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OverviewAn Invitation to Computational Homotopy is an introduction to elementary algebraic topology for those with an interest in computers and computer programming. It expertly illustrates how the basics of the subject can be implemented on a computer through its focus on fully-worked examples designed to develop problem solving techniques. The transition from basic theory to practical computation raises a range of non-trivial algorithmic issues which will appeal to readers already familiar with basic theory and who are interested in developing computational aspects. The book covers a subset of standard introductory material on fundamental groups, covering spaces, homology, cohomology and classifying spaces as well as some less standard material on crossed modules. These topics are covered in a way that hints at potential applications of topology in areas of computer science and engineering outside the usual territory of pure mathematics, and also in a way that demonstrates how computers can be used to perform explicit calculations within the domain of pure algebraic topology itself. The initial chapters include in-depth examples from data mining, biology and digital image analysis, while the later chapters cover a range of computational examples on the cohomology of classifying spaces that are likely beyond the reach of a purely paper-and-pen approach to the subject. An Invitation to Computational Homotopy serves as a self-contained and informal introduction to these topics and their implementation in the sphere of computer science. Written in a dynamic and engaging style, it skilfully showcases a range of useful machine computations, and will serve as an invaluable aid to graduate students working with algebraic topology. Full Product DetailsAuthor: Professor of Mathematics Graham Ellis (National University of Ireland Galway)Publisher: Oxford University Press, USA Imprint: Oxford University Press, USA ISBN: 9780191871375ISBN 10: 0191871370 Publication Date: 21 November 2019 Audience: General/trade , General Format: Undefined Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsReviewsAuthor InformationGraham Ellis, Professor of Mathematics, National University of Ireland, Galway Graham Ellis received his PhD from the University of Wales, Bangor, in 1984 and has taught at the National University of Ireland, Galway since 1987. He is the Established Professor of Mathematics at Galway. He has published research articles on computational algebra, group theory and low-dimensional topology. Tab Content 6Author Website:Countries AvailableAll regions |
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