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Explorations in Topology

Explorations in Topology
  • Author : David Gay
  • Publisher :Unknown
  • Release Date :2013
  • Total pages :315
  • ISBN : 0124166482
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Summary : 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
  • Author : Alejandro Uribe A.,Daniel A. Visscher
  • Publisher :Unknown
  • Release Date :2020-05-21
  • Total pages :178
  • ISBN : 9781470452704
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Summary : 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
  • Author : Jeff Malpas
  • Publisher :Unknown
  • Release Date :2017-03-03
  • Total pages :388
  • ISBN : 9780262533676
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Summary : 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
  • Author : David Gay
  • Publisher :Unknown
  • Release Date :2013-12-04
  • Total pages :332
  • ISBN : 9780124166400
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Summary : 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
  • Author : Itamar Gal
  • Publisher :Unknown
  • Release Date :2016
  • Total pages :294
  • ISBN : OCLC:973338543
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Summary : 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
  • Author : Jeff Malpas
  • Publisher :Unknown
  • Release Date :2008-08-29
  • Total pages :424
  • ISBN : 9780262250337
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Summary : 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
  • Author : Anonim
  • Publisher :Unknown
  • Release Date :2012
  • Total pages :229
  • ISBN : OCLC:1066355340
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Summary :

Topologies of the Flesh

Topologies of the Flesh
  • Author : Steven M. Rosen
  • Publisher :Unknown
  • Release Date :2006
  • Total pages :335
  • ISBN : 9780821416761
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Summary : 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.

Explorations in Analysis, Topology, and Dynamics

Explorations in Analysis, Topology, and Dynamics
  • Author : Alejandro Uribe Ahumada,Daniel Alan Visscher
  • Publisher :Unknown
  • Release Date :2020
  • Total pages :229
  • ISBN : 1470456850
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Summary : 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

Topology for Analysis

Topology for Analysis
  • Author : Albert Wilansky
  • Publisher :Unknown
  • Release Date :2008-10-17
  • Total pages :383
  • ISBN : 9780486469034
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Summary : 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.

Topology for Analysis

Topology for Analysis
  • Author : Albert Wilansky
  • Publisher :Unknown
  • Release Date :1970
  • Total pages :383
  • ISBN : 0898743435
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Summary : 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
  • Author : Stefan Artmann
  • Publisher :Unknown
  • Release Date :2006
  • Total pages :147
  • ISBN : 3898380769
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Summary :

Geometry, Topology and Dynamics of Character Varieties

Geometry, Topology and Dynamics of Character Varieties
  • Author : William Goldman,Caroline Series,Ser Peow Tan
  • Publisher :Unknown
  • Release Date :2012
  • Total pages :349
  • ISBN : 9789814401357
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Summary : 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
  • Author : Victor Kooi Ming Chua
  • Publisher :Unknown
  • Release Date :2013
  • Total pages :298
  • ISBN : OCLC:858922600
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Summary : 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.

Beginning Topology

Beginning Topology
  • Author : Sue Goodman
  • Publisher :Unknown
  • Release Date :2005
  • Total pages :236
  • ISBN : UVA:X004995809
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Summary : 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.

A Guide to the Classification Theorem for Compact Surfaces

A Guide to the Classification Theorem for Compact Surfaces
  • Author : Jean Gallier,Dianna Xu
  • Publisher :Unknown
  • Release Date :2013-02-05
  • Total pages :178
  • ISBN : 9783642343643
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Summary : 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.

Modeling, Solving and Application for Topology Optimization of Continuum Structures: ICM Method Based on Step Function

Modeling, Solving and Application for Topology Optimization of Continuum Structures: ICM Method Based on Step Function
  • Author : Yunkang Sui,Xirong Peng
  • Publisher :Unknown
  • Release Date :2017-08-29
  • Total pages :394
  • ISBN : 9780128126561
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Summary : Modelling, Solving and Applications for Topology Optimization of Continuum Structures: ICM Method Based on Step Function provides an introduction to the history of structural optimization, along with a summary of the existing state-of-the-art research on topology optimization of continuum structures. It systematically introduces basic concepts and principles of ICM method, also including modeling and solutions to complex engineering problems with different constraints and boundary conditions. The book features many numerical examples that are solved by the ICM method, helping researchers and engineers solve their own problems on topology optimization. This valuable reference is ideal for researchers in structural optimization design, teachers and students in colleges and universities working, and majoring in, related engineering fields, and structural engineers. Offers a comprehensive discussion that includes both the mathematical basis and establishment of optimization models Centers on the application of ICM method in various situations with the introduction of easily coded software Provides illustrations of a large number of examples to facilitate the applications of ICM method across a variety of disciplines

Bus Topology Exploration and Memory Allocation for Heterogeneous Systems

Bus Topology Exploration and Memory Allocation for Heterogeneous Systems
  • 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 Date :2007
  • Total pages :122
  • ISBN : OCLC:857650080
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Summary :

An Exploration of Topology with the Goal of Understanding the Poincaré Conjecture, Or, "What's So Special about 3 Dimensions, Anyway?"

An Exploration of Topology with the Goal of Understanding the Poincaré Conjecture, Or, 'What's So Special about 3 Dimensions, Anyway?'
  • Author : Devon C. McNare
  • Publisher :Unknown
  • Release Date :1992
  • Total pages :36
  • ISBN : OCLC:666040314
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Summary :

Topology

Topology
  • Author : George McCarty
  • Publisher :Unknown
  • Release Date :2006-01-03
  • Total pages :288
  • ISBN : 0486450821
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Summary : "Admirably meets the topology requirements for the pregraduate training of research mathematicians." — American Mathematical Monthly Topology, sometimes described as "rubber-sheet geometry," is crucial to modern mathematics and to many other disciplines — from quantum mechanics to sociology. This stimulating introduction to the field will give the student a familiarity with elementary point set topology, including an easy acquaintance with the line and the plane, knowledge often useful in graduate mathematics programs. The book is not a collection of topics, rather it early employs the language of point set topology to define and discuss topological groups. These geometric objects in turn motivate a further discussion of set-theoretic topology and of its applications in function spaces. An introduction to homotopy and the fundamental group then brings the student's new theoretical knowledge to bear on very concrete problems: the calculation of the fundamental group of the circle and a proof of the fundamental theorem of algebra. Finally, the abstract development is brought to satisfying fruition with the classification of topological groups by equivalence under local isomorphism. Throughout the book there is a sustained geometric development — a single thread of reasoning which unifies the topological course. One of the special features of this work is its well-chosen exercises, along with a selection of problems in each chapter that contain interesting applications and further theory. Careful study of the text and diligent performance of the exercises will enable the student to achieve an excellent working knowledge of topology and a useful understanding of its applications. Moreover, the author's unique teaching approach lends an extra dimension of effectiveness to the books: "Of particular interest is the remarkable pedagogy evident in this work. The author converses with the reader on a personal basis. He speaks with him, questions him, challenges him, and — best of all — occasionally leaves him to his own devices." — American Scientist

An Exploration of Campus Topology and Women Students

An Exploration of Campus Topology and Women Students
  • Author : Cathy J. Stilwell
  • Publisher :Unknown
  • Release Date :2007
  • Total pages :350
  • ISBN : OCLC:166144687
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Summary :