Softcover ISBN:  9780821837146 
Product Code:  STML/28 
List Price:  $59.00 
Individual Price:  $47.20 
eBook ISBN:  9781470421397 
Product Code:  STML/28.E 
List Price:  $49.00 
Individual Price:  $39.20 
Softcover ISBN:  9780821837146 
eBook: ISBN:  9781470421397 
Product Code:  STML/28.B 
List Price:  $108.00$83.50 
Softcover ISBN:  9780821837146 
Product Code:  STML/28 
List Price:  $59.00 
Individual Price:  $47.20 
eBook ISBN:  9781470421397 
Product Code:  STML/28.E 
List Price:  $49.00 
Individual Price:  $39.20 
Softcover ISBN:  9780821837146 
eBook ISBN:  9781470421397 
Product Code:  STML/28.B 
List Price:  $108.00$83.50 

Book DetailsStudent Mathematical LibraryVolume: 28; 2005; 150 ppMSC: Primary 60;
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 theorems—statements 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.ReadershipUndergraduates and beginning graduate students interested in mathematical probability.

Table of Contents

Chapters

Prerequisites and overview

Chapter 1. Modeling a probabilistic experiment

Chapter 2. Random variables

Chapter 3. Independence

Chapter 4. The binomial distribution

Chapter 5. The weak law of large numbers

Chapter 6. The large deviations estimate

Chapter 7. The central limit theorem

Chapter 8. The moderate deviations estimate

Chapter 9. The local limit theorem

Chapter 10. The arcsine law

Chapter 11. The strong law of large numbers

Chapter 12. The law of the iterated logarithm

Chapter 13. Recurrence of random walks

Chapter 14. Epilogue


Additional Material

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


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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 theorems—statements 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.
Undergraduates and beginning graduate students interested in mathematical probability.

Chapters

Prerequisites and overview

Chapter 1. Modeling a probabilistic experiment

Chapter 2. Random variables

Chapter 3. Independence

Chapter 4. The binomial distribution

Chapter 5. The weak law of large numbers

Chapter 6. The large deviations estimate

Chapter 7. The central limit theorem

Chapter 8. The moderate deviations estimate

Chapter 9. The local limit theorem

Chapter 10. The arcsine law

Chapter 11. The strong law of large numbers

Chapter 12. The law of the iterated logarithm

Chapter 13. Recurrence of random walks

Chapter 14. Epilogue

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