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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.

Category theory. Homological algebra --- Homology theory --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Theory --- Geometry --- Engineering & Applied Sciences --- Applied Mathematics --- Mathematics. --- Category theory (Mathematics). --- Homological algebra. --- Dynamics. --- Ergodic theory. --- Applied mathematics. --- Engineering mathematics. --- Computer mathematics. --- Topology. --- Algebraic topology. --- Applications of Mathematics. --- Category Theory, Homological Algebra. --- Dynamical Systems and Ergodic Theory. --- Computational Mathematics and Numerical Analysis. --- Algebraic Topology. --- Algebra. --- Differentiable dynamical systems. --- Computer science --- Homologie --- Homologie. --- Homology theory. --- Algorithmus. --- Topology --- Computer mathematics --- Electronic data processing --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Homological algebra --- Algebra, Abstract --- Category theory (Mathematics) --- Algebra, Homological --- Algebra, Universal --- Group theory --- Logic, Symbolic and mathematical --- Functor theory --- Engineering --- Engineering analysis --- Mathematical analysis --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Algebra, Homological. --- Dynamical systems. --- Dynamical Systems. --- Data processing.

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Mathematics