06183cam a2200937 i 4500 ocn842307638 OCoLC 20171106121053.0 m o d cr ||||||||||| 130501s2013 nju ob 001 0 eng 2013018014 9781118548707 (pdf) 1118548701 (pdf) 9781118405710 (hardback) 9781118407431 1118407431 9781118407455 1118407458 9781118548745 1118548744 9781299775824 1299775829 9781118514948 9781118514924 9781118514931 9781118514900 EB00066787 Recorded Books AU@ 000050949262 AU@ 000053306178 CHBIS 010027045 CHVBK 306231743 DEBBG BV041291832 DEBBG BV041908992 DEBSZ 397611242 DEBSZ 431471754 DEBSZ 449376818 DKDLA 820120-katalog:000664829 NZ1 15290987 DEBBG BV043395813 (OCoLC)842307638 (OCoLC)855504050 (OCoLC)857428550 (OCoLC)865012289 (OCoLC)927508125 (OCoLC)961668898 (OCoLC)962585992 (OCoLC)966211376 508833 MIL DLC eng rda DLC YDX N$T YDXCP DG1 CUS E7B EBLCP IDEBK COO DEBSZ RECBK OCLCF CDX CNMTR DEBBG AZK LOA pcc MAIN QA612 MAT 005000 bisacsh MAT 034000 bisacsh 515/.8 23 MAT034000 bisacsh Vallin, Robert W. The elements of Cantor sets : with applications / Robert W. Vallin. [electronic resource] First edition. Hoboken, New Jersey : Wiley, [2013] 1 online resource. text rdacontent computer rdamedia online resource rdacarrier 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. 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. 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. 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. "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"-- Provided by publisher. Description based on print version record and CIP data provided by publisher. Cantor, George, 1941- Cantor, George, 1941- fast (OCoLC)fst00020672 Cantor sets. Measure theory. Mathematical analysis. MATHEMATICS / Mathematical Analysis. bisacsh Cantor, George, 1941- Cantor sets. fast (OCoLC)fst00846144 Mathematical analysis. fast (OCoLC)fst01012068 Measure theory. fast (OCoLC)fst01013175 Electronic books. Electronic books. local Print version: Vallin, Robert W. Elements of Cantor sets First edition. Hoboken, New Jersey : John Wiley & Sons, Inc., [2013] 9781118405710 (DLC) 2013009452 http://onlinelibrary.wiley.com/book/10.1002/9781118548745 Wiley Online Library ddc BK 206701 206701