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Topology for Computing : Cambridge Monographs on Applied and Computational Mathematics - Afra J. Zomorodian

Topology for Computing

Cambridge Monographs on Applied and Computational Mathematics


Published: 1st September 2004
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The emerging field of computational topology utilizes theory from topology and the power of computing to solve problems in diverse fields. Recent applications include computer graphics, computer-aided design (CAD), and structural biology, all of which involve understanding the intrinsic shape of some real or abstract space. A primary goal of this book is to present basic concepts from topology and Morse theory to enable a non-specialist to grasp and participate in current research in computational topology. The author gives a self-contained presentation of the mathematical concepts from a computer scientist's point of view, combining point set topology, algebraic topology, group theory, differential manifolds, and Morse theory. He also presents some recent advances in the area, including topological persistence and hierarchical Morse complexes. Throughout, the focus is on computational challenges and on presenting algorithms and data structures when appropriate.

'In my knowledge, it is the first book covering these topics.' Numerical Algorithms

Spaces and filtrations
Group theory
Morse theory
New results
The persistence algorithms
Topological simplification
The Morse-Smale algorithm
The linking number algorithm
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521836661
ISBN-10: 0521836662
Series: Cambridge Monographs on Applied and Computational Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 258
Published: 1st September 2004
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 22.8 x 15.2  x 1.6
Weight (kg): 0.52