| 000 -LEADER |
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| fixed length control field |
a |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
250225b xxu||||| |||| 00| 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9783031066665 |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
514.2 |
| Item number |
SCH |
| 100 ## - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Schenck, Hal |
| 245 ## - TITLE STATEMENT |
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| Title |
Algebraic Foundations for Applied Topology and Data Analysis |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Name of publisher, distributor, etc |
Springer, |
| Date of publication, distribution, etc |
2022 |
| Place of publication, distribution, etc |
Cham : |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
xii,224 p. ; |
| Other physical details |
ill., |
| Dimensions |
24 cm |
| 365 ## - TRADE PRICE |
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| Unit of pricing |
00 |
| 490 ## - SERIES STATEMENT |
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| Series statement |
Mathematics of data ; |
| Volume number/sequential designation |
v.1 |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
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| Bibliography, etc |
Includes bibliographical references and index. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc |
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 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 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Algebraic topology |
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| Topical term or geographic name as entry element |
Topological algebras |
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| Topical term or geographic name as entry element |
Associated primes |
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| Topical term or geographic name as entry element |
Čech cohomology |
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| Topical term or geographic name as entry element |
Cohomology |
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| Topical term or geographic name as entry element |
CW complex;Injective resolution |
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| Topical term or geographic name as entry element |
Open sets |
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| Topical term or geographic name as entry element |
Persistence diagrams |
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| Topical term or geographic name as entry element |
Persistent homology |
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| Topical term or geographic name as entry element |
Poincaré duality |
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| Topical term or geographic name as entry element |
Principal ideal domain |
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| Topical term or geographic name as entry element |
R-module |
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| Topical term or geographic name as entry element |
Short exact sequence |
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| Topical term or geographic name as entry element |
Snake Lemma |
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| Topical term or geographic name as entry element |
Topological space |
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| Topical term or geographic name as entry element |
Vector bundles |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
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| Item type |
Books |