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Probability Theory: A Concise Course
This book, a concise introduction to modern probability theory and certain of its ramifications, deals with a subject indispensable to natural scientists and mathematicians alike. Here the readers, with some knowledge of mathematics, will find an excellent treatment of the elements of probability together with numerous applications. Professor Y. A. Rozanov, an internationally known mathematician whose work in probability theory and stochastic processes has received wide acclaim, combines succinctness of style with a judicious selection of topics. His book is highly readable, fast-moving, and self-contained.
The author begins with basic concepts and moves on to combination of events, dependent events and random variables. He then covers Bernoulli trials and the De Moivre-Laplace theorem, which involve three important probability distributions (binomial, Poisson, and normal or Gaussian). The last three chapters are devoted to limit theorems, a detailed treatment of Markov chains, continuous Markov processes. Also included are appendixes on information theory, game theory, branching processes, and problems of optimal control. Each of the eight chapters and four appendixes has been equipped with numerous relevant problems (150 of them), many with hints and answers.
This volume is another in the popular series of fine translations from the Russian by Richard A. Silverman. Dr. Silverman, a former member of the Courant Institute of Mathematical Sciences of New York University and the Lincoln Laboratory of the Massachusetts Institute of Technology, is himself the author of numerous papers on applied probability theory. He has heavily revised the English edition and added new material. The clear exposition, the ample illustrations and problems, the cross-references, index, and bibliography make this book useful for self-study or the classroom.
The author begins with basic concepts and moves on to combination of events, dependent events and random variables. He then covers Bernoulli trials and the De Moivre-Laplace theorem, which involve three important probability distributions (binomial, Poisson, and normal or Gaussian). The last three chapters are devoted to limit theorems, a detailed treatment of Markov chains, continuous Markov processes. Also included are appendixes on information theory, game theory, branching processes, and problems of optimal control. Each of the eight chapters and four appendixes has been equipped with numerous relevant problems (150 of them), many with hints and answers.
This volume is another in the popular series of fine translations from the Russian by Richard A. Silverman. Dr. Silverman, a former member of the Courant Institute of Mathematical Sciences of New York University and the Lincoln Laboratory of the Massachusetts Institute of Technology, is himself the author of numerous papers on applied probability theory. He has heavily revised the English edition and added new material. The clear exposition, the ample illustrations and problems, the cross-references, index, and bibliography make this book useful for self-study or the classroom.
262 pages, Kindle Edition
First published June 1, 1977
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Displaying 1 - 11 of 11 reviews
September 24, 2016
Short and concise. Every sentence is meaningful. For those who does not like to waste their time.
August 22, 2015
A great book. I like how it actually explains the symbols that they use to describe the problems rather than expecting you to know right away or before hand. Among the topics discussed in this book are; the Weak and Strong Laws of Large Numbers, Binomial, Poisson and Normal distributions, random variables and Markov Chains.
This is a very densely packed little volume, and it is well worth the price to me. It contains some problems but not all of them have answers. At the end of the book is a bibliography if you want to find some more books like this one, and a few appendices that describe Game Theory and Information Theory to an extent.
This is a very densely packed little volume, and it is well worth the price to me. It contains some problems but not all of them have answers. At the end of the book is a bibliography if you want to find some more books like this one, and a few appendices that describe Game Theory and Information Theory to an extent.
June 24, 2017
My knowledge of probability theory was rather basic. I took my time to read every chapter thoroughly, in order to understand each of the formulas. This 140p-book makes every word count. Each example makes clear which of the formulas are really important and how they are applied. Every chapter is built upon the material from previous chapters. The Markov chains/processes were less interesting but the shorter appendices on information theory and game theory were more appealing. Recommended for anybody starting on probability theory.
August 2, 2013
Very happy to learn the secretary problem...
August 18, 2024
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{\displaystyle {1 \over n}\sum _{k=1}^{n}a_{k}b_{k}\geq \left({1 \over n}\sum _{k=1}^{n}a_{k}\right)\!\!\left({1 \over n}\sum _{k=1}^{n}b_{k}\right)\!.}
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{\displaystyle {1 \over n}\sum _{k=1}^{n}a_{k}b_{k}\geq \left({1 \over n}\sum _{k=1}^{n}a_{k}\right)\!\!\left({1 \over n}\sum _{k=1}^{n}b_{k}\right)\!.}
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{\displaystyle {1 \over n}\sum _{k=1}^{n}a_{k}b_{k}\leq \left({1 \over n}\sum _{k=1}^{n}a_{k}\right)\!\!\left({1 \over n}\sum _{k=1}^{n}b_{k}\right)\!.}
December 1, 2024
The greatest introduction to Probability Theory. The book is very concise and each sentence matters. An excellent set of problems too. In 8 chapters, I went from high school level knowledge to Stochastics. We need more such books!
March 5, 2019
Contents were fine, but I need something a bit friendlier.
November 27, 2021
Dover books in general rarely dissapoint. This book confirmed this theory once more. Very compact introduction to Probability theory, and some applications of it like Information theory. Must have.
January 25, 2025
Short and sweet. Has awkward notation and not the most comprehensive or interesting book on probability theory. IMO a bad first book, but a decent refresher if that's all you're looking for.
June 14, 2016
*Probably* the best reference book for anyone who deals with probability concepts frequently. Surprisingly readable for a math book. I've looked things up, and then lost time as I kept reading until someone snapped me out of it. Unpretentious... and only 160 pages. You could carry it around in your back pocket.
September 9, 2016
This was not a good intro book for probability it's more for someone that has already studied the subject and needs a refresher, or as a supplemental material.
Displaying 1 - 11 of 11 reviews