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ISBN: 0521360900 9780521360906 Year: 1989 Volume: 91 Publisher: Cambridge Cambridge University Press
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ISBN: 0683045008 9780683045000 Year: 1975 Publisher: Baltimore, Md.
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ISBN: 9810242409 9789810242404 Year: 2000 Publisher: Singapore World Scientific
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ISBN: 3540072802 Year: 1975 Publisher: Berlin Springer
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Year: 1961 Publisher: Oxford London New York Paris : Panstwowe Wydawnictwo Naukowe (PWN) = Polish scientific publishers,
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ISBN: 1009103199 1009099957 Year: 2022 Publisher: Cambridge : Cambridge University Press,
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Topological data analysis (TDA) has emerged recently as a viable tool for analyzing complex data, and the area has grown substantially both in its methodologies and applicability. Providing a computational and algorithmic foundation for techniques in TDA, this comprehensive, self-contained text introduces students and researchers in mathematics and computer science to the current state of the field. The book features a description of mathematical objects and constructs behind recent advances, the algorithms involved, computational considerations, as well as examples of topological structures or ideas that can be used in applications. It provides a thorough treatment of persistent homology together with various extensions - like zigzag persistence and multiparameter persistence - and their applications to different types of data, like point clouds, triangulations, or graph data. Other important topics covered include discrete Morse theory, the Mapper structure, optimal generating cycles, as well as recent advances in embedding TDA within machine learning frameworks.
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ISBN: 9781439871959 Year: 2013 Publisher: Boca Raton : CRC Press,
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"Topology is a large subject with many branches broadly categorized as algebraic topology, point-set topology, and geometric topology. Point-set topology is the main language for a broad variety of mathematical disciplines. Algebraic topology serves as a powerful tool for studying the problems in geometry and numerous other areas of mathematics. Elements of Topology provides a basic introduction to point-set topology and algebraic topology. It is intended for advanced undergraduate and beginning graduate students with working knowledge of analysis and algebra. Topics discussed include the theory of convergence, function spaces, topological transformation groups, fundamental groups, and covering spaces.The author makes the subject accessible by providing more than 250 worked examples and counterexamples with applications. The text also includes numerous end-of-section exercises to put the material into context"
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Year: 1965 Publisher: Bronx (N.Y.): Chelsea,
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