Explorations In Topology
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Explorations In Topology
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Author : David Gay
language : en
Publisher: Elsevier
Release Date : 2013-12-04
Explorations In Topology written by David Gay and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-04 with Mathematics categories.
Explorations in Topology, Second Edition, provides students a rich experience with low-dimensional topology (map coloring, surfaces, and knots), enhances their geometrical and topological intuition, empowers them with new approaches to solving problems, and provides them with experiences that will help them make sense of future, more formal topology courses. The book's innovative story-line style models the problem-solving process, presents the development of concepts in a natural way, and engages students in meaningful encounters with the material. The updated end-of-chapter investigations provide opportunities to work on many open-ended, non-routine problems and, through a modified "Moore method," to make conjectures from which theorems emerge. The revised end-of-chapter notes provide historical background to the chapter's ideas, introduce standard terminology, and make connections with mainstream mathematics. The final chapter of projects provides ideas for continued research. Explorations in Topology, Second Edition, enhances upper division courses and is a valuable reference for all levels of students and researchers working in topology. Students begin to solve substantial problems from the start Ideas unfold through the context of a storyline, and students become actively involved The text models the problem-solving process, presents the development of concepts in a natural way, and helps the reader engage with the material
Explorations In Analysis Topology And Dynamics An Introduction To Abstract Mathematics
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Author : Alejandro Uribe A.
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-05-21
Explorations In Analysis Topology And Dynamics An Introduction To Abstract Mathematics written by Alejandro Uribe A. 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 2020-05-21 with Education categories.
This book is an introduction to the theory of calculus in the style of inquiry-based learning. The text guides students through the process of making mathematical ideas rigorous, from investigations and problems to definitions and proofs. The format allows for various levels of rigor as negotiated between instructor and students, and the text can be of use in a theoretically oriented calculus course or an analysis course that develops rigor gradually. Material on topology (e.g., of higher dimensional Euclidean spaces) and discrete dynamical systems can be used as excursions within a study of analysis or as a more central component of a course. The themes of bisection, iteration, and nested intervals form a common thread throughout the text. The book is intended for students who have studied some calculus and want to gain a deeper understanding of the subject through an inquiry-based approach.
Topology For Analysis
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Author : Albert Wilansky
language : en
Publisher: John Wiley & Sons Incorporated
Release Date : 1970
Topology For Analysis written by Albert Wilansky and has been published by John Wiley & Sons Incorporated this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Mathematics categories.
Appropriate for both students and professionals, this volume starts with the first principles of topology and advances to general analysis. Three levels of examples and problems, ordered and numbered by degree of difficulty, illustrate important concepts. A 40-page appendix, featuring tables of theorems and counter examples, provides a valuable reference. From explorations of topological space, convergence, and separation axioms, the text proceeds to considerations of sup and weak topologies, products and quotients, compactness and compactification, and complete semimetric space. The concluding chapters explore metrization, topological groups, and function spaces. Each subject area is supplemented with examples, problems, and exercises that progress to increasingly rigorous levels. All examples and problems are classified as essential, optional, and advanced.
Explorations In Algebra And Topology
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Author : Itamar Gal
language : en
Publisher:
Release Date : 2016
Explorations In Algebra And Topology written by Itamar Gal and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with categories.
Three independent investigations are expounded, two in the domain of algebra and one in the domain of topology. We first consider algebraic extensions generated by elements of bounded degree and consider the question of whether or not the finite sub-extensions of such fields can be bounded. We give partial results which will hopefully lead to a full classification in the future. These results are fundamentally group theoretic but have applications to number theory. Next we develop the notational system originated by Conway and Sloane for working with quadratic forms over the 2-adic integers and prove its correctness. This provides a proof which was missing from the literature. Finally we study distributions of persistent homology barcodes obtained by sampling finite point sets from metric measure spaces. The main result here is the derivation of robust statistics for topological data analysis.
Royal Road To Topology A Convergence Of Filters
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Author : Szymon Dolecki
language : en
Publisher: World Scientific
Release Date : 2024-01-03
Royal Road To Topology A Convergence Of Filters written by Szymon Dolecki and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-03 with Mathematics categories.
Topological spaces are a special case of convergence spaces. This textbook introduces topology within a broader context of convergence theory. The title alludes to advantages of the present approach, which is more gratifying than many traditional ones: you travel more comfortably through mathematical landscapes and you see more.The book is addressed both to those who wish to learn topology and to those who, being already knowledgeable about topology, are curious to review it from a different perspective, which goes well beyond the traditional knowledge.Usual topics of classic courses of set-theoretic topology are treated at an early stage of the book — from a viewpoint of convergence of filters, but in a rather elementary way. Later on, most of these facts reappear as simple consequences of more advanced aspects of convergence theory.The mentioned virtues of the approach stem from the fact that the class of convergences is closed under several natural, essential operations, under which the class of topologies is not! Accordingly, convergence theory complements topology like the field of complex numbers algebraically completes the field of real numbers.Convergence theory is intuitive and operational because of appropriate level of its abstraction, general enough to grasp the underlying laws, but not too much in order not to lose intuitive appeal.
Heidegger And The Thinking Of Place
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Author : Jeff Malpas
language : en
Publisher: MIT Press
Release Date : 2017-03-03
Heidegger And The Thinking Of Place written by Jeff Malpas and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-03 with Philosophy categories.
The philosophical significance of place—in Heidegger's work and as the focus of a distinctive mode of philosophical thinking. The idea of place—topos—runs through Martin Heidegger's thinking almost from the very start. It can be seen not only in his attachment to the famous hut in Todtnauberg but in his constant deployment of topological terms and images and in the situated, “placed” character of his thought and of its major themes and motifs. Heidegger's work, argues Jeff Malpas, exemplifies the practice of “philosophical topology.” In Heidegger and the Thinking of Place, Malpas examines the topological aspects of Heidegger's thought and offers a broader elaboration of the philosophical significance of place. Doing so, he provides a distinct and productive approach to Heidegger as well as a new reading of other key figures—notably Kant, Aristotle, Gadamer, and Davidson, but also Benjamin, Arendt, and Camus. Malpas, expanding arguments he made in his earlier book Heidegger's Topology (MIT Press, 2007), discusses such topics as the role of place in philosophical thinking, the topological character of the transcendental, the convergence of Heideggerian topology with Davidsonian triangulation, the necessity of mortality in the possibility of human life, the role of materiality in the working of art, the significance of nostalgia, and the nature of philosophy as beginning in wonder. Philosophy, Malpas argues, begins in wonder and begins in place and the experience of place. The place of wonder, of philosophy, of questioning, he writes, is the very topos of thinking.
Introduction To Topology
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Author : Bert Mendelson
language : en
Publisher: Courier Corporation
Release Date : 2012-04-26
Introduction To Topology written by Bert Mendelson and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-26 with Mathematics categories.
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.
Encyclopedia Of General Topology
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Author : K.P. Hart
language : en
Publisher: Elsevier
Release Date : 2003-11-18
Encyclopedia Of General Topology written by K.P. Hart and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-11-18 with Mathematics categories.
This book is designed for the reader who wants to get a general view of the terminology of General Topology with minimal time and effort. The reader, whom we assume to have only a rudimentary knowledge of set theory, algebra and analysis, will be able to find what they want if they will properly use the index. However, this book contains very few proofs and the reader who wants to study more systematically will find sufficiently many references in the book. Key features: • More terms from General Topology than any other book ever published• Short and informative articles• Authors include the majority of top researchers in the field• Extensive indexing of terms
Topology For Analysis
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Author : Albert Wilansky
language : en
Publisher: Courier Corporation
Release Date : 2008-10-17
Topology For Analysis written by Albert Wilansky and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-17 with Mathematics categories.
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.
Introduction To Topology
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Author : Solomon Lefschetz
language : en
Publisher: Princeton University Press
Release Date : 2015-12-08
Introduction To Topology written by Solomon Lefschetz and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-08 with Mathematics categories.
In this book, which may be used as a self-contained text for a beginning course, Professor Lefschetz aims to give the reader a concrete working knowledge of the central concepts of modern combinatorial topology: complexes, homology groups, mappings in spheres, homotopy, transformations and their fixed points, manifolds and duality theorems. Each chapter ends with a group of problems. Originally published in 1949. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
