Beltrami What Is Random?

Chance and Order in Mathematics and Life
Erscheinungsjahr 2012
ISBN: 978-1-4612-1472-4
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 201 Seiten

Reihe: Mathematics and Statistics

This book is intended to provoke, entertain, and inform by challenging the reader's ideas about randomness, providing first one and then another interpretation of what this elusive concept means. As the book progresses, the author teases out the various threads and shows how mathematics, communication engineering, computer science, philosophy, physics, and psychology all contribute to the discourse by illuminating different facets of the same idea.
The material in this book should be readily accessible to anyone with experience in undergraduate mathematics, no calculus needed. Three appendices provide some of the background information regarding binary representations and logarithms that are needed. Although an effort is made to justify most statements of a mathematical nature, a few are presented without corroboration, since they entail close-knit arguments that would detract from the main ideas. Readers can safely bypass the details without any loss, andin any case, the fine points are available in the technical notes assembled at the end.

       

Zielgruppe

Popular/general

Autoren/Hrsg.

Beltrami, Edward

Inhaltsverzeichnis

[1] The Taming of Chance.- From Unpredictable to Lawful.- Probability.- Order in the Large.- The Normal Law.- Is It Random?.- More About the Law of Large Numbers.- Where We Stand Now.- [2] Uncertainty and Information.- Messages and Information.- Entropy.- Messages, Codes, and Entropy.- Approximate Entropy.- Again, Is It Random?.- The Perception of Randomness.- [3] Janus-Faced Randomness.- Is Determinism an Illusion?.- Generating Randomness.- Janus and the Demons.- [4] Algorithms, Information, and Chance.- Algorithmic Randomness.- Algorithmic Complexity and Undecidability.- Algorithmic Probability.- [5] The Edge of Randomness.- Between Order and Disorder.- Self-Similarity and Complexity.- What Good is Randomness?.- Sources and Further Readings.- Technical Notes.- Appendix A: Geometric Sums.- Appendix B: Binary Numbers.- Appendix C: Logarithims.- References.