Search results for: understanding-topology

Understanding Topology

Author : Shaun V. Ault
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"Topology can present significant challenges for undergraduate students of mathematics and the sciences. 'Understanding topology' aims to change that. The perfect introductory topology textbook, 'Understanding topology' requires only a knowledge of calculus and a general familiarity with set theory and logic. Equally approachable and rigorous, the book's clear organization, worked examples, and concise writing style support a thorough understanding of basic topological principles. Professor Shaun V. Ault's unique emphasis on fascinating applications, from chemical dynamics to determining the shape of the universe, will engage students in a way traditional topology textbooks do not"--Back cover.

Topological in Hegel

Author : Borislav G. Dimitrov
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The aim of this book is to critically examine whether it is methodologically possible to combine mathematical rigor – topology with a systematic dialectical methodology in Hegel, and if so, to provide as result of my interpretation the outline of Hegel’s Analysis Situs, also with the proposed models (build on the topological manifold, cobordism, topological data analysis, persistent homology, simplicial complexes and graph theory, to provide an indication of how the merger of Hegel’s dialectical logic and topology may be instrumental to a systematic logician and of how a systematic dialectical logic perspective may help mathematical model builders.

Topology for Computing

Author : Afra J. Zomorodian
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The emerging field of computational topology utilizes theory from topology and the power of computing to solve problems in diverse fields. Recent applications include computer graphics, computer-aided design (CAD), and structural biology, all of which involve understanding the intrinsic shape of some real or abstract space. A primary goal of this book is to present basic concepts from topology and Morse theory to enable a non-specialist to grasp and participate in current research in computational topology. The author gives a self-contained presentation of the mathematical concepts from a computer scientist's point of view, combining point set topology, algebraic topology, group theory, differential manifolds, and Morse theory. He also presents some recent advances in the area, including topological persistence and hierarchical Morse complexes. Throughout, the focus is on computational challenges and on presenting algorithms and data structures when appropriate.

From Sets and Types to Topology and Analysis

Author : Laura Crosilla
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Bridging the foundations and practice of constructive mathematics, this text focusses on the contrast between the theoretical developments - which have been most useful for computer science - and more specific efforts on constructive analysis, algebra and topology.

Topology with Applications

Author : Somashekhar A. Naimpally
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The principal aim of this book is to introduce topology and its many applications viewed within a framework that includes a consideration of compactness, completeness, continuity, filters, function spaces, grills, clusters and bunches, hyperspace topologies, initial and final structures, metric spaces, metrization, nets, proximal continuity, proximity spaces, separation axioms, and uniform spaces.This book provides a complete framework for the study of topology with a variety of applications in science and engineering that include camouflage filters, classification, digital image processing, forgery detection, Hausdorff raster spaces, image analysis, microscopy, paleontology, pattern recognition, population dynamics, stem cell biology, topological psychology, and visual merchandising.It is the first complete presentation on topology with applications considered in the context of proximity spaces, and the nearness and remoteness of sets of objects. A novel feature throughout this book is the use of near and far, discovered by F Riesz over 100 years ago. In addition, it is the first time that this form of topology is presented in the context of a number of new applications.

New Theoretical Concepts for Understanding Organic Reactions

Author : Juan Bertrán
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People who attended the NATO Advanced Study Institute (ASI) entitled NEW THEORETICAL CONCEPTS FOR UNDERSTANDING ORGANIC REAC TIONS held at Sant Feliu de Gufxols on the Costa Brava of Spain had a unique experience. They have seen the evolution of the field from qualitative arguments through the generation of Potential Energy Surfaces (PES) to the use of PES in molecular dynamics. The excellent lectures that were dedicated to the various aspects of Potential Energy Surfaces clearly revealed a colossal amount of ma terial that represents our current understanding of the overall problem. It is our hope that the present volume will recreate the excitement in the readers that we all experienced during the meeting in Spain. One can say, without too much exaggeration, that chemistry has become and exercise on potential energy surfaces (PES). Structural (position of the energy minima), spectroscopic (vicinity around the minima), and reactivity (reaction path along the surface) properties may be determined from the analysis of PES. New theoretical tools, together with recent developments in computer technology and programming, have allowed to obtain a better knowledge of these surfaces, and to extract further chemical information from them, so new horizons have been added to Theoretical Organic Chemistry.

Understanding Operating Systems

Author : Ann McHoes
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Now in its Sixth Edition, UNDERSTANDING OPERATING SYSTEMS continues to provide a clear and straightforward explanation of operating theory and practice. As in previous editions, the book's highly-regarded structure begins with a discussion of fundamentals before moving on to specific operating systems. This edition has been updated and modernized; now included are enhanced discussions of the latest innovation evolutions (multi-core processing, wireless technologies, PDA and telephone operating systems, and Blu-ray optical storage) and how they affect operating systems. Revised Research Topics in the exercise section encourage independent research among students. Content in the final four chapters has been updated to include information about a few of the latest versions of UNIX (including specific mention of the latest Macintosh OS), Linux, and Windows. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Topological Data Structures for Surfaces

Author : Sanjay Rana
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In Geography and GIS, surfaces can be analysed and visualised through various data structures, and topological data structures describe surfaces in the form of a relationship between certain surface-specific features. Drawn from many disciplines with a strong applied aspect, this is a research-led, interdisciplinary approach to the creation, analysis and visualisation of surfaces, focussing on topological data structures. Topological Data Structures for Surfaces: an introduction for Geographical Information Science describes the concepts and applications of these data structures. The book focuses on how these data structures can be used to analyse and visualise surface datasets from a range of disciplines such as human geography, computer graphics, metrology, and physical geography. Divided into two Parts, Part I defines the topological surface data structures and explains the various automated methods used for their generation. Part II demonstrates a number of applications of surface networks in diverse fields, ranging from sub-atomic particle collision visualisation to the study of population density patterns. To ensure that the material is accessible, each Part is prefaced by an overview of the techniques and application. Provides GI scientists and geographers with an accessible overview of current surface topology research. Algorithms are presented and explained with practical examples of their usage. Features an accompanying website developed by the Editor - This book is invaluable for researchers and postgraduate students working in departments of GI Science, Geography and Computer Science. It also constitutes key reference material for Masters students working on surface analysis projects as part of a GI Science or Computer Science programme.

On the Topology of Cultural Memory

Author : Thiemo Breyer
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Understanding Alain Robbe Grillet

Author : Roch C. Smith
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"Transforming bewilderment into understanding and pleasure while preserving a sense of Robbe-Grillet's considerable richness and complexity, Smith elucidates the defining elements of the writer's fictional world - characters that barely exist, changeable narrators, plots that defy logic, notoriously meticulous descriptions that never quite form a complete story. Smith examines Robbe-Grillet's embrace of discontinuity, circularity, indeterminacy, and linguistic play. Smith also poses questions about how we should view this perplexing writer: as an author of hyperobjective novels and short stories, a subjective novelist, a realist, or a writer who undermines the narrative's claim to represent reality. In addition Smith evaluates the sado-erotic imagery of Robbe-Grillet's middle and late novels as a metaphorical play with textual and social conventions."--BOOK JACKET.

Introduction to Topology

Author : Colin Conrad Adams
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Learn the basics of point-set topology with the understanding of its real-world application to a variety of other subjects including science, economics, engineering, and other areas of mathematics. KEY TOPICS: Introduces topology as an important and fascinating mathematics discipline to retain the readers interest in the subject. Is written in an accessible way for readers to understand the usefulness and importance of the application of topology to other fields. Introduces topology concepts combined with their real-world application to subjects such DNA, heart stimulation, population modeling, cosmology, and computer graphics. Covers topics including knot theory, degree theory, dynamical systems and chaos, graph theory, metric spaces, connectedness, and compactness. MARKET: A useful reference for readers wanting an intuitive introduction to topology.

Creative Understanding

Author : Roberto Torretti
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"A pleasure to read. Gracefully written by a scholar well grounded in the relevant philosophical, historical, and technical background. . . . a helpfully clarifying review and analysis of some issues of importance to recent philosophy of science and a source of some illuminating insights."—Burke Townsend, Philosophy of Science

Point Set Topology

Author : Steven A. Gaal
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Suitable for a complete course in topology, this text also functions as a self-contained treatment for independent study. Additional enrichment materials make it equally valuable as a reference. 1964 edition.

Computational Methods for Understanding Riboswitches

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This new volume of Methods in Enzymology continues the legacy of this premier serial with quality chapters authored by leaders in the field. This volume covers computational prediction RNA structure and dynamics, including such topics as computational modeling of RNA secondary and tertiary structures, riboswitch dynamics, and ion-RNA, ligand-RNA and DNA-RNA interactions. Continues the legacy of this premier serial with quality chapters authored by leaders in the field Covers computational methods and applications in RNA structure and dynamics Contains chapters with emerging topics such as RNA structure prediction, riboswitch dynamics and thermodynamics, and effects of ions and ligands.

Understanding Telecommunications Networks

Author : Andy Valdar
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This book explains how telecommunications networks work. It uses straightforward language supported by copious block-schematic diagrams so that non-engineers and engineers alike can learn about the principles of fixed and mobile telecommunications networks carrying voice and data. The book covers all aspects of today's networks, including how they are planned, formed and operated, plus next generation networks and how they will be implemented. After an introductory chapter on telephony the book briefly describes all of today's networks – PSTN, mobile, cable television, the Internet, etc. – and considers how they interconnect. Individual chapters then consider the principles, technologies and network structures relating to transmission, circuit switching, signalling and control, data (including voice-over-IP) networks, and mobile networks. The important subject of numbering and addressing for telephony and IP is then covered. The book concludes with a chapter designed to pull everything together, considering architecture, quality of service and performance, operations and network evolution. Despite the rapid changes taking place in telecommunications today - covering customer expectations, commercial arrangements, regulation, markets and services, as well as technology - this book's coverage of the basic principles makes it a helpful and enduring reference for undergraduate and postgraduate students, and for professionals working in the industry.

Understanding Imagination

Author : Dennis L Sepper
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This book discusses that imagination is as important to thinking and reasoning as it is to making and acting. By reexamining our philosophical and psychological heritage, it traces a framework, a conceptual topology, that underlies the most disparate theories: a framework that presents imagination as founded in the placement of appearances. It shows how this framework was progressively developed by thinkers like Plato, Aristotle, Descartes, and Kant, and how it is reflected in more recent developments in theorists as different as Peirce, Saussure, Wittgenstein, Benjamin, and Bachelard. The conceptual topology of imagination incorporates logic, mathematics, and science as well as production, play, and art. Recognizing this topology can move us past the confusions to a unifying view of imagination for the future. ​

Singularities and Topology of Hypersurfaces

Author : Alexandru Dimca
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From the very beginning, algebraic topology has developed under the influ­ ence of the problems posed by trying to understand the topological properties of complex algebraic varieties (e.g., the pioneering work by Poincare and Lefschetz). Especially in the work of Lefschetz [Lf2], the idea is made explicit that singularities are important in the study of the topology even in the case of smooth varieties. What is known nowadays about the topology of smooth and singular vari­ eties is quite impressive. The many existing results may be roughly divided into two classes as follows: (i) very general results or theories, like stratified Morse theory and (mixed) Hodge theory, see, for instance, Goresky-MacPherson [GM], Deligne [Del], and Steenbrink [S6]; and (ii) specific topics of great subtlety and beauty, like the study of the funda­ mental group of the complement in [p>2 of a singular plane curve initiated by Zariski or Griffiths' theory relating the rational differential forms to the Hodge filtration on the middle cohomology group of a smooth projec­ tive hypersurface. The aim of this book is precisely to introduce the reader to some topics in this latter class. Most of the results to be discussed, as well as the related notions, are at least two decades old, and specialists use them intensively and freely in their work. Nevertheless, it is impossible to find an adequate intro­ duction to this subject, which gives a good feeling for its relations with other parts of algebraic geometry and topology.

Critical Point Theory in Global Analysis and Differential Topology

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Critical Point Theory in Global Analysis and Differential Topology

A Topological Introduction to Nonlinear Analysis

Author : Robert F. Brown
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This third edition is addressed to the mathematician or graduate student of mathematics - or even the well-prepared undergraduate - who would like, with a minimum of background and preparation, to understand some of the beautiful results at the heart of nonlinear analysis. Based on carefully-expounded ideas from several branches of topology, and illustrated by a wealth of figures that attest to the geometric nature of the exposition, the book will be of immense help in providing its readers with an understanding of the mathematics of the nonlinear phenomena that characterize our real world. Included in this new edition are several new chapters that present the fixed point index and its applications. The exposition and mathematical content is improved throughout. This book is ideal for self-study for mathematicians and students interested in such areas of geometric and algebraic topology, functional analysis, differential equations, and applied mathematics. It is a sharply focused and highly readable view of nonlinear analysis by a practicing topologist who has seen a clear path to understanding. "For the topology-minded reader, the book indeed has a lot to offer: written in a very personal, eloquent and instructive style it makes one of the highlights of nonlinear analysis accessible to a wide audience."-Monatshefte fur Mathematik (2006)

Algebraic and Differential Topology

Author : R. V. Gamkrelidze
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Algebraic and Differential Topology presents in a clear, concise, and detailed manner the fundamentals of homology theory. It first defines the concept of a complex and its Betti groups, then discusses the topolgoical invariance of a Betti group. The book next presents various applications of homology theory, such as mapping of polyhedrons onto other polyhedrons as well as onto themselves. The third volume in L.S. Pontryagin's Selected Works, this book provides as many insights into algebraic topology for today's mathematician as it did when the author was making his initial endeavors into this field.