The Theory of Probability
Explorations and Applications

From classical foundations to modern theory, this comprehensive guide to probability interweaves mathematical proofs, historical context and detailed illustrative applications.

Santosh S. Venkatesh (Author)

9781107024472, Cambridge University Press

Hardback, published 8 November 2012

827 pages, 100 b/w illus. 26 tables 528 exercises
25.3 x 17.9 x 4.1 cm, 1.75 kg

'… 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 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.

Subject Areas: Maths for engineers [TBJ], Engineering: general [TBC], Technology: general issues [TB], Applied physics [PHV], Stochastics [PBWL], Applied mathematics [PBW], Probability & statistics [PBT], Mathematics [PB]