introduction
About this Title
Herbert Edelsbrunner, Duke University, Durham, NC and John L. Harer, Duke University, Durham, NC
Publication: Miscellaneous Books
Publication Year: 2010; Volume 69
ISBNs: 978-0-8218-4925-5 (print); 978-1-4704-1208-1 (online)
MathSciNet review: MR2572029
MSC: Primary 00-02; Secondary 05C10, 52-02, 55-02, 57-02, 65D18, 68U05
Combining concepts from topology and algorithms, this book delivers what its title promises: an introduction to the field of computational topology. Starting with motivating problems in both mathematics and computer science and building up from classic topics in geometric and algebraic topology, the third part of the text advances to persistent homology. This point of view is critically important in turning a mostly theoretical field of mathematics into one that is relevant to a multitude of disciplines in the sciences and engineering.
The main approach is the discovery of topology through algorithms. The book is ideal for teaching a graduate or advanced undergraduate course in computational topology, as it develops all the background of both the mathematical and algorithmic aspects of the subject from first principles. Thus the text could serve equally well in a course taught in a mathematics department or computer science department.
Graduate students and research mathematicians interested in topology, algorithms, and applications to science and engineering.
Table of Contents
A. Computational geometric topology
B. Computational algebraic topology
C. Computational persistent topology