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| Author | : Gordon Thomas Whyburn |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 295 |
| Release | : 1963 |
| Genre | : Mathematics |
| ISBN | : 0821810286 |
"The material here presented represents an elaboration on my Colloquium Lectures delivered before the American Mathematical Society at its September, 1940 meeting at Dartmouth College." - Preface.
| Author | : José Seade |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 243 |
| Release | : 2006-03-21 |
| Genre | : Mathematics |
| ISBN | : 3764373954 |
Offers an overview of selected topics on the topology of singularities, with emphasis on its relations to other branches of geometry and topology. This book studies real analytic singularities which arise from the topological and geometric study of holomorphic vector fields and foliations.
| Author | : Tamal Krishna Dey |
| Publisher | : Cambridge University Press |
| Total Pages | : 456 |
| Release | : 2022-03-10 |
| Genre | : Mathematics |
| ISBN | : 1009103199 |
Topological data analysis (TDA) has emerged recently as a viable tool for analyzing complex data, and the area has grown substantially both in its methodologies and applicability. Providing a computational and algorithmic foundation for techniques in TDA, this comprehensive, self-contained text introduces students and researchers in mathematics and computer science to the current state of the field. The book features a description of mathematical objects and constructs behind recent advances, the algorithms involved, computational considerations, as well as examples of topological structures or ideas that can be used in applications. It provides a thorough treatment of persistent homology together with various extensions – like zigzag persistence and multiparameter persistence – and their applications to different types of data, like point clouds, triangulations, or graph data. Other important topics covered include discrete Morse theory, the Mapper structure, optimal generating cycles, as well as recent advances in embedding TDA within machine learning frameworks.
| Author | : Jerzy Kąkol |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 494 |
| Release | : 2011-08-30 |
| Genre | : Mathematics |
| ISBN | : 1461405297 |
"Descriptive Topology in Selected Topics of Functional Analysis" is a collection of recent developments in the field of descriptive topology, specifically focused on the classes of infinite-dimensional topological vector spaces that appear in functional analysis. Such spaces include Fréchet spaces, (LF)-spaces and their duals, and the space of continuous real-valued functions C(X) on a completely regular Hausdorff space X, to name a few. These vector spaces appear in functional analysis in distribution theory, differential equations, complex analysis, and various other analytical settings. This monograph provides new insights into the connections between the topological properties of linear function spaces and their applications in functional analysis.
| Author | : Albert Wilansky |
| Publisher | : Courier Corporation |
| Total Pages | : 399 |
| Release | : 2008-10-17 |
| Genre | : Mathematics |
| ISBN | : 0486469034 |
Starting with the first principles of topology, this volume advances to general analysis. Three levels of examples and problems make it appropriate for students and professionals. Abundant exercises, ordered and numbered by degree of difficulty, illustrate important concepts, and a 40-page appendix includes tables of theorems and counterexamples. 1970 edition.
| Author | : Raúl Rabadán |
| Publisher | : Cambridge University Press |
| Total Pages | : 521 |
| Release | : 2019-10-31 |
| Genre | : Science |
| ISBN | : 1108753396 |
Biology has entered the age of Big Data. The technical revolution has transformed the field, and extracting meaningful information from large biological data sets is now a central methodological challenge. Algebraic topology is a well-established branch of pure mathematics that studies qualitative descriptors of the shape of geometric objects. It aims to reduce questions to a comparison of algebraic invariants, such as numbers, which are typically easier to solve. Topological data analysis is a rapidly-developing subfield that leverages the tools of algebraic topology to provide robust multiscale analysis of data sets. This book introduces the central ideas and techniques of topological data analysis and its specific applications to biology, including the evolution of viruses, bacteria and humans, genomics of cancer and single cell characterization of developmental processes. Bridging two disciplines, the book is for researchers and graduate students in genomics and evolutionary biology alongside mathematicians interested in applied topology.
| Author | : D.D. Bleecker |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 467 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1468406272 |
The Motivation. With intensified use of mathematical ideas, the methods and techniques of the various sciences and those for the solution of practical problems demand of the mathematician not only greater readi ness for extra-mathematical applications but also more comprehensive orientations within mathematics. In applications, it is frequently less important to draw the most far-reaching conclusions from a single mathe matical idea than to cover a subject or problem area tentatively by a proper "variety" of mathematical theories. To do this the mathematician must be familiar with the shared as weIl as specific features of differ ent mathematical approaches, and must have experience with their inter connections. The Atiyah-Singer Index Formula, "one of the deepest and hardest results in mathematics", "probably has wider ramifications in topology and analysis than any other single result" (F. Hirzebruch) and offers perhaps a particularly fitting example for such an introduction to "Mathematics": In spi te of i ts difficulty and immensely rich interrela tions, the realm of the Index Formula can be delimited, and thus its ideas and methods can be made accessible to students in their middle * semesters. In fact, the Atiyah-Singer Index Formula has become progressively "easier" and "more transparent" over the years. The discovery of deeper and more comprehensive applications (see Chapter 111. 4) brought with it, not only a vigorous exploration of its methods particularly in the many facetted and always new presentations of the material by M. F.
| Author | : Cabiria Andreian Cazacu |
| Publisher | : World Scientific |
| Total Pages | : 737 |
| Release | : 1998-11-06 |
| Genre | : Mathematics |
| ISBN | : 9814498599 |
The goal of this book is to investigate further the interdisciplinary interaction between Mathematical Analysis and Topology. It provides an attempt to study various approaches in the topological applications and influence to Function Theory, Calculus of Variations, Functional Analysis and Approximation Theory. The volume is dedicated to the memory of S Stoilow.
| Author | : Stephen Willard |
| Publisher | : Courier Corporation |
| Total Pages | : 386 |
| Release | : 2012-07-12 |
| Genre | : Mathematics |
| ISBN | : 0486131785 |
Among the best available reference introductions to general topology, this volume is appropriate for advanced undergraduate and beginning graduate students. Includes historical notes and over 340 detailed exercises. 1970 edition. Includes 27 figures.
| Author | : Alan F. Beardon |
| Publisher | : Courier Dover Publications |
| Total Pages | : 259 |
| Release | : 2019-12-18 |
| Genre | : Mathematics |
| ISBN | : 0486837181 |
Text for advanced undergraduates and graduate students provides geometrical insights by covering angles, basic complex analysis, and interactions with plane topology while focusing on concepts of angle and winding numbers. 1979 edition.
