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
