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Computational Homology

by

Computational Homology Cover

 

Synopses & Reviews

Publisher Comments:

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.

Synopsis:

Homology is a powerful tool used by mathematicians to study the properties of spaces and maps that are insensitive to small perturbations. This book uses a computer to develop a combinatorial computational approach to the subject. The core of the book deals with homology theory and its computation. Following this is a section containing extensions to further developments in algebraic topology, applications to computational dynamics, and applications to image processing. Included are exercises and software that can be used to compute homology groups and maps. The book will appeal to researchers and graduate students in mathematics, computer science, engineering, and nonlinear dynamics.

Table of Contents

Preview.- Cubical Homology.- Computing Homology Groups.- Chain Maps and Reduction Algorithms.- Preview of Maps.- Homology of Maps.- Computing Homology of Maps.- Prospects in Digital Image Processing.- Homological Algebra.- Nonlinear Dynamics.- Homology of Topological Polyhedra.- Topology.- Algebra.- Syntax of Algorithms.- References.- Symbol Index.- Subject Index.

Product Details

ISBN:
9780387408538
Author:
Kaczynski, Tomasz
Publisher:
Springer
Author:
Mischaikow, Konstantin
Author:
Mrozek, Marian
Location:
New York, NY
Subject:
Applied
Subject:
Combinatorics
Subject:
Homology theory
Subject:
Algebraic topology
Subject:
Topology - General
Subject:
computational mathematics
Subject:
APPLICATIONS OF MATHEMATICS
Subject:
Category Theory, Homological Algebra
Subject:
Dynamical Systems and Ergodic Theory
Subject:
Computational Mathematics and Numerical Analysis
Subject:
Algebraic Topology <P>This interdisciplinary book uses the computer to take a combinatorial computational approach to homological problems. It will appeal especially to researchers and students in mathematics, computer science, nonlinear dynamics, and eng
Subject:
MATHEMATICS / Topology
Subject:
Applications of Mathe
Subject:
matics
Subject:
Mathematics
Subject:
B
Subject:
mathematics and statistics
Subject:
Algebra
Subject:
Differentiable dynamical systems
Subject:
Computer science_xMathematics
Copyright:
Edition Number:
1
Edition Description:
Book
Series:
Applied Mathematical Sciences
Series Volume:
157
Publication Date:
January 2004
Binding:
HARDCOVER
Language:
English
Illustrations:
Y
Pages:
500
Dimensions:
235 x 155 mm 1950 gr

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Related Subjects

Science and Mathematics » Mathematics » Applied
Science and Mathematics » Mathematics » Probability and Statistics » General
Science and Mathematics » Mathematics » Probability and Statistics » Statistics
Science and Mathematics » Mathematics » Topology

Computational Homology New Hardcover
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$108.50 In Stock
Product details 500 pages Springer-Verlag - English 9780387408538 Reviews:
"Synopsis" by , Homology is a powerful tool used by mathematicians to study the properties of spaces and maps that are insensitive to small perturbations. This book uses a computer to develop a combinatorial computational approach to the subject. The core of the book deals with homology theory and its computation. Following this is a section containing extensions to further developments in algebraic topology, applications to computational dynamics, and applications to image processing. Included are exercises and software that can be used to compute homology groups and maps. The book will appeal to researchers and graduate students in mathematics, computer science, engineering, and nonlinear dynamics.
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