Algebraic Foundations For Applied Topology And Data Analysis

Author : Hal Schenck
Publisher : Springer Nature
Page : 231 pages
File Size : 46,6 Mb
Release : 2022-11-21
Category : Mathematics
ISBN : 9783031066641

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Algebraic Foundations for Applied Topology and Data Analysis by Hal Schenck Pdf

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.

Author : Gunnar Carlsson,Mikael Vejdemo-Johansson
Publisher : Cambridge University Press
Page : 233 pages
File Size : 52,8 Mb
Release : 2021-12-16
Category : Computers
ISBN : 9781108838658

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Topological Data Analysis with Applications by Gunnar Carlsson,Mikael Vejdemo-Johansson Pdf

This timely text introduces topological data analysis from scratch, with detailed case studies.

Author : Steve Y. Oudot
Publisher : Unknown
Page : 218 pages
File Size : 50,8 Mb
Release : 2015
Category : MATHEMATICS
ISBN : 1470427958

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Persistence Theory by Steve Y. Oudot Pdf

"Persistence theory emerged in the early 2000s as a new theory in the area of applied and computational topology. This book provides a broad and modern view of the subject, including its algebraic, topological, and algorithmic aspects. It also elaborates on applications in data analysis. The level of detail of the exposition has been set so as to keep a survey style, while providing sufficient insights into the proofs so the reader can understand the mechanisms at work. The book is organizaed into three parts. The first part is dedicated to the foundations of persistence and emphasizes its connection to quiver representation theory. The second part focuses on its connection to applications through a few selected topics. The third part provides perspectives for both the theory and its applications. The book can be used as a text for a course on applied topology or data analysis"--Back cover.

Author : Tamal Krishna Dey,Yusu Wang
Publisher : Cambridge University Press
Page : 455 pages
File Size : 43,7 Mb
Release : 2022-03-10
Category : Computers
ISBN : 9781009098168

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Computational Topology for Data Analysis by Tamal Krishna Dey,Yusu Wang Pdf

This book provides a computational and algorithmic foundation for techniques in topological data analysis, with examples and exercises.

Author : Samuel Eilenberg,Norman Earl Steenrod
Publisher : Unknown
Page : 352 pages
File Size : 47,7 Mb
Release : 1952
Category : Mathematics
ISBN : STANFORD:36105002026198

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Foundations of Algebraic Topology by Samuel Eilenberg,Norman Earl Steenrod Pdf

"The principal contribution of this book is an axiomatic approach to that part of algebraic topology called Homology theory. It is the oldest and most extensively developed portion of algebraic topology and may be regarded as the main body of the subject" - preface.

Author : Jérôme Scherer
Publisher : American Mathematical Soc.
Page : 308 pages
File Size : 53,5 Mb
Release : 2018-05-30
Category : Algebraic topology
ISBN : 9781470429119

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An Alpine Bouquet of Algebraic Topology by Jérôme Scherer Pdf

This volume contains the proceedings of the Alpine Algebraic and Applied Topology Conference, held from August 15–21, 2016, in Saas-Almagell, Switzerland. The papers cover a broad range of topics in modern algebraic topology, including the theory of highly structured ring spectra, infinity-categories and Segal spaces, equivariant homotopy theory, algebraic -theory and topological cyclic, periodic, or Hochschild homology, intersection cohomology, and symplectic topology.

Author : Robert L. Devaney,Kit C. Chan,P.B. Vinod Kumar
Publisher : Springer Nature
Page : 278 pages
File Size : 43,7 Mb
Release : 2021-09-23
Category : Mathematics
ISBN : 9789811601743

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Topological Dynamics and Topological Data Analysis by Robert L. Devaney,Kit C. Chan,P.B. Vinod Kumar Pdf

This book collects select papers presented at the International Workshop and Conference on Topology & Applications, held in Kochi, India, from 9–11 December 2018. The book discusses topics on topological dynamical systems and topological data analysis. Topics are ranging from general topology, algebraic topology, differential topology, fuzzy topology, topological dynamical systems, topological groups, linear dynamics, dynamics of operator network topology, iterated function systems and applications of topology. All contributing authors are eminent academicians, scientists, researchers and scholars in their respective fields, hailing from around the world. The book is a valuable resource for researchers, scientists and engineers from both academia and industry.

Author : Ulrike Tillmann, Søren Galatius, Dev Sinha
Publisher : American Mathematical Soc.
Page : 350 pages
File Size : 40,8 Mb
Release : 2014-07-14
Category : Mathematics
ISBN : 9780821894743

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Algebraic Topology: Applications and New Directions by Ulrike Tillmann, Søren Galatius, Dev Sinha Pdf

This volume contains the proceedings of the Stanford Symposium on Algebraic Topology: Applications and New Directions, held from July 23-27, 2012, at Stanford University, Stanford, California. The symposium was held in honor of Gunnar Carlsson, Ralph Cohen and Ib Madsen, who celebrated their 60th and 70th birthdays that year. It showcased current research in Algebraic Topology reflecting the celebrants' broad interests and profound influence on the subject. The topics varied broadly from stable equivariant homotopy theory to persistent homology and application in data analysis, covering topological aspects of quantum physics such as string topology and geometric quantization, examining homology stability in algebraic and geometric contexts, including algebraic -theory and the theory of operads.

Author : Ched E. Stedman
Publisher : Nova Publishers
Page : 178 pages
File Size : 46,6 Mb
Release : 2007
Category : Mathematics
ISBN : 1600211879

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Algebra and Algebraic Topology by Ched E. Stedman Pdf

This volume gathers results in pure and applied algebra including algebraic topology from researchers around the globe. The selection of these papers was carried out under the auspices of a special editorial board.

Author : Leonid Polterovich,Daniel Rosen,Karina Samvelyan,Jun Zhang
Publisher : American Mathematical Soc.
Page : 128 pages
File Size : 47,5 Mb
Release : 2020-05-11
Category : Education
ISBN : 9781470454951

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Topological Persistence in Geometry and Analysis by Leonid Polterovich,Daniel Rosen,Karina Samvelyan,Jun Zhang Pdf

The theory of persistence modules originated in topological data analysis and became an active area of research in algebraic topology. This book provides a concise and self-contained introduction to persistence modules and focuses on their interactions with pure mathematics, bringing the reader to the cutting edge of current research. In particular, the authors present applications of persistence to symplectic topology, including the geometry of symplectomorphism groups and embedding problems. Furthermore, they discuss topological function theory, which provides new insight into oscillation of functions. The book is accessible to readers with a basic background in algebraic and differential topology.

Author : Samuel Eilenberg,Norman Steenrod
Publisher : Unknown
Page : 328 pages
File Size : 41,5 Mb
Release : 1982
Category : Topology
ISBN : OCLC:256730407

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Foundations of Algebraic Topology by Samuel Eilenberg,Norman Steenrod Pdf

Author : Jeff M. Phillips
Publisher : Springer Nature
Page : 299 pages
File Size : 49,9 Mb
Release : 2021-03-29
Category : Mathematics
ISBN : 9783030623418

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Mathematical Foundations for Data Analysis by Jeff M. Phillips Pdf

This textbook, suitable for an early undergraduate up to a graduate course, provides an overview of many basic principles and techniques needed for modern data analysis. In particular, this book was designed and written as preparation for students planning to take rigorous Machine Learning and Data Mining courses. It introduces key conceptual tools necessary for data analysis, including concentration of measure and PAC bounds, cross validation, gradient descent, and principal component analysis. It also surveys basic techniques in supervised (regression and classification) and unsupervised learning (dimensionality reduction and clustering) through an accessible, simplified presentation. Students are recommended to have some background in calculus, probability, and linear algebra. Some familiarity with programming and algorithms is useful to understand advanced topics on computational techniques.

Author : American Mathematical Society. Short Course on Computational Topology
Publisher : American Mathematical Soc.
Page : 250 pages
File Size : 48,9 Mb
Release : 2012-07-05
Category : Mathematics
ISBN : 9780821853276

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Advances in Applied and Computational Topology by American Mathematical Society. Short Course on Computational Topology Pdf

What is the shape of data? How do we describe flows? Can we count by integrating? How do we plan with uncertainty? What is the most compact representation? These questions, while unrelated, become similar when recast into a computational setting. Our input is a set of finite, discrete, noisy samples that describes an abstract space. Our goal is to compute qualitative features of the unknown space. It turns out that topology is sufficiently tolerant to provide us with robust tools. This volume is based on lectures delivered at the 2011 AMS Short Course on Computational Topology, held January 4-5, 2011 in New Orleans, Louisiana. The aim of the volume is to provide a broad introduction to recent techniques from applied and computational topology. Afra Zomorodian focuses on topological data analysis via efficient construction of combinatorial structures and recent theories of persistence. Marian Mrozek analyzes asymptotic behavior of dynamical systems via efficient computation of cubical homology. Justin Curry, Robert Ghrist, and Michael Robinson present Euler Calculus, an integral calculus based on the Euler characteristic, and apply it to sensor and network data aggregation. Michael Erdmann explores the relationship of topology, planning, and probability with the strategy complex. Jeff Erickson surveys algorithms and hardness results for topological optimization problems.

Author : Maria Cristina Pedicchio,Walter Tholen
Publisher : Cambridge University Press
Page : 452 pages
File Size : 47,7 Mb
Release : 2004
Category : Mathematics
ISBN : 0521834147

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Categorical Foundations by Maria Cristina Pedicchio,Walter Tholen Pdf

Publisher Description

Author : Satya Deo
Publisher : Springer
Page : 344 pages
File Size : 51,8 Mb
Release : 2018-03-13
Category : Mathematics
ISBN : 9789811087349

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Algebraic Topology by Satya Deo Pdf

This book presents the first concepts of the topics in algebraic topology such as the general simplicial complexes, simplicial homology theory, fundamental groups, covering spaces and singular homology theory in greater detail. Originally published in 2003, this book has become one of the seminal books. Now, in the completely revised and enlarged edition, the book discusses the rapidly developing field of algebraic topology. Targeted to undergraduate and graduate students of mathematics, the prerequisite for this book is minimal knowledge of linear algebra, group theory and topological spaces. The book discusses about the relevant concepts and ideas in a very lucid manner, providing suitable motivations and illustrations. All relevant topics are covered, including the classical theorems like the Brouwer’s fixed point theorem, Lefschetz fixed point theorem, Borsuk-Ulam theorem, Brouwer’s separation theorem and the theorem on invariance of the domain. Most of the exercises are elementary, but sometimes challenging, for the reader to provoke their curiosity for problem-solving.