Student Mathematical Library 2005; 150 pp; softcover Volume: 28 ISBN10: 0821837141 ISBN13: 9780821837146 List Price: US$32 Institutional Members: US$25.60 All Individuals: US$25.60 Order Code: STML/28
See also: Probability Tales  Charles M Grinstead, William P Peterson and J Laurie Snell  Everyone knows some of the basics of probability, perhaps enough to play cards. Beyond the introductory ideas, there are many wonderful results that are unfamiliar to the layman, but which are well within our grasp to understand and appreciate. Some of the most remarkable results in probability are those that are related to limit theoremsstatements about what happens when the trial is repeated many times. The most famous of these is the Law of Large Numbers, which mathematicians, engineers, economists, and many others use every day. In this book, Lesigne has made these limit theorems accessible by stating everything in terms of a game of tossing of a coin: heads or tails. In this way, the analysis becomes much clearer, helping establish the reader's intuition about probability. Moreover, very little generality is lost, as many situations can be modelled from combinations of coin tosses. This book is suitable for anyone who would like to learn more about mathematical probability and has had a oneyear undergraduate course in analysis. Readership Undergraduates and beginning graduate students interested in mathematical probability. Reviews "This is a delightful little book ... the author converys an impressive and wellwritten account of central ideas of limit theorems in probability ... It is refreshing to have a book that starts with such a simple experiment with two outcomes and takes us as far as it does into the world of probability theory."  MAA Reviews "The proposal is very attractive. ... (It) is helpful for the probability community to have access to this book, which contains a unified and elementary presentation of limit theorems..."  Zentralblatt Math Table of Contents  Prerequisites and overview
 Modeling a probabilistic experiment
 Random variables
 Independence
 The binomial distribution
 The weak law of large numbers
 The large deviations estimate
 The central limit theorem
 The moderate deviations estimate
 The local limit theorem
 The arcsine law
 The strong law of large numbers
 The law of the iterated logarithm
 Recurrence of random walks
 Epilogue
 Biographies
 Bibliography
 Index
