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Mathematics - Geometry & Topology | Computational Homology

Computational Homology

Series: Applied Mathematical Sciences, Vol. 157

Kaczynski, Tomasz, Mischaikow, Konstantin, Mrozek, Marian

2004, XVIII, 482 p.

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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.

Content Level » Graduate

Keywords » Algebraic topology - Homotopy - Lefschetz fixed-point theorem - algorithms - fixed-point theorem - homological algebra - homology - nonlinear dynamics

Related subjects » Algebra - Applications - Computational Science & Engineering - Dynamical Systems & Differential Equations - Geometry & Topology

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