000			01822 a2200241 4500
003			OSt
005			20250103132913.0
008			250103b xxu||||| |||| 00| 0 eng d
020			_a9783031066665
040			_cIIT Kanpur
041			_aeng
082			_a514.2 _bSch27a
100			_aSchenck, Hal
245			_aAlgebraic foundations for applied topology and data analysis _cHal Schenck
260			_bSpringer _c2022 _aSwitzerland
300			_axii, 224p
440			_aMathematics of data
490			_a/ edited by Benjamin Gess ...[et al.] _v; v.1
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 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.
650			_aAlgebraic topology
650			_aTopological algebras
942			_cBK
999			_c567313 _d567313