000			a
999			_c33737 _d33737
008			250225b xxu||||| |||| 00| 0 eng d
020			_a9783031066665
082			_a514.2 _bSCH
100			_aSchenck, Hal
245			_aAlgebraic Foundations for Applied Topology and Data Analysis
260			_bSpringer, _c2022 _aCham :
300			_axii,224 p. ; _bill., _c24 cm
365			_d00
490			_aMathematics of data ; _vv.1
504			_aIncludes bibliographical references and index.
520			_aThis 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 users 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.
650			_aAlgebraic topology
650			_aTopological algebras
650			_aAssociated primes
650			_aČech cohomology
650			_aCohomology
650			_aCW complex;Injective resolution
650			_aOpen sets
650			_aPersistence diagrams
650			_aPersistent homology
650			_aPoincaré duality
650			_aPrincipal ideal domain
650			_aR-module
650			_aShort exact sequence
650			_aSnake Lemma
650			_aTopological space
650			_aVector bundles
942			_2ddc _cBK