Topology for computing

By:

Zomorodian, Afra J

Material type: Text

TextSeries: Cambridge monographs on applied and computational mathematicsPublication details: Cambridge University Press 2005 New YorkDescription: xiii, 243 p. Includes bibliographical references and indexISBN:

9780521136099

Subject(s):

DDC classification:

514 Z6T6

Summary: 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. https://www.cambridge.org/core/books/topology-for-computing/1171035B570105A57865CEA390BA5E74#fndtn-information

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Holdings
Item type	Current library	Collection	Call number	Status	Date due	Barcode	Item holds
Book	Ahmedabad General Stacks	Non-fiction	514 Z6T6 (Browse shelf(Opens below))	Not For Loan		201675

Total holds: 0

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Previous	514 E2T6 Topology: a very short introduction	514 G4E5 Elementary applied topology	514 S4I6 Introduction to topology	514 Z6T6 Topology for computing	514.23 K2C6 Computational homology	514.32 S2P7 Probabilistic metric spaces	514.72 M4T6 Topology from the differentiable viewpoint	Next

Table of Contents

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

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.

https://www.cambridge.org/core/books/topology-for-computing/1171035B570105A57865CEA390BA5E74#fndtn-information

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