Edward Beltrami

What Is Random? (eBook, PDF)

Chance and Order in Mathematics and Life

• Format: PDF

Produktbeschreibung

We all know what randomness is. Or do we? Randomness turns out to be one of those concepts that works just fine on an everyday level, but becomes muddled upon close inspection. People familiar with quantum indeterminacy tell us that order is an illusion and that the world is fundamentally random. Yet these same people also say that randomness is an illusion: The appearance of randomness is only a sign of our ignorance and inability to detect the pattern.

By applying mathematical thinking, mathematician Edward Beltrami removes much of the vagueness that encumbers the concept of randomness. You will discover how to quantify what would otherwise remain elusive. As the book progresses, you will see how mathematics provides a framework for unifying how chance is interpreted across diverse disciplines. Communication engineering, computer science, philosophy, physics, and psychology join mathematics in the discourse to illuminate different facets of the same idea.

Thisbook will provoke, entertain, and inform by challenging your ideas about randomness, providing different interpretations of what this concept means, and showing how order and randomness are really two sides of the same mysterious coin.

This second edition brings the question of randomness into the twenty-first century, adding compelling new topics such as quantum uncertainty, cognitive illusions caused by chance, Poisson processes, and Bayesian probability. An expanded technical notes section offers deeper explorations of a variety of mathematical concepts.

On the first edition:

I strongly recommend [What is Random?] to all who are interested in science and would like to see how the ideas of both theoretical mathematics and statistics have been observed and used in real life throughout history. The American Statistician

Produktdetails

• Verlag: Springer US
• Erscheinungstermin: 30. Juli 2020
• Englisch
• ISBN-13: 9781071607992
• Artikelnr.: 59896045

Autorenporträt

Edward Beltrami is Professor Emeritus in the Department of Applied Mathematics at Stony Brook University in Long Island, New York. His research interests include probability theory, mathematical biology, mathematical modelling, and many more. He is the author of several books on the applications of mathematics.

Beltrami lives with his wife and several cats in suburban Long Island. He enjoys cooking, listening to music, and being a part-time wine critic.

Inhaltsangabe

The Taming of Chance.- Uncertainty and Information.- Janus-Faced Randomness.- Algorithms, Information, and Chance.- The Edge of Randomness.- Fooled by Chance.- Sources and Further Readings.- Technical Notes.- Appendix A: Geometric Sums.- Appendix B: Binary Numbers.- Appendix C: Logarithms.

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[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.

Rezensionen

From the reviews: THE AMERICAN STATISTICIAN "In summary, I think that many readers with a strong interest in mathematics, statistics, physics, or other areas of science will find this book interesting and challenging. I strongly recommend it to all who are interested in science and would like to see how the ideas of both theoretical mathematics and statistics have been observed and used in real life throughout history." MATHEMATICAL REVIEWS "The book is nicely written and should entertain many readers..."