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| 001 | ocn842307638 | ||
| 003 | OCoLC | ||
| 005 | 20171106121053.0 | ||
| 006 | m o d | ||
| 007 | cr ||||||||||| | ||
| 008 | 130501s2013 nju ob 001 0 eng | ||
| 010 | _a 2013018014 | ||
| 020 | _a9781118548707 (pdf) | ||
| 020 | _a1118548701 (pdf) | ||
| 020 | _z9781118405710 (hardback) | ||
| 020 | _a9781118407431 | ||
| 020 | _a1118407431 | ||
| 020 | _a9781118407455 | ||
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| 020 | _a9781118548745 | ||
| 020 | _a1118548744 | ||
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| 020 | _z9781118514924 | ||
| 020 | _z9781118514931 | ||
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| 100 | 1 | _aVallin, Robert W. | |
| 245 | 1 | 4 |
_aThe elements of Cantor sets : with applications / _cRobert W. Vallin. _h[electronic resource] |
| 250 | _aFirst edition. | ||
| 264 | 1 |
_aHoboken, New Jersey : _bWiley, _c[2013] |
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| 300 | _a1 online resource. | ||
| 336 |
_atext _2rdacontent |
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| 337 |
_acomputer _2rdamedia |
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| 338 |
_aonline resource _2rdacarrier |
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| 504 | _aIncludes bibliographical references and index. | ||
| 505 | 0 | _aCover; 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 | _a5.2.1 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 | _a8.1 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 | _a10.4 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"-- _cProvided by publisher. |
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| 588 | _aDescription based on print version record and CIP data provided by publisher. | ||
| 600 | 1 | 0 |
_aCantor, George, _d1941- |
| 600 | 1 | 7 |
_aCantor, George, _d1941- _2fast _0(OCoLC)fst00020672 |
| 650 | 0 | _aCantor sets. | |
| 650 | 0 | _aMeasure theory. | |
| 650 | 0 | _aMathematical analysis. | |
| 650 | 7 |
_aMATHEMATICS / Mathematical Analysis. _2bisacsh |
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| 650 | 4 | _aCantor, George, 1941- | |
| 650 | 7 |
_aCantor sets. _2fast _0(OCoLC)fst00846144 |
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| 650 | 7 |
_aMathematical analysis. _2fast _0(OCoLC)fst01012068 |
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| 650 | 7 |
_aMeasure theory. _2fast _0(OCoLC)fst01013175 |
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| 655 | 4 | _aElectronic books. | |
| 655 | 7 |
_aElectronic books. _2local |
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| 776 | 0 | 8 |
_iPrint version: _aVallin, Robert W. _tElements of Cantor sets _bFirst edition. _dHoboken, New Jersey : John Wiley & Sons, Inc., [2013] _z9781118405710 _w(DLC) 2013009452 |
| 856 | 4 | 0 |
_uhttp://onlinelibrary.wiley.com/book/10.1002/9781118548745 _zWiley Online Library |
| 942 |
_2ddc _cBK |
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| 999 |
_c206701 _d206701 |
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