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The elements of Cantor sets[electronic resource] :with applications /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
杜威分類號:	515/.8
書名/作者:	The elements of Cantor sets : with applications // Robert W. Vallin.
作者:	Vallin, Robert W.
出版者:	Hoboken, New Jersey : : Wiley,, 2013.
面頁冊數:	1 online resource.
標題:	Cantor sets.
標題:	Measure theory.
標題:	Mathematical analysis.
ISBN:	9781118548745 (electronic bk.)
ISBN:	1118548744 (electronic bk.)
ISBN:	9781118548707 (electronic bk.)
ISBN:	1118548701 (electronic bk.)
ISBN:	1118405714 (hardback)
ISBN:	9781118405710 (hardback)
ISBN:	9781299775824 (MyiLibrary)
ISBN:	1299775829 (MyiLibrary)
書目註:	Includes bibliographical references and index.
內容註:	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
摘要、提要註:	"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"--
電子資源:	http://onlinelibrary.wiley.com/book/10.1002/9781118548745

The elements of Cantor sets[electronic resource] :with applications /
Vallin, Robert W.

The elements of Cantor setswith applications /[electronic resource] :Robert W. Vallin. - Hoboken, New Jersey :Wiley,2013. - 1 online resource.

Includes bibliographical references and index.

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

"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"--

ISBN: 9781118548745 (electronic bk.)

LCCN: 2013018014Subjects--Personal Names:

587940
Cantor, George,
1941-Subjects--Topical Terms:

587941
Cantor sets.

LC Class. No.: QA612 / .V35 2013

Dewey Class. No.: 515/.8

The elements of Cantor sets[electronic resource] :with applications /
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020 $a 9781118548745 (electronic bk.)
020 $a 1118548744 (electronic bk.)
020 $a 9781118548707 (electronic bk.)
020 $a 1118548701 (electronic bk.)
020 $z 9781118407431
020 $z 1118407431
020 $z 9781118407455
020 $z 1118407458
020 $z 9781118405710 (hardback)
020 $a 1118405714 (hardback)
020 $a 9781118405710 (hardback)
020 $a 9781299775824 (MyiLibrary)
020 $a 1299775829 (MyiLibrary)
035 $a ocn842307638
040 $a DLC $b eng $c DLC $d YDX $d OCLCO $d N $d YDXCP $d DG1 $d CUS $d E7B $d EBLCP $d IDEBK $d OCLCO $d COO
050 1 4 $a QA612 $b .V35 2013
082 0 0 $a 515/.8 $2 23
100 1 $a Vallin, Robert W. $3 587939
245 1 4 $a The elements of Cantor sets $h [electronic resource] : $b with applications / $c Robert W. Vallin.
260 $a Hoboken, New Jersey : $b Wiley, $c 2013.
300 $a 1 online resource.
504 $a Includes bibliographical references and index.
505 0 $a 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
505 8 $a 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
505 8 $a 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
505 8 $a 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
520 $a "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"-- $c Provided by publisher.
588 $a Description based on online resource; title from digital title page (viewed on August 22, 2013).
600 1 0 $a Cantor, George, $d 1941- $3 587940
650 0 $a Cantor sets. $3 587941
650 0 $a Measure theory. $3 495639
650 0 $a Mathematical analysis. $3 227335
856 4 0 $u http://onlinelibrary.wiley.com/book/10.1002/9781118548745