Explorations In Topology

Author : David Gay
Publisher : Elsevier
ISBN 13 : 0124166407
Total Pages : 332 pages
Book Rating : 4.00/5 ( download)

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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

Author : Jeff Malpas
Publisher : MIT Press
ISBN 13 : 0262533677
Total Pages : 389 pages
Book Rating : 4.76/5 ( download)

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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.

Author : Albert Wilansky
Publisher : Courier Corporation
ISBN 13 : 0486469034
Total Pages : 399 pages
Book Rating : 4.34/5 ( download)

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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.

Author : Jeff Malpas
Publisher : MIT Press
ISBN 13 : 0262250330
Total Pages : 425 pages
Book Rating : 4.37/5 ( download)

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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.

Author : Victor Guillemin
Publisher : American Mathematical Soc.
ISBN 13 : 0821851934
Total Pages : 242 pages
Book Rating : 4.37/5 ( download)

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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.

Author : Juha Heinonen
Publisher : Courier Dover Publications
ISBN 13 : 048682425X
Total Pages : 417 pages
Book Rating : 4.53/5 ( download)

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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 undergraduate and graduate students, this volume offers a detailed development of the necessary background for its survey of the nonlinear potential theory of superharmonic functions. Starting with the theory of weighted Sobolev spaces, the text advances to the theory of weighted variational capacity. Succeeding chapters investigate solutions and supersolutions of equations, with emphasis on refined Sobolev spaces, variational integrals, and harmonic functions. Chapter 7 defines superharmonic functions via the comparison principle, and chapters 8 through 14 form the core of the nonlinear potential theory of superharmonic functions. Topics include balayage; Perron's method, barriers, and resolutivity; polar sets; harmonic measure; fine topology; harmonic morphisms; and quasiregular mappings. The book concludes with explorations of axiomatic nonlinear potential theory and helpful appendixes.

Author : Mark P. Silverman
Publisher : Springer Science & Business Media
ISBN 13 : 1461225043
Total Pages : 224 pages
Book Rating : 4.41/5 ( download)

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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 2012-12-06 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: "I think I can safely say that nobody understands quantum mechanics." #Richard Feynman# Basing his discussion on a small number of conceptually simple models (the two-level atom, the two-slit interferometer), the author addresses a number of conceptually interesting questions concerning the puzzles of quantum mechanics. Though the phenomena arising from quantum interference are central, he maintains that they are not the only mystery in quantum mechanics: the deep connection between spin and the statistics of identical particles, the "ghostly" long-range effects that correlated particles exert on each other, and the perplexing role of topology in the interactions of charged particles and electromagnetic fields, are all conundrums yet to be understood.

Author : Colin Conrad Adams
Publisher : American Mathematical Soc.
ISBN 13 : 0821836781
Total Pages : 330 pages
Book Rating : 4.81/5 ( download)

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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.

Author : Bert Mendelson
Publisher : Courier Corporation
ISBN 13 : 0486135098
Total Pages : 226 pages
Book Rating : 4.90/5 ( download)

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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.

Author : A. Marden
Publisher : Cambridge University Press
ISBN 13 : 1139463764
Total Pages : 393 pages
Book Rating : 4.68/5 ( download)

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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.