Topology for Computing
Topology for Computing
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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.
- Presents classical topological subject of Morse theory in a computer science context
- Material is widely used within computation geometry and computer graphics
Reviews & endorsements
"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
Product details
May 2005Adobe eBook Reader
9780511081309
0 pages
0kg
118 b/w illus. 2 colour illus.
This ISBN is for an eBook version which is distributed on our behalf by a third party.
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.
