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Topology for Computing

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ISBN-10: 0521836662

ISBN-13: 9780521836661

Edition: 2004

Authors: Afra J. Zomorodian, P. G. Ciarlet, A. Iserles, R. V. Kohn, M. H. Wright

List price: $124.00
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Description:

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.
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Book details

List price: $124.00
Copyright year: 2004
Publisher: Cambridge University Press
Publication date: 1/10/2005
Binding: Hardcover
Pages: 258
Size: 6.25" wide x 9.25" long x 1.00" tall
Weight: 1.012

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 f�r Informatik in Saarbr�cken, Germany. Using the material contained in this book, he has organized classes on computational topology at Stanford University, the MPI, and Dartmouth College.

Introduction
Mathematics
Spaces and filtrations
Group theory
Homology
Morse theory
New results
Algorithms
The persistence algorithms
Topological simplification
The Morse-Smale algorithm
The linking number algorithm
Applications
Software
Experiments
Applications