Taking an innovative approach to both content and methods, this book explores the foundations, basic concepts, and fundamental results of probability theory. Geared toward those unfamiliar with probability theory, it offers a firm basis for the study of topics related to the probability of mathematic... read more
Probability Theory by Alfred Renyi This introductory text features problems and exercises illustrating algebras of events, discrete random variables, characteristic functions, and limit theorems. An extensive appendix introduces information theory. 1970 edition.
Probability Theory: A Concise Course by Y. A. Rozanov This clear exposition begins with basic concepts and moves on to combination of events, dependent events and random variables, Bernoulli trials and the De Moivre-Laplace theorem, and more. Includes 150 problems, many with answers.
Good Thinking: The Foundations of Probability and Its Applications by Irving John Good This in-depth treatment of probability theory by a famous British statistician explores Keynesian principles and surveys such topics as Bayesian rationality, corroboration, hypothesis testing, and mathematical tools for induction and simplicity. 1983 edition.
Elements of the Theory of Markov Processes and Their Applications by A. T. Bharucha-Reid Graduate-level text and reference in probability, with numerous scientific applications. Nonmeasure-theoretic introduction to theory of Markov processes and to mathematical models based on the theory. Appendixes. Bibliographies. 1960 edition.
Introduction to Probability by John E. Freund Featured topics include permutations and factorials, probabilities and odds, frequency interpretation, mathematical expectation, decision making, postulates of probability, rule of elimination, much more. Exercises with some solutions. Summary. 1973 edition.
Games and Decisions: Introduction and Critical Survey by R. Duncan Luce, Howard Raiffa Superb non-technical introduction to game theory, primarily applied to social sciences. Clear, comprehensive coverage of utility theory, 2-person zero-sum games, 2-person non-zero-sum games, n-person games, individual and group decision-making, more. Bibliography.
Taking an innovative approach to both content and methods, this book explores the foundations, basic concepts, and fundamental results of probability theory. Geared toward those unfamiliar with probability theory, it offers a firm basis for the study of topics related to the probability of mathematical statistics and to information theory. The effective construction of probability spaces receives particular attention. Author Alfred Rényi—former Director of the Mathematical Institute of the Hungarian Academy of Sciences and an expert in the fields of probability theory, mathematical statistics, and number theory—considered effective construction of probability spaces particularly important to applying methods and results of probability theory to other branches of mathematics. Professor Rényi discusses basic theorems of probability theory in terms specific to the theorem in question, rather than in the most general form. His rigorous treatment also covers the mathematical notions of experiments and independence, the laws of chance for independent random variables, and the effects of dependence. Two brief appendixes offer helpful background in measure theory and functional analysis.
Reprint of the Holden-Day, Inc., San Francisco, 1970 edition.
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
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