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The Theory of Probability: Explorations and Applications

The Theory of Probability: Explorations and Applications

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Santosh S. Venkatesh
Cambridge University Press, 11/8/2012
EAN 9781107024472, ISBN10: 1107024471

Hardcover, 827 pages, 25.4 x 18 x 4.1 cm
Language: English

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.

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.