The Theory of Probability: Explorations and Applications

by Santosh S. Venkatesh

Overview

From classical foundations to advanced modern theory, this self-contained and comprehensive guide to probability weaves together mathematical proofs, historical context and richly detailed illustrative applications. A theorem discovery approach is used throughout, setting each proof within its historical setting and is accompanied by a consistent emphasis on elementary methods of proof. Each topic is presented in a modular framework, combining fundamental concepts with worked examples, problems and digressions which, although mathematically rigorous, require no specialised or advanced mathematical background. Augmenting this core material are over 80 richly embellished practical applications of probability theory, drawn from a broad spectrum of areas both classical and modern, each tailor-made to illustrate the magnificent scope of the formal results. Providing a solid grounding in practical probability, without sacrificing mathematical rigour or historical richness, this insightful book is a fascinating reference and essential resource, for all engineers, computer scientists and mathematicians.

Product Details

ISBN-13:	9781107024472
Publisher:	Cambridge University Press
Publication date:	11/08/2012
Edition description:	New Edition
Pages:	827
Product dimensions:	7.10(w) x 9.80(h) x 1.60(d)

About the Author

Santosh S. Venkatesh is an Associate Professor of Electrical and Systems Engineering at the University of Pennsylvania, whose research interests include probability, information, communication and learning theory, pattern recognition, computational neuroscience, epidemiology and computer security. He is a member of the David Mahoney Institute for Neurological Sciences and has been awarded the Lindback Award for Distinguished Teaching.

Table of Contents

Part I. Elements: 1. Probability spaces; 2. Conditional probability; 3. A first look at independence; 4. Probability sieves; 5. Numbers play a game of chance; 6. The normal law; 7. Probabilities on the real line; 8. The Bernoulli schema; 9. The essence of randomness; 10. The coda of the normal; Part II. Foundations: 11. Distribution functions and measure; 12. Random variables; 13. Great expectations; 14. Variations on a theme of integration; 15. Laplace transforms; 16. The law of large numbers; 17. From inequalities to concentration; 18. Poisson approximation; 19. Convergence in law, selection theorems; 20. Normal approximation; Part III. Appendices: 21. Sequences, functions, spaces.

What People are Saying About This

From the Publisher

'This is a gentle and rich book that is a delight to read. Gentleness comes from the attention to detail; few readers will ever find themselves 'stuck' on any steps of the derivations or proofs. Richness comes from the many examples and historical anecdotes that support the central themes. The text will support courses of many styles and it is especially attractive for self-guided study.' J. J. Michael Steele, University of Pennsylvania

'This book does an excellent job of covering the basic material for a first course in the theory of probability. It is notable for the entertaining coverage of many interesting examples, several of which give a taste of significant fields where the subject is applied.' Venkat Anantharam, University of California, Berkeley

'This book presents one of the most refreshing treatments of the theory of probability. By providing excellent coverage with both intuition and rigor, together with engaging examples and applications, [it] presents a wonderfully readable and thorough introduction to this important subject.' Sanjeev Kulkarni, Princeton University

Editorial Reviews

"This is a remarkable book, a theory of probability that succeeds in being both readable and rigorous, both expository and entertaining. One might have thought that there was no space left in the market for books on the fundamentals of probability theory, but this volume provides a refreshing new approach … it is a magnificent undertaking, impeccably presented, and one that is sure to reward repeated reading."
Tom Fanshawe, Significance (magazine of The Royal Statistical Society)

"… well-written, and although the topics are discussed with all mathematical rigour, it usually does not exceed the capabilities of an advanced undergraduate student … it can be recommended without constraint as a textbook for advanced undergraduates, but also as a reference and interesting read for experts."
Manuel Vogel, Contemporary Physics

From the Publisher