Topology for Computing

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More About This Textbook

Overview

Written by a computer scientist for computer scientists, this book teaches topology from a computational point of view, and shows how to solve real problems that have topological aspects involving computers. Such problems arise in many areas, such as computer graphics, robotics, structural biology, and chemistry. The author starts from the basics of topology, assuming no prior exposure to the subject, and moves rapidly up to recent advances in the area, including topological persistence and hierarchical Morse complexes. Algorithms and data structures are presented when appropriate.
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Editorial Reviews

From the Publisher
"In my knowledge, it is the first book covering these topics."
Numerical Algorithms

"This authoritative, well-written, and highly focused book will explain to the reader the considerable power of topology. It is an eye-opener that I highly recommend."
George Hacken, reviews.com

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Product Details

Meet the Author

Afra J. Zomorodian is an assistant professor in the Department of Computer Science at Dartmouth College. He is a former Post-Doctoral Fellow in Bio-X and the Department of Computer Science at Stanford University and has been a researcher at the Max-Planck-Institut für Informatik in Saarbrücken, Germany. Using the material contained in this book, he has organized classes on computational topology at Stanford University, the MPI, and Dartmouth College.
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Table of Contents

1. Introduction; Part I. Mathematics: 2. Spaces and filtrations; 3. Group theory; 4. Homology; 5. Morse theory; 6. New results; Part II. Algorithms: 7. The persistence algorithms; 8. Topological simplification; 9. The Morse-Smale algorithm; 10. The linking number algorithm; Part III. Applications: 11. Software; 12. Experiments; 13. Applications.
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