
Computational Topology
An Introduction
American Mathematical Society (Publisher)
Published on 1. January 2010
Book
Hardback
241 pages
978-0-8218-4925-5 (ISBN)
Description
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.
Reviews / Votes
This book is a very welcome, untraditional, thorough and well-organized introduction to a young and quickly developing discipline on the crossroads between mathematics, computer science, and engineering." - DMV NewsletterMore details
Series
Language
English
Place of publication
Providence
United States
Target group
College/higher education
Weight
605 gr
ISBN-13
978-0-8218-4925-5 (9780821849255)
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Schweitzer Classification
Persons
Herbert Edelsbrunner, Duke University, Durham, NC and Geomagic, Research Triangle Park, NC, USA
John L. Harer, Duke University, Durham, NC, USA
John L. Harer, Duke University, Durham, NC, USA
Content
Preface
Part I. Computational geometric topology
Graphs
Surfaces
Complexes
Part II. Computational algebraic topology
Homology
Duality
Morse functions
Part III. Computational persistent topology
Persistence
Stability
Applications
References
Index
Part I. Computational geometric topology
Graphs
Surfaces
Complexes
Part II. Computational algebraic topology
Homology
Duality
Morse functions
Part III. Computational persistent topology
Persistence
Stability
Applications
References
Index