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Algebraic Foundations for Applied Topology and Data Analysis
Angličtina
195 b
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36.38
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104.82
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This book, aimed at a general mathematical audience, introduces the key structures and algebraic tools used in topological data analysis (TDA). The first third of the book reviews several core areas of mathematics, beginning with basic linear algebra and applications to data fitting and web search algorithms, followed by quick primers on algebra and topology. The middle third of the book introduces algebraic topology, along with applications to sensor networks and voter ranking. The last third of the book covers key contemporary tools in TDA: persistent and multiparameter persistent homology. The book concludes with a user's guide to derived functors and spectral sequences (useful but somewhat technical tools which have recently found applications in TDA), and an appendix illustrating a number of the software packages used in the field. The book is based on a course taught to masters degree students in statistics, and is appropriate for graduate students.
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