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Explorations in Topology

Explorations in Topology Book
Author : David Gay
Publisher : Elsevier Science Limited
Release : 2013
ISBN : 9780124166486
Language : En, Es, Fr & De

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Book Description :

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

Explorations in Analysis  Topology  and Dynamics  An Introduction to Abstract Mathematics Book
Author : Alejandro Uribe A.,Daniel A. Visscher
Publisher : American Mathematical Soc.
Release : 2020-05-21
ISBN : 1470452707
Language : En, Es, Fr & De

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Book Description :

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.

Heidegger and the Thinking of Place

Heidegger and the Thinking of Place Book
Author : Jeff Malpas
Publisher : MIT Press
Release : 2017-03-03
ISBN : 0262533677
Language : En, Es, Fr & De

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Book Description :

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.

Explorations in Topology

Explorations in Topology Book
Author : David Gay
Publisher : Elsevier
Release : 2013-12-04
ISBN : 0124166407
Language : En, Es, Fr & De

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Book Description :

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 Algebra and Topology

Explorations in Algebra and Topology Book
Author : Itamar Gal
Publisher : Unknown
Release : 2016
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

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.

Heidegger s Topology

Heidegger s Topology Book
Author : Jeff Malpas
Publisher : MIT Press
Release : 2008-08-29
ISBN : 0262250330
Language : En, Es, Fr & De

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Book Description :

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.

Topology Exploration with Hierarchical Landscapes

Topology Exploration with Hierarchical Landscapes Book
Author : Anonim
Publisher : Unknown
Release : 2012
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Topology Exploration with Hierarchical Landscapes book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Explorations in Analysis Topology and Dynamics

Explorations in Analysis  Topology  and Dynamics Book
Author : Alejandro Uribe Ahumada,Daniel Alan Visscher
Publisher : Unknown
Release : 2020
ISBN : 9781470456856
Language : En, Es, Fr & De

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Book Description :

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 a

Topologies of the Flesh

Topologies of the Flesh Book
Author : Steven M. Rosen
Publisher : Ohio University Press
Release : 2006
ISBN : 0821416766
Language : En, Es, Fr & De

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Book Description :

This is an unprecedented marriage of topology (a branch of mathematics dealing with the properties of geometric figures that stay the same when the figures are distorted) and phenomenology. Through his unique application of qualitative mathematics, Rosen offers a detailed exploration of previously uncharted dimensions of human experience and the natural world.

Topology for Analysis

Topology for Analysis Book
Author : Albert Wilansky
Publisher : John Wiley & Sons Incorporated
Release : 1970
ISBN : 9780898743432
Language : En, Es, Fr & De

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Book Description :

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 the Complexity of Possible Life

Explorations in the Complexity of Possible Life Book
Author : Stefan Artmann
Publisher : IOS Press
Release : 2006
ISBN : 9783898380768
Language : En, Es, Fr & De

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Book Description :

Download Explorations in the Complexity of Possible Life book written by Stefan Artmann, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Beginning Topology

Beginning Topology Book
Author : Sue Goodman
Publisher : Amer Mathematical Society
Release : 2005
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

With a nice balance of mathematical precision and accessibility, this text provides a broad introduction to the field of topology. Author Sue Goodman piques student curiosity and interest without losing necessary rigor so that they can appreciate the beauty and fun of mathematics. The text demonstrates that mathematics is an active and ever-changing field with many problems still unsolved, and students will see how the various areas of mathematics – algebra, combinatorics, geometry, calculus, and differential equations – interact with topology. Students learn some of the major ideas and results in the field, do explorations and fairly elementary proofs, and become aware of some recent questions. By presenting a wide range of topics, exercises, and examples, Goodman creates an interactive and enjoyable atmosphere in which to learn topology.

Geometry Topology and Dynamics of Character Varieties

Geometry  Topology and Dynamics of Character Varieties Book
Author : William Goldman,Caroline Series,Ser Peow Tan
Publisher : World Scientific
Release : 2012
ISBN : 9814401358
Language : En, Es, Fr & De

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Book Description :

This book aims to describe, for readers uneducated in science, the development of humanity's desire to know and understand the world around us through the various stages of its development to the present, when science is almost universally recognized - at least in the Western world - as the most reliable way of knowing. The book describes the history of the large-scale exploration of the surface of the earth by sea, beginning with the Vikings and the Chinese, and of the unknown interiors of the American and African continents by foot and horseback. After the invention of the telescope, visual exploration of the surfaces of the Moon and Mars were made possible, and finally a visit to the Moon. The book then turns to our legacy from the ancient Greeks of wanting to understand rather than just know, and why the scientific way of understanding is valued. For concreteness, it relates the lives and accomplishments of six great scientists, four from the nineteenth century and two from the twentieth. Finally, the book explains how chemistry came to be seen as the most basic of the sciences, and then how physics became the most fundamental.

Explorations Into the Role of Topology and Disorder in Some Exactly Solvable Hamiltonians

Explorations Into the Role of Topology and Disorder in Some Exactly Solvable Hamiltonians Book
Author : Victor Kooi Ming Chua
Publisher : Unknown
Release : 2013
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

In this dissertation, two exactly solvable models from the Kitaev class [Ann. Phys. 321, 2 (2006)] of exactly solvable models are analysed. In the second chapter, Kitaev models and their generic properties are reviewed. Majorana fermions are introduced and discussed. Then their relationship with the solution of Kitaev models are discussed which involves the emergence of a Z2 gauge symmetry and anyonic particles of both Abelian and non-Abelian varieties. The third chapter, which is based on the research article [Phys. Rev. B (Rapid Comm.) 83, (2011)], examines the Kitaev model on the kagome lattice. A rich phase diagram of this model is found to include a topological (gapped) chiral spin liquid with gapless chiral edge states, and a gapless chiral spin liquid phase with a spin Fermi surface. The ground state of the current model contains an odd number of electrons per unit cell which qualitatively distinguishes it from previously studied exactly solvable models with a spin Fermi surface. Moreover, it is shown that the spin Fermi surface is stable against weak perturbations. The fourth chapter is based on the article [Phys. Rev. B 84,(2011)] and analyses a disordered generalisation of the Yao-Kivelson [Phys. Rev. Lett. 99,247203 (2007)] chiral spin-liquid on the decorated honeycomb lattice. The model is generalised by the inclusion of random exchange couplings. The phase diagram was determined and it is found that disorder enlarges the region of the topological non-Abelian phase with finite Chern number. A study of the energy level statistics as a function of disorder and other parameters in the Hamiltonian show that the phase transition between the non-Abelian and Abelian phases of the model at large disorder can be associated with pair annihilation of extended states at zero energy. Analogies to integer quantum Hall systems, topological Anderson insulators, and disordered topological Chern insulators are discussed.

An Exploration of Topology with the Goal of Understanding the Poincar Conjecture Or What s So Special about 3 Dimensions Anyway

An Exploration of Topology with the Goal of Understanding the Poincar   Conjecture  Or   What s So Special about 3 Dimensions  Anyway   Book
Author : Devon C. McNare
Publisher : Unknown
Release : 1992
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download An Exploration of Topology with the Goal of Understanding the Poincar Conjecture Or What s So Special about 3 Dimensions Anyway book written by Devon C. McNare, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Bus Topology Exploration and Memory Allocation for Heterogeneous Systems

Bus Topology Exploration and Memory Allocation for Heterogeneous Systems Book
Author : 吳志勇,鄺獻榮,國立中山大學資訊工程學系研究所
Publisher : Unknown
Release : 2007
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Bus Topology Exploration and Memory Allocation for Heterogeneous Systems book written by 吳志勇,鄺獻榮,國立中山大學資訊工程學系研究所, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Topological in Hegel

Topological  in  Hegel Book
Author : Borislav G. Dimitrov
Publisher : Borislav Dimitrov
Release : 2018-01-23
ISBN : 1370071213
Language : En, Es, Fr & De

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Book Description :

The aim of this book is to critically examine whether it is methodologically possible to combine mathematical rigor – topology with a systematic dialectical methodology in Hegel, and if so, to provide as result of my interpretation the outline of Hegel’s Analysis Situs, also with the proposed models (build on the topological manifold, cobordism, topological data analysis, persistent homology, simplicial complexes and graph theory, to provide an indication of how the merger of Hegel’s dialectical logic and topology may be instrumental to a systematic logician and of how a systematic dialectical logic perspective may help mathematical model builders.

An Exploration of Campus Topology and Women Students

An Exploration of Campus Topology and Women Students Book
Author : Cathy J. Stilwell
Publisher : Unknown
Release : 2007
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download An Exploration of Campus Topology and Women Students book written by Cathy J. Stilwell, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

A Guide to the Classification Theorem for Compact Surfaces

A Guide to the Classification Theorem for Compact Surfaces Book
Author : Jean Gallier,Dianna Xu
Publisher : Springer Science & Business Media
Release : 2013-02-05
ISBN : 3642343643
Language : En, Es, Fr & De

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Book Description :

This welcome boon for students of algebraic topology cuts a much-needed central path between other texts whose treatment of the classification theorem for compact surfaces is either too formalized and complex for those without detailed background knowledge, or too informal to afford students a comprehensive insight into the subject. Its dedicated, student-centred approach details a near-complete proof of this theorem, widely admired for its efficacy and formal beauty. The authors present the technical tools needed to deploy the method effectively as well as demonstrating their use in a clearly structured, worked example. Ideal for students whose mastery of algebraic topology may be a work-in-progress, the text introduces key notions such as fundamental groups, homology groups, and the Euler-Poincaré characteristic. These prerequisites are the subject of detailed appendices that enable focused, discrete learning where it is required, without interrupting the carefully planned structure of the core exposition. Gently guiding readers through the principles, theory, and applications of the classification theorem, the authors aim to foster genuine confidence in its use and in so doing encourage readers to move on to a deeper exploration of the versatile and valuable techniques available in algebraic topology.

Explorations in Complex and Riemannian Geometry

Explorations in Complex and Riemannian Geometry Book
Author : Robert Everist Greene,John Bland,Kang-Tae Kim,Steven George Krantz
Publisher : American Mathematical Soc.
Release : 2003
ISBN : 0821832735
Language : En, Es, Fr & De

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Book Description :

This book contains contributions by an impressive list of leading mathematicians. The articles include high-level survey and research papers exploring contemporary issues in geometric analysis, differential geometry, and several complex variables. Many of the articles will provide graduate students with a good entry point into important areas of modern research. The material is intended for researchers and graduate students interested in several complex variables and complex geometry.