Author | Kaczynski, Tomasz. author |
---|---|

Title | Computational Homology [electronic resource] / by Tomasz Kaczynski, Konstantin Mischaikow, Marian Mrozek |

Imprint | New York, NY : Springer New York : Imprint: Springer, 2004 |

Connect to | http://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