Foundations of Probability (Dover Books on Mathematics) by Alfred Renyi (PDF)

Description

Introducing many innovations in content and methods, this book involves the foundations, basic concepts, and fundamental results of probability theory. Geared toward readers seeking a firm basis for study of mathematical statistics or information theory, it also covers the mathematical notions of experiments and independence. 1970 edition.

User’s Reviews

Editorial Reviews: About the Author Alfred Renyi was Director of the Mathematical Institute of the Hungarian Academy of Sciences. Alfred Renyi: The Happy Mathematician Alfred Renyi (1921–1970) was one of the giants of twentieth-century mathematics who, during his relatively short life, made major contributions to combinatorics, graph theory, number theory, and other fields. Reviewing Probability Theory and Foundations of Probability simultaneously for the Bulletin of the American Mathematical Society in 1973, Alberto R. Galmarino wrote: “Both books complement each other well and have, as said before, little overlap. They represent nearly opposite approaches to the question of how the theory should be presented to beginners. Rényi excels in both approaches. Probability Theory is an imposing textbook. Foundations is a masterpiece.” In the Author’s Own Words:”If I feel unhappy, I do mathematics to become happy. If I am happy, I do mathematics to keep happy.” “Can the difficulty of an exam be measured by how many bits of information a student would need to pass it? This may not be so absurd in the encyclopedic subjects but in mathematics it doesn’t make any sense since things follow from each other and, in principle, whoever knows the bases knows everything. All of the results of a mathematical theorem are in the axioms of mathematics in embryonic form, aren’t they?” — Alfred Rényi

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐A. Renyi is an outstanding mathematician. I am interested in his axioms for probability theory. No measure theory is really required. This book has a brief introduction to measure theory (Appendix A). It is a lovely concentrated book on probability.

⭐This book is particularly useful as providing a foundation for Bayesian statistical methods, especially using continuous variables.

⭐This book is by a noted mathematician, but I found the presentation not to my likingj.Chung, Breiman or Loeve are better

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