rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    non sort: The
    title: elements of Cantor sets
    sub title: with applications
  name:
    name part: Vallin, Robert W.
    role:
      role term: creator
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: nju
    date issued: 2013
    edition: First edition.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource.
  abstract: "This book is a thorough introduction to the Cantor (Ternary) Set and its applications and brings together many of the topics (advanced calculus, probability, topology, and algebra) that mathematics students are required to study, but unfortunately are treated as separate ideas. This book successfully bridges the gap between how several mathematical fields interact using Cantor Sets as the common theme. While the book is mathematically self-contained, readers should be comfortable with mathematical formalism and have some experience in reading and writing mathematical proofs. Chapter coverage includes: a biography of Cantor; an introduction to the Cantor (Ternary) Set; Self-Similar Sets and Fractal Dimensions; sums of Cantor Sets; the role of Cantor Sets to create pathological functions; and additional topics such as continued fractions, Ana Sets, and p-adic numbers"--
  table of contents: Cover; Title Page; Copyright Page; CONTENTS; Foreword; Preface; Acknowledgments; Introduction; 1 A Quick Biography of Cantor; 2 Basics; 2.1 Review; Exercises; 3 Introducing the Cantor Set; 3.1 Some Definitions and Basics; 3.2 Size of a Cantor Set; 3.2.1 Cardinality; 3.2.2 Category; 3.2.3 Measure; 3.3 Large and Small; Exercises; 4 Cantor Sets and Continued Fractions; 4.1 Introducing Continued Fractions; 4.2 Constructing a Cantor Set; 4.3 Diophantine Equations; 4.4 Miscellaneous; Exercises; 5 p-adic Numbers and Valuations; 5.1 Some Abstract Algebra; 5.2 p-adic Numbers.
  table of contents: 5.2.1 An Analysis Point of View5.2.2 An Algebra Point of View; 5.3 p-adic Integers and Cantor Sets; 5.4 p-adic Rational Numbers; Exercises; 6 Self-Similar Objects; 6.1 The Meaning of Self-Similar; 6.2 Metric Spaces; 6.3 Sequences in (S, d); 6.4 Affine Transformations; 6.5 An Application for an IFS; Exercises; 7 Various Notions of Dimension; 7.1 Limit Supremum and Limit Infimum; 7.2 Topological Dimension; 7.3 Similarity Dimension; 7.4 Box-Counting Dimension; 7.5 Hausdorff Measure and Dimension; 7.6 Miscellaneous Notions of Dimension; Exercises; 8 Porosity and Thickness-Looking at the Gaps.
  table of contents: 8.1 The Porosity of a Set8.2 Symmetric Sets and Symmetric Porosity; 8.3 A New and Different Definition of Cantor Set; 8.4 Thickness of a Cantor Set; 8.5 Applying Thickness; 8.6 A Bit More on Thickness; 8.7 Porosity in a Metric Space; Exercises; 9 Creating Pathological Functions via C; 9.1 Sequences of Functions; 9.2 The Cantor Function; 9.3 Space-Filling Curves; 9.4 Baire Class One Functions; 9.5 Darboux Functions; 9.6 Linearly Continuous Functions; Exercises; 10 Generalizations and Applications; 10.1 Generalizing Cantor Sets; 10.2 Fat Cantor Sets; 10.3 Sums of Cantor Sets.
  table of contents: 10.4 Differences of Cantor Sets10.5 Products of Cantor Sets; 10.6 Cantor Target; 10.7 Ana Sets; 10.8 Average Distance; 10.9 Non-Averaging Sets; 10.10 Cantor Series and Cantor Sets; 10.11 Liouville Numbers and Irrationality Exponents; 10.12 Sets of Sums of Convergent Alternating Series; 10.13 The Monty Hall Problem; 11 Epilogue; References; Index.
  note: Robert W. Vallin.
  note: Includes bibliographical references and index.
  subject:
    name:
      name part: Cantor, George
      name part: 1941-
  subject:
    name:
      name part: Cantor, George
      name part: 1941-
  subject:
    topic: Cantor sets
  subject:
    topic: Measure theory
  subject:
    topic: Mathematical analysis
  subject:
    topic: MATHEMATICS / Mathematical Analysis
  subject:
    topic: Cantor, George, 1941-
  subject:
    topic: Cantor sets
  subject:
    topic: Mathematical analysis
  subject:
    topic: Measure theory
  classification: QA612
  classification: 515/.8
  classification: MAT034000
  related item:
    title info:
      title: Elements of Cantor sets
    name:
      name part: Vallin, Robert W.
    origin info:
      publisher: Hoboken, New Jersey : John Wiley & Sons, Inc., [2013]
      edition: First edition.
    identifier: (DLC) 2013009452
  identifier: 9781118548707 (pdf)
  identifier: 1118548701 (pdf)
  identifier: 9781118405710 (hardback)
  identifier: 9781118407431
  identifier: 1118407431
  identifier: 9781118407455
  identifier: 1118407458
  identifier: 9781118548745
  identifier: 1118548744
  identifier: 9781299775824
  identifier: 1299775829
  identifier: 9781118514948
  identifier: 9781118514924
  identifier: 9781118514931
  identifier: 9781118514900
  identifier: 2013018014
  identifier: EB00066787 Recorded Books
  identifier: 508833 MIL
  identifier: https://doi.org/10.1002/9781118548745
  record info:
    record content source: DLC
    record creation date: 130501
    record change date: 20170124071238.9
    record identifier: ocn842307638
    language of cataloging:
      language term: eng