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Essentials Of Topology With Applications
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Book Synopsis Essentials of Topology with Applications by : Steven G. Krantz
Download or read book Essentials of Topology with Applications written by Steven G. Krantz and published by CRC Press. This book was released on 2009-07-28 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: Brings Readers Up to Speed in This Important and Rapidly Growing AreaSupported by many examples in mathematics, physics, economics, engineering, and other disciplines, Essentials of Topology with Applications provides a clear, insightful, and thorough introduction to the basics of modern topology. It presents the traditional concepts of topological
Book Synopsis Topology and Its Applications by : William F. Basener
Download or read book Topology and Its Applications written by William F. Basener and published by John Wiley & Sons. This book was released on 2013-06-12 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover a unique and modern treatment of topology employing a cross-disciplinary approach Implemented recently to understand diverse topics, such as cell biology, superconductors, and robot motion, topology has been transformed from a theoretical field that highlights mathematical theory to a subject that plays a growing role in nearly all fields of scientific investigation. Moving from the concrete to the abstract, Topology and Its Applications displays both the beauty and utility of topology, first presenting the essentials of topology followed by its emerging role within the new frontiers in research. Filling a gap between the teaching of topology and its modern uses in real-world phenomena, Topology and Its Applications is organized around the mathematical theory of topology, a framework of rigorous theorems, and clear, elegant proofs. This book is the first of its kind to present applications in computer graphics, economics, dynamical systems, condensed matter physics, biology, robotics, chemistry, cosmology, material science, computational topology, and population modeling, as well as other areas of science and engineering. Many of these applications are presented in optional sections, allowing an instructor to customize the presentation. The author presents a diversity of topological areas, including point-set topology, geometric topology, differential topology, and algebraic/combinatorial topology. Topics within these areas include: Open sets Compactness Homotopy Surface classification Index theory on surfaces Manifolds and complexes Topological groups The fundamental group and homology Special "core intuition" segments throughout the book briefly explain the basic intuition essential to understanding several topics. A generous number of figures and examples, many of which come from applications such as liquid crystals, space probe data, and computer graphics, are all available from the publisher's Web site.
Book Synopsis Topology with Applications by : Somashekhar A. Naimpally
Download or read book Topology with Applications written by Somashekhar A. Naimpally and published by World Scientific. This book was released on 2013 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author :Martin D. Crossley Publisher :Springer Science & Business Media ISBN 13 :9781852337827 Total Pages :244 pages Book Rating :4.3/5 (378 download)
Book Synopsis Essential Topology by : Martin D. Crossley
Download or read book Essential Topology written by Martin D. Crossley and published by Springer Science & Business Media. This book was released on 2011-02-11 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings the most important aspects of modern topology within reach of a second-year undergraduate student. It successfully unites the most exciting aspects of modern topology with those that are most useful for research, leaving readers prepared and motivated for further study. Written from a thoroughly modern perspective, every topic is introduced with an explanation of why it is being studied, and a huge number of examples provide further motivation. The book is ideal for self-study and assumes only a familiarity with the notion of continuity and basic algebra.
Book Synopsis Topology Essentials by : Emil G. Milewski
Download or read book Topology Essentials written by Emil G. Milewski and published by Research & Education Assoc.. This book was released on 2013-01-01 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: REA’s Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Topology includes an overview of elementary set theory, relations and functions, ordinals and cardinals, topological spaces, continuous functions, metric spaces and normed spaces, countable spaces, and separation axioms.
Book Synopsis Elements of Point Set Topology by : John D. Baum
Download or read book Elements of Point Set Topology written by John D. Baum and published by Courier Corporation. This book was released on 1991-01-01 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topology continues to be a topic of prime importance in contemporary mathematics, but until the publication of this book there were few if any introductions to topology for undergraduates. This book remedied that need by offering a carefully thought-out, graduated approach to point set topology at the undergraduate level. To make the book as accessible as possible, the author approaches topology from a geometric and axiomatic standpoint; geometric, because most students come to the subject with a good deal of geometry behind them, enabling them to use their geometric intuition; axiomatic, because it parallels the student's experience with modern algebra, and keeps the book in harmony with current trends in mathematics. After a discussion of such preliminary topics as the algebra of sets, Euler-Venn diagrams and infinite sets, the author takes up basic definitions and theorems regarding topological spaces (Chapter 1). The second chapter deals with continuous functions (mappings) and homeomorphisms, followed by two chapters on special types of topological spaces (varieties of compactness and varieties of connectedness). Chapter 5 covers metric spaces. Since basic point set topology serves as a foundation not only for functional analysis but also for more advanced work in point set topology and algebraic topology, the author has included topics aimed at students with interests other than analysis. Moreover, Dr. Baum has supplied quite detailed proofs in the beginning to help students approaching this type of axiomatic mathematics for the first time. Similarly, in the first part of the book problems are elementary, but they become progressively more difficult toward the end of the book. References have been supplied to suggest further reading to the interested student.
Book Synopsis A Combinatorial Introduction to Topology by : Michael Henle
Download or read book A Combinatorial Introduction to Topology written by Michael Henle and published by Courier Corporation. This book was released on 1994-01-01 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excellent text covers vector fields, plane homology and the Jordan Curve Theorem, surfaces, homology of complexes, more. Problems and exercises. Some knowledge of differential equations and multivariate calculus required.Bibliography. 1979 edition.
Book Synopsis Elementary Concepts of Topology by : Paul Alexandroff
Download or read book Elementary Concepts of Topology written by Paul Alexandroff and published by Courier Corporation. This book was released on 2012-08-13 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concise work presents topological concepts in clear, elementary fashion, from basics of set-theoretic topology, through topological theorems and questions based on concept of the algebraic complex, to the concept of Betti groups. Includes 25 figures.
Book Synopsis Elements of Topological Dynamics by : J. de Vries
Download or read book Elements of Topological Dynamics written by J. de Vries and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 762 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is designed as an introduction into what I call 'abstract' Topological Dynamics (TO): the study of topological transformation groups with respect to problems that can be traced back to the qualitative theory of differential equa is in the tradition of the books [GH] and [EW. The title tions. So this book (,Elements . . . ' rather than 'Introduction . . . ') does not mean that this book should be compared, either in scope or in (intended) impact, with the 'Ele ments' of Euclid or Bourbaki. Instead, it reflects the choice and organisation of the material in this book: elementary and basic (but sufficient to understand recent research papers in this field). There are still many challenging prob lems waiting for a solution, and especially among general topologists there is a growing interest in this direction. However, the technical inaccessability of many research papers makes it almost impossible for an outsider to under stand what is going on. To a large extent, this inaccessability is caused by the lack of a good and systematic exposition of the fundamental methods and techniques of abstract TO. This book is an attempt to fill this gap. The guiding principle for the organization of the material in this book has been the exposition of methods and techniques rather than a discussion of the leading problems and their solutions. though the latter are certainly not neglected: they are used as a motivation wherever possible.
Book Synopsis Topology Through Inquiry by : Michael Starbird
Download or read book Topology Through Inquiry written by Michael Starbird and published by American Mathematical Soc.. This book was released on 2020-09-10 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topology Through Inquiry is a comprehensive introduction to point-set, algebraic, and geometric topology, designed to support inquiry-based learning (IBL) courses for upper-division undergraduate or beginning graduate students. The book presents an enormous amount of topology, allowing an instructor to choose which topics to treat. The point-set material contains many interesting topics well beyond the basic core, including continua and metrizability. Geometric and algebraic topology topics include the classification of 2-manifolds, the fundamental group, covering spaces, and homology (simplicial and singular). A unique feature of the introduction to homology is to convey a clear geometric motivation by starting with mod 2 coefficients. The authors are acknowledged masters of IBL-style teaching. This book gives students joy-filled, manageable challenges that incrementally develop their knowledge and skills. The exposition includes insightful framing of fruitful points of view as well as advice on effective thinking and learning. The text presumes only a modest level of mathematical maturity to begin, but students who work their way through this text will grow from mathematics students into mathematicians. Michael Starbird is a University of Texas Distinguished Teaching Professor of Mathematics. Among his works are two other co-authored books in the Mathematical Association of America's (MAA) Textbook series. Francis Su is the Benediktsson-Karwa Professor of Mathematics at Harvey Mudd College and a past president of the MAA. Both authors are award-winning teachers, including each having received the MAA's Haimo Award for distinguished teaching. Starbird and Su are, jointly and individually, on lifelong missions to make learning—of mathematics and beyond—joyful, effective, and available to everyone. This book invites topology students and teachers to join in the adventure.
Book Synopsis Introduction to Topology by : Colin Conrad Adams
Download or read book Introduction to Topology written by Colin Conrad Adams and published by Pearson. This book was released on 2008 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. 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. A useful reference for readers wanting an intuitive introduction to topology.
Book Synopsis Introduction to Topology by : Bert Mendelson
Download or read book Introduction to Topology written by Bert Mendelson and published by Courier Corporation. This book was released on 2012-04-26 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concise undergraduate introduction to fundamentals of topology — clearly and engagingly written, and filled with stimulating, imaginative exercises. Topics include set theory, metric and topological spaces, connectedness, and compactness. 1975 edition.
Book Synopsis Introduction to Topology by : Theodore W. Gamelin
Download or read book Introduction to Topology written by Theodore W. Gamelin and published by Courier Corporation. This book was released on 2013-04-22 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text explains nontrivial applications of metric space topology to analysis. Covers metric space, point-set topology, and algebraic topology. Includes exercises, selected answers, and 51 illustrations. 1983 edition.
Book Synopsis Understanding Topology by : Shaun V. Ault
Download or read book Understanding Topology written by Shaun V. Ault and published by JHU Press. This book was released on 2018-01-30 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.
Book Synopsis Principles of Topology by : Fred H. Croom
Download or read book Principles of Topology written by Fred H. Croom and published by Courier Dover Publications. This book was released on 2016-02-17 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published: Philadelphia: Saunders College Publishing, 1989; slightly corrected.
Book Synopsis Point Set Topology by : Steven A. Gaal
Download or read book Point Set Topology written by Steven A. Gaal and published by Courier Corporation. This book was released on 2009-04-23 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis A Concise Course in Algebraic Topology by : J. P. May
Download or read book A Concise Course in Algebraic Topology written by J. P. May and published by University of Chicago Press. This book was released on 1999-09 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
