東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Algebraic foundations for applied to...

Schenck, Hal.

Linked to FindBook

Google Book

Amazon

博客來

Algebraic foundations for applied topology and data analysis

Record Type:	Electronic resources : Monograph/item
Title/Author:	Algebraic foundations for applied topology and data analysis/ by Hal Schenck.
Author:	Schenck, Hal.
Published:	Cham :Springer International Publishing : : 2022.,
Description:	xii, 224 p. :ill., digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer Nature eBook
Subject:	Algebraic topology. -
Online resource:	https://doi.org/10.1007/978-3-031-06664-1
ISBN:	9783031066641

Algebraic foundations for applied topology and data analysis
Schenck, Hal.

Algebraic foundations for applied topology and data analysis[electronic resource] /by Hal Schenck. - Cham :Springer International Publishing :2022. - xii, 224 p. :ill., digital ;24 cm. - Mathematics of data,v. 12731-4111 ;. - Mathematics of data ;v. 1..

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.

ISBN: 9783031066641

Standard No.: 10.1007/978-3-031-06664-1doiSubjects--Topical Terms:

532744
Algebraic topology.

LC Class. No.: QA612

Dewey Class. No.: 514.2

Algebraic foundations for applied topology and data analysis
LDR:02656nmm a2200337 a 4500 001 2305806
003 DE-He213
005 20221121065534.0
006 m d
007 cr nn 008maaau
008 230409s2022 sz s 0 eng d
020 $a 9783031066641 $q (electronic bk.)
020 $a 9783031066634 $q (paper)
024 7 $a 10.1007/978-3-031-06664-1 $2 doi
035 $a 978-3-031-06664-1
040 $a GP $c GP
041 0 $a eng
050 4 $a QA612
072 7 $a PBPD $2 bicssc
072 7 $a MAT038000 $2 bisacsh
072 7 $a PBPD $2 thema
082 0 4 $a 514.2 $2 23
090 $a QA612 $b .S324 2022
100 1 $a Schenck, Hal. $3 864917
245 1 0 $a Algebraic foundations for applied topology and data analysis $h [electronic resource] / $c by Hal Schenck.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2022.
300 $a xii, 224 p. : $b ill., digital ; $c 24 cm.
490 1 $a Mathematics of data, $x 2731-4111 ; $v v. 1
505 0 $a 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.
520 $a 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.
650 0 $a Algebraic topology. $3 532744
650 0 $a Topological algebras. $3 725781
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Mathematics of data ; $v v. 1. $3 3609249
856 4 0 $u https://doi.org/10.1007/978-3-031-06664-1
950 $a Mathematics and Statistics (SpringerNature-11649)