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Computational homology

By: Kaczynski, Tomasz.
Contributor(s): Mischaikow, Konstantin [Co author] | Mrozek, Marian [Co author].
Material type: materialTypeLabelBookSeries: Applied mathematical sciences - Vol. 157. Publisher: New York Springer 2004Description: xvii, 480 p. Includes bibliographical references, indexes and 78 figures.ISBN: 9780387408538.Subject(s): Homology theory | Cubical homology | Homology - Topological polyhedra | Homological algebra | Algorithms - SyntaxDDC classification: 514​.23 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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Slot 1370 (0 Floor, East Wing) Non-fiction 514​.23 K2C6 (Browse shelf) Checked out 20/11/2019 199748

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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