Elements of Cantor sets - with applications / Robert W. Vallin.
Material type:
TextPublication details: New Jersey : John Wiley & Sons, ©2013.Description: 225 pages : illustrations ; 24 cmISBN: - 9781118405710
- 515.8 23 V188
| Item type | Current library | Call number | Status | Date due | Barcode | Item holds | |
|---|---|---|---|---|---|---|---|
| Books | ISI Library, Kolkata | 515.8 V188 (Browse shelf(Opens below)) | Available | 137498 |
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| 515.8 T748 Functions of real variables | 515.8 T748 Functions of real variables | 515.8 Un61 Fourfold way in real analysis | 515.8 V188 Elements of Cantor sets - with applications / | 515.8 W582 Real analysis | 515.8 Y43 Problems and proofs in real analysis : theory of measure and integration / | 515.8 Z22 Convex analysis in general vector spaces |
Includes bibliographical references and index.
1. Quick Biography of Cantor --
2. Basics --
3. Introducing the Cantor Set --
4. Cantor Sets and Continued Fractions --
5. p-adic Numbers and Valuations --
6. Self-Similar Objects --
7. Various Notions of Dimension --
8. Porosity and Thickness-Looking at the Gaps --
9. Creating Pathological Functions via C --
10. Generalizations and Applications --
11. Epilogue.
"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"--
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