Computational homology

By:

Kaczynski, Tomasz

Contributor(s):

Material type: Text

TextSeries: Applied mathematical sciences - Vol. 157Publication details: 2004 New York SpringerDescription: xvii, 480 p. Includes bibliographical references, indexes and 78 figuresISBN:

9780387408538

Subject(s):

DDC classification:

514.23 K2C6

Summary: In recent years, there has been a growing interest in applying homology to problems involving geometric data sets, whether obtained from physical measurements or generated through numerical simulations. This book presents a novel approach to homology that emphasizes the development of efficient algorithms for computation. As well as providing a highly accessible introduction to the mathematical theory, the authors describe a variety of potential applications of homology in fields such as digital image processing and nonlinear dynamics. The material is aimed at a broad audience of engineers, computer scientists, nonlinear scientists, and applied mathematicians. Mathematical prerequisites have been kept to a minimum and there are numerous examples and exercises throughout the text. The book is complemented by a website containing software programs and projects that help to further illustrate the material described within. https://www.springer.com/gp/book/9780387408538

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Holdings
Item type	Current library	Collection	Call number	Status	Date due	Barcode	Item holds
Book	Ahmedabad General Stacks	Non-fiction	514.23 K2C6 (Browse shelf(Opens below))	Available		199748

Total holds: 0

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Previous						No cover image available		Next
Previous	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	514.742 F3C4 Chaos and dynamical systems	Next

Table of contents:

Pt. I. Homology
1. Preview
2. Cubical Homology
3. Computing Homology Groups
4. Chain Maps and Reduction Algorithms
5. Preview of Maps
6. Homology of Maps
7. Computing Homology of Maps
Pt. II. Extensions
8. Prospects in Digital Image Processing
9. Homological Algebra
10. Nonlinear Dynamics
11. Homology of Topological Polyhedra
Pt. III. Tools from Topology and Algebra
12. Topology
13. Algebra
14. Syntax of Algorithms

In recent years, there has been a growing interest in applying homology to problems involving geometric data sets, whether obtained from physical measurements or generated through numerical simulations. This book presents a novel approach to homology that emphasizes the development of efficient algorithms for computation.

As well as providing a highly accessible introduction to the mathematical theory, the authors describe a variety of potential applications of homology in fields such as digital image processing and nonlinear dynamics. The material is aimed at a broad audience of engineers, computer scientists, nonlinear scientists, and applied mathematicians.

Mathematical prerequisites have been kept to a minimum and there are numerous examples and exercises throughout the text. The book is complemented by a website containing software programs and projects that help to further illustrate the material described within.

https://www.springer.com/gp/book/9780387408538

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