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Anderson M , Feil T A First Course In Abstract Algebra 3ed 2015
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. This book 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 The Taming of Chance Uncertainty and Information Janus-Faced Randomness Algorithms, Information, and Chance The Edge of Randomness Fooled by Chance
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