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Explorations in Topology

Explorations in Topology
Author: David Gay
Publisher: Elsevier
Total Pages: 332
Release: 2013-12-04
Genre: Mathematics
ISBN: 0124166407

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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


Heidegger and the Thinking of Place

Heidegger and the Thinking of Place
Author: Jeff Malpas
Publisher: MIT Press
Total Pages: 389
Release: 2017-03-03
Genre: Philosophy
ISBN: 0262533677

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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.


Topology for Analysis

Topology for Analysis
Author: Albert Wilansky
Publisher: Courier Corporation
Total Pages: 399
Release: 2008-10-17
Genre: Mathematics
ISBN: 0486469034

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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's Topology

Heidegger's Topology
Author: Jeff Malpas
Publisher: MIT Press
Total Pages: 425
Release: 2008-08-29
Genre: Philosophy
ISBN: 0262250330

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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

Differential Topology
Author: Victor Guillemin
Publisher: American Mathematical Soc.
Total Pages: 242
Release: 2010
Genre: Mathematics
ISBN: 0821851934

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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.


More Than One Mystery

More Than One Mystery
Author: Mark P. Silverman
Publisher: Springer Science & Business Media
Total Pages: 224
Release: 2012-12-06
Genre: Science
ISBN: 1461225043

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"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.


The Knot Book

The Knot Book
Author: Colin Conrad Adams
Publisher: American Mathematical Soc.
Total Pages: 330
Release: 2004
Genre: Mathematics
ISBN: 0821836781

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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.


Nonlinear Potential Theory of Degenerate Elliptic Equations

Nonlinear Potential Theory of Degenerate Elliptic Equations
Author: Juha Heinonen
Publisher: Courier Dover Publications
Total Pages: 416
Release: 2018-05-16
Genre: Mathematics
ISBN: 0486830462

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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.


Outer Circles

Outer Circles
Author: A. Marden
Publisher: Cambridge University Press
Total Pages: 393
Release: 2007-05-31
Genre: Mathematics
ISBN: 1139463764

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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.


Playing with Infinity

Playing with Infinity
Author: Rozsa Peter
Publisher:
Total Pages:
Release: 1986-01
Genre:
ISBN: 9780844652351

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Popular account ranges from counting to mathematical logic and covers many concepts related to infinity: graphic representation of functions; pairings, other combinations; prime numbers; logarithms, circular functions; more. 216 illustrations.