The Theory of Probability : Explorations and Applications
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.
- Electronic book text
- 05 Dec 2012
- CAMBRIDGE UNIVERSITY PRESS
- Cambridge University Press (Virtual Publishing)
- Cambridge, United Kingdom
- 100 b/w illus. 26 tables 528 exercises
'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 'This is a remarkable book, a theory of probability that succeeds in being both readable and rigorous, both expository and entertaining ... 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
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.