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＜電子ブック＞
Algebraic Foundations for Applied Topology and Data Analysis / by Hal Schenck
(Mathematics of Data. ISSN:27314111 ; 1)

版	1st ed. 2022.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2022
大きさ	XII, 224 p. 1 illus : online resource
著者標目	*Schenck, Hal author SpringerLink (Online service)
件　名	LCSH:Algebraic topology LCSH:Mathematics—Data processing LCSH:Commutative algebra LCSH:Commutative rings LCSH:Algebra, Homological LCSH:Computer science—Mathematics FREE:Algebraic Topology FREE:Computational Science and Engineering FREE:Commutative Rings and Algebras FREE:Category Theory, Homological Algebra FREE:Symbolic and Algebraic Manipulation
一般注記	Preface -- 1. Linear Algebra Tools for Data Analysis -- 2. Basics of Algebra: Groups, Rings, Modules -- 3. Basics of Topology: Spaces and Sheaves -- 4. Homology I: Simplicial Complexes to Sensor Networks -- 5. Homology II: Cohomology to Ranking Problems -- 6. Persistent Algebra: Modules over a PID -- 7. Persistent Homology -- 8. Multiparameter Persistent Homology -- 9. Derived Functors and Spectral Sequences -- Appendix A. Examples of Software Packages -- Bibliography. This book gives an intuitive and hands-on introduction to Topological Data Analysis (TDA). Covering a wide range of topics at levels of sophistication varying from elementary (matrix algebra) to esoteric (Grothendieck spectral sequence), it offers a mirror of data science aimed at a general mathematical audience. The required algebraic background is developed in detail. 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 introduces algebraic topology, along with applications to sensor networks and voter ranking. The last third covers key contemporary tools in TDA: persistent and multiparameter persistent homology. Also included is 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 software packages used in the field. Based on a course given as part of a masters degree in statistics, the book is appropriate for graduate students. HTTP:URL=https://doi.org/10.1007/978-3-031-06664-1

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