Explorations In Topology

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Explorations in Topology

Author : David Gay
Publisher : Elsevier
ISBN 13 : 0124166407
Total Pages : 332 pages
Book Rating : 4.1/5 (241 download)

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Book Synopsis Explorations in Topology by : David Gay

Download or read book Explorations in Topology written by David Gay and published by Elsevier. This book was released on 2013-12-04 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Topology for Analysis

Author : Albert Wilansky
Publisher : Courier Corporation
ISBN 13 : 0486469034
Total Pages : 399 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis Topology for Analysis by : Albert Wilansky

Download or read book Topology for Analysis written by Albert Wilansky and published by Courier Corporation. This book was released on 2008-10-17 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Heidegger and the Thinking of Place

Author : Jeff Malpas
Publisher : MIT Press
ISBN 13 : 0262533677
Total Pages : 389 pages
Book Rating : 4.2/5 (625 download)

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Book Synopsis Heidegger and the Thinking of Place by : Jeff Malpas

Download or read book Heidegger and the Thinking of Place written by Jeff Malpas and published by MIT Press. This book was released on 2017-03-03 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Heidegger's Topology

Author : Jeff Malpas
Publisher : MIT Press
ISBN 13 : 0262250330
Total Pages : 425 pages
Book Rating : 4.2/5 (622 download)

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Book Synopsis Heidegger's Topology by : Jeff Malpas

Download or read book Heidegger's Topology written by Jeff Malpas and published by MIT Press. This book was released on 2008-08-29 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: This groundbreaking inquiry into the centrality of place in Martin Heidegger's thinking offers not only an illuminating reading of Heidegger's thought but a detailed investigation into the way in which the concept of place relates to core philosophical issues. In Heidegger's Topology, Jeff Malpas argues that an engagement with place, explicit in Heidegger's later work, informs Heidegger's thought as a whole. What guides Heidegger's thinking, Malpas writes, is a conception of philosophy's starting point: our finding ourselves already "there," situated in the world, in "place". Heidegger's concepts of being and place, he argues, are inextricably bound together. Malpas follows the development of Heidegger's topology through three stages: the early period of the 1910s and 1920s, through Being and Time, centered on the "meaning of being"; the middle period of the 1930s into the 1940s, centered on the "truth of being"; and the late period from the mid-1940s on, when the "place of being" comes to the fore. (Malpas also challenges the widely repeated arguments that link Heidegger's notions of place and belonging to his entanglement with Nazism.) The significance of Heidegger as a thinker of place, Malpas claims, lies not only in Heidegger's own investigations but also in the way that spatial and topographic thinking has flowed from Heidegger's work into that of other key thinkers of the past 60 years.

Differential Topology

Author : Victor Guillemin
Publisher : American Mathematical Soc.
ISBN 13 : 0821851934
Total Pages : 242 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Differential Topology by : Victor Guillemin

Download or read book Differential Topology written by Victor Guillemin and published by American Mathematical Soc.. This book was released on 2010 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential Topology provides an elementary and intuitive introduction to the study of smooth manifolds. In the years since its first publication, Guillemin and Pollack's book has become a standard text on the subject. It is a jewel of mathematical exposition, judiciously picking exactly the right mixture of detail and generality to display the richness within. The text is mostly self-contained, requiring only undergraduate analysis and linear algebra. By relying on a unifying idea--transversality--the authors are able to avoid the use of big machinery or ad hoc techniques to establish the main results. In this way, they present intelligent treatments of important theorems, such as the Lefschetz fixed-point theorem, the Poincaré-Hopf index theorem, and Stokes theorem. The book has a wealth of exercises of various types. Some are routine explorations of the main material. In others, the students are guided step-by-step through proofs of fundamental results, such as the Jordan-Brouwer separation theorem. An exercise section in Chapter 4 leads the student through a construction of de Rham cohomology and a proof of its homotopy invariance. The book is suitable for either an introductory graduate course or an advanced undergraduate course.

Explorations in Analysis, Topology, and Dynamics: An Introduction to Abstract Mathematics

Author : Alejandro Uribe A.
Publisher : American Mathematical Soc.
ISBN 13 : 1470452707
Total Pages : 178 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Explorations in Analysis, Topology, and Dynamics: An Introduction to Abstract Mathematics by : Alejandro Uribe A.

Download or read book Explorations in Analysis, Topology, and Dynamics: An Introduction to Abstract Mathematics written by Alejandro Uribe A. and published by American Mathematical Soc.. This book was released on 2020-05-21 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Nonlinear Potential Theory of Degenerate Elliptic Equations

Author : Juha Heinonen
Publisher : Courier Dover Publications
ISBN 13 : 0486830462
Total Pages : 417 pages
Book Rating : 4.4/5 (868 download)

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Book Synopsis Nonlinear Potential Theory of Degenerate Elliptic Equations by : Juha Heinonen

Download or read book Nonlinear Potential Theory of Degenerate Elliptic Equations written by Juha Heinonen and published by Courier Dover Publications. This book was released on 2018-05-16 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained treatment appropriate for advanced undergraduates and graduate students, this text offers a detailed development of the necessary background for its survey of the nonlinear potential theory of superharmonic functions. 1993 edition.

Normal Topological Spaces

Author : Richard A. Alo
Publisher : Cambridge University Press
ISBN 13 : 9780521095303
Total Pages : 0 pages
Book Rating : 4.0/5 (953 download)

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Book Synopsis Normal Topological Spaces by : Richard A. Alo

Download or read book Normal Topological Spaces written by Richard A. Alo and published by Cambridge University Press. This book was released on 2009-01-11 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text bridges the gap existing in the field of set theoretical topology between the introductory texts and the more specialised monographs. The authors review fit developments in general topology and discuss important new areas of research and the importance of defining a methodology applicable to this active field of mathematics. The concept of normal cover and related ideas is considered in detail, as are the characterisations of normal spaces, collectionwise normal spaces and their interrelationships with paracompact spaces (and other weaker forms of compactness). Various methods of embedding subspaces are studied, before considering newer concepts such as M-spaces and their relationships with established ideas. These ideas are applied to give new results pertaining to the extension of continuous vector-valued functions. Wallman-Frink compactifications and realcompactifications are also studied to assist in unifying the ideas through the use of the more general L-filter.

Problems and Theorems in Classical Set Theory

Author : Peter Komjath
Publisher : Springer Science & Business Media
ISBN 13 : 038730293X
Total Pages : 492 pages
Book Rating : 4.3/5 (873 download)

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Book Synopsis Problems and Theorems in Classical Set Theory by : Peter Komjath

Download or read book Problems and Theorems in Classical Set Theory written by Peter Komjath and published by Springer Science & Business Media. This book was released on 2006-05-02 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a variety of problems from classical set theory and represents the first comprehensive collection of such problems. Many of these problems are also related to other fields of mathematics, including algebra, combinatorics, topology and real analysis. Rather than using drill exercises, most problems are challenging and require work, wit, and inspiration. They vary in difficulty, and are organized in such a way that earlier problems help in the solution of later ones. For many of the problems, the authors also trace the history of the problems and then provide proper reference at the end of the solution.

Introduction to Topology

Author : Theodore W. Gamelin
Publisher : Courier Corporation
ISBN 13 : 0486320189
Total Pages : 258 pages
Book Rating : 4.4/5 (863 download)

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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.

Outer Circles

Author : A. Marden
Publisher : Cambridge University Press
ISBN 13 : 1139463764
Total Pages : 393 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Outer Circles by : A. Marden

Download or read book Outer Circles written by A. Marden and published by Cambridge University Press. This book was released on 2007-05-31 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: We live in a three-dimensional space; what sort of space is it? Can we build it from simple geometric objects? The answers to such questions have been found in the last 30 years, and Outer Circles describes the basic mathematics needed for those answers as well as making clear the grand design of the subject of hyperbolic manifolds as a whole. The purpose of Outer Circles is to provide an account of the contemporary theory, accessible to those with minimal formal background in topology, hyperbolic geometry, and complex analysis. The text explains what is needed, and provides the expertise to use the primary tools to arrive at a thorough understanding of the big picture. This picture is further filled out by numerous exercises and expositions at the ends of the chapters and is complemented by a profusion of high quality illustrations. There is an extensive bibliography for further study.

More than one mystery

Author : Mark P. Silverman
Publisher : Springer Science & Business Media
ISBN 13 : 9780387943763
Total Pages : 236 pages
Book Rating : 4.9/5 (437 download)

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Book Synopsis More than one mystery by : Mark P. Silverman

Download or read book More than one mystery written by Mark P. Silverman and published by Springer Science & Business Media. This book was released on 1995 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Because atomic behavior is so unlike ordinary experience," wrote Richard Feynman, "it is very difficult to get used to, and it appears strange and mysterious to everyone - both to the novice and to the experienced physicist." At the core of the strange behavior lies quantum interference: "In reality," Feynman wrote, "it contains the only mystery." To author Mark Silverman, however, the puzzling nature of quantum behavior is multifaceted.

Royal Road To Topology, A: Convergence Of Filters

Author : Szymon Dolecki
Publisher : World Scientific
ISBN 13 : 9811232121
Total Pages : 733 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Royal Road To Topology, A: Convergence Of Filters by : Szymon Dolecki

Download or read book Royal Road To Topology, A: Convergence Of Filters written by Szymon Dolecki and published by World Scientific. This book was released on 2024-01-03 with total page 733 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Knot Book

Author : Colin Conrad Adams
Publisher : American Mathematical Soc.
ISBN 13 : 0821836781
Total Pages : 330 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Knot Book by : Colin Conrad Adams

Download or read book The Knot Book written by Colin Conrad Adams and published by American Mathematical Soc.. This book was released on 2004 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Knots are familiar objects. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. This work offers an introduction to this theory, starting with our understanding of knots. It presents the applications of knot theory to modern chemistry, biology and physics.

Mathematical Explorations

Author : Alan F. Beardon
Publisher : Cambridge University Press
ISBN 13 : 131661056X
Total Pages : 129 pages
Book Rating : 4.3/5 (166 download)

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Book Synopsis Mathematical Explorations by : Alan F. Beardon

Download or read book Mathematical Explorations written by Alan F. Beardon and published by Cambridge University Press. This book was released on 2016-10-13 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides readers with experience of working on difficult unsolved problems. No deep mathematical background is required.

Categorical Homotopy Theory

Author : Emily Riehl
Publisher : Cambridge University Press
ISBN 13 : 1139952633
Total Pages : 371 pages
Book Rating : 4.1/5 (399 download)

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Book Synopsis Categorical Homotopy Theory by : Emily Riehl

Download or read book Categorical Homotopy Theory written by Emily Riehl and published by Cambridge University Press. This book was released on 2014-05-26 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops abstract homotopy theory from the categorical perspective with a particular focus on examples. Part I discusses two competing perspectives by which one typically first encounters homotopy (co)limits: either as derived functors definable when the appropriate diagram categories admit a compatible model structure, or through particular formulae that give the right notion in certain examples. Emily Riehl unifies these seemingly rival perspectives and demonstrates that model structures on diagram categories are irrelevant. Homotopy (co)limits are explained to be a special case of weighted (co)limits, a foundational topic in enriched category theory. In Part II, Riehl further examines this topic, separating categorical arguments from homotopical ones. Part III treats the most ubiquitous axiomatic framework for homotopy theory - Quillen's model categories. Here, Riehl simplifies familiar model categorical lemmas and definitions by focusing on weak factorization systems. Part IV introduces quasi-categories and homotopy coherence.

Category Theory in Context

Author : Emily Riehl
Publisher : Courier Dover Publications
ISBN 13 : 0486820807
Total Pages : 273 pages
Book Rating : 4.4/5 (868 download)

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Book Synopsis Category Theory in Context by : Emily Riehl

Download or read book Category Theory in Context written by Emily Riehl and published by Courier Dover Publications. This book was released on 2017-03-09 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to concepts of category theory — categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads — revisits a broad range of mathematical examples from the categorical perspective. 2016 edition.