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AuthorKaczynski, Tomasz. author
TitleComputational Homology [electronic resource] / by Tomasz Kaczynski, Konstantin Mischaikow, Marian Mrozek
ImprintNew York, NY : Springer New York : Imprint: Springer, 2004
Connect tohttp://dx.doi.org/10.1007/b97315
Descript XVIII, 482 p. online resource

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


CONTENT

Homology -- Preview -- Cubical Homology -- Computing Homology Groups -- Chain Maps and Reduction Algorithms -- Preview of Maps -- Homology of Maps -- Computing Homology of Maps -- Extensions -- Prospects in Digital Image Processing -- Homological Algebra -- Nonlinear Dynamics -- Homology of Topological Polyhedra -- Tools from Topology and Algebra -- Topology -- Algebra -- Syntax of Algorithms


Mathematics Category theory (Mathematics) Homological algebra Dynamics Ergodic theory Applied mathematics Engineering mathematics Computer mathematics Topology Algebraic topology Mathematics Topology Applications of Mathematics Category Theory Homological Algebra Dynamical Systems and Ergodic Theory Computational Mathematics and Numerical Analysis Algebraic Topology



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