Elementary Applied Topology
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Elementary Applied Topology
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Author : Robert W. Ghrist
language : en
Publisher:
Release Date : 2014
Elementary Applied Topology written by Robert W. Ghrist and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Topology categories.
Elementary Applied Topology
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Author : Robert W. Ghrist
language : en
Publisher: Createspace Independent Publishing Platform
Release Date : 2014
Elementary Applied Topology written by Robert W. Ghrist and has been published by Createspace Independent Publishing Platform this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Mathematics categories.
This book gives an introduction to the mathematics and applications comprising the new field of applied topology. The elements of this subject are surveyed in the context of applications drawn from the biological, economic, engineering, physical, and statistical sciences.
Algebraic Foundations For Applied Topology And Data Analysis
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Author : Hal Schenck
language : en
Publisher: Springer Nature
Release Date : 2022-11-21
Algebraic Foundations For Applied Topology And Data Analysis written by Hal Schenck and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-21 with Mathematics categories.
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.
Elementary Topology
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Author : O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov
language : en
Publisher: American Mathematical Soc.
Release Date :
Elementary Topology written by O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
This text contains a detailed introduction to general topology and an introduction to algebraic topology via its most classical and elementary segment. Proofs of theorems are separated from their formulations and are gathered at the end of each chapter, making this book appear like a problem book and also giving it appeal to the expert as a handbook. The book includes about 1,000 exercises.
Elementary Topology
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Author : Donald W. Blackett
language : en
Publisher:
Release Date : 1967
Elementary Topology written by Donald W. Blackett and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Topology categories.
Applications Of Algebraic Topology
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Author : S. Lefschetz
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Applications Of Algebraic Topology written by S. Lefschetz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This monograph is based, in part, upon lectures given in the Princeton School of Engineering and Applied Science. It presupposes mainly an elementary knowledge of linear algebra and of topology. In topology the limit is dimension two mainly in the latter chapters and questions of topological invariance are carefully avoided. From the technical viewpoint graphs is our only requirement. However, later, questions notably related to Kuratowski's classical theorem have demanded an easily provided treatment of 2-complexes and surfaces. January 1972 Solomon Lefschetz 4 INTRODUCTION The study of electrical networks rests upon preliminary theory of graphs. In the literature this theory has always been dealt with by special ad hoc methods. My purpose here is to show that actually this theory is nothing else than the first chapter of classical algebraic topology and may be very advantageously treated as such by the well known methods of that science. Part I of this volume covers the following ground: The first two chapters present, mainly in outline, the needed basic elements of linear algebra. In this part duality is dealt with somewhat more extensively. In Chapter III the merest elements of general topology are discussed. Graph theory proper is covered in Chapters IV and v, first structurally and then as algebra. Chapter VI discusses the applications to networks. In Chapters VII and VIII the elements of the theory of 2-dimensional complexes and surfaces are presented.
Elementary Topology
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Author : Donald Watson Blackett
language : en
Publisher:
Release Date : 1967
Elementary Topology written by Donald Watson Blackett and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with categories.
Persistence Theory From Quiver Representations To Data Analysis
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Author : Steve Y. Oudot
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-05-17
Persistence Theory From Quiver Representations To Data Analysis written by Steve Y. Oudot and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-17 with categories.
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 organized 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.
Introduction To Topology
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Author : Tej Bahadur Singh
language : en
Publisher:
Release Date : 2019
Introduction To Topology written by Tej Bahadur Singh and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Topology categories.
Topology is a large subject with several branches, broadly categorized as algebraic topology, point-set topology, and geometric topology. Point-set topology is the main language for a broad range of mathematical disciplines, while algebraic topology offers as a powerful tool for studying problems in geometry and numerous other areas of mathematics. This book presents the basic concepts of topology, including virtually all of the traditional topics in point-set topology, as well as elementary topics in algebraic topology such as fundamental groups and covering spaces. It also discusses topological groups and transformation groups. When combined with a working knowledge of analysis and algebra, this book offers a valuable resource for advanced undergraduate and beginning graduate students of mathematics specializing in algebraic topology and harmonic analysis.
A Concise Course In Algebraic Topology
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Author : J. P. May
language : en
Publisher: University of Chicago Press
Release Date : 1999-09
A Concise Course In Algebraic Topology written by J. P. May and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-09 with Mathematics categories.
Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field.