Algebraic foundations for applied topology and data analysis
By: Schenck, Hal.
Series: Mathematics of data. / edited by Benjamin Gess ...[et al.] ; v.1.Publisher: Switzerland Springer 2022Description: xii, 224p.ISBN: 9783031066665.Subject(s): Algebraic topology | Topological algebrasDDC classification: 514.2 | Sch27a Summary: 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.| Item type | Current location | Collection | Call number | Status | Date due | Barcode | Item holds |
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Books
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PK Kelkar Library, IIT Kanpur | On Display | 514.2 Sch27a (Browse shelf) | Available | A186645 |
Browsing PK Kelkar Library, IIT Kanpur Shelves , Collection code: On Display Close shelf browser
| 332.015195 Se94t6 Tools for compuational finance [6th ed.] | 511.8 P171m Mathematical modeling | 514.2 Sch27a Algebraic foundations for applied topology and data analysis | 515.7 T871a Analysis and quantum groups | 515.7 W666f2 Functional analysis [2nd ed.] | 515.7222 B648s Spectral theory |
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.
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