Probability and Information
Probability and Information
This updated textbook is an excellent way to introduce probability and information theory to new students in mathematics, computer science, engineering, statistics, economics, or business studies. Only requiring knowledge of basic calculus, it starts by building a clear and systematic foundation to the subject: the concept of probability is given particular attention via a simplified discussion of measures on Boolean algebras. The theoretical ideas are then applied to practical areas such as statistical inference, random walks, statistical mechanics and communications modelling. Topics covered include discrete and continuous random variables, entropy and mutual information, maximum entropy methods, the central limit theorem and the coding and transmission of information, and added for this new edition is material on Markov chains and their entropy. Lots of examples and exercises are included to illustrate how to use the theory in a wide range of applications, with detailed solutions to most exercises available online for instructors.
- Integrated approach to probability and information suitable for pure or applied students
- Illustrates a wide range of applications in science and mathematics
- Modern, rigorous approach that needs only a background in basic calculus
Reviews & endorsements
"... the writing is authoritative, and well-tailored to the intended readership. Places where more advanced mathematics is required are indicated clearly, the illustrative material is well-chosen. Any lecturer seeking a text, at this level, to recommend to students, should give this book serious consideration."
John Haigh for Significance
Product details
September 2008Paperback
9780521727884
290 pages
247 × 174 × 14 mm
0.59kg
65 b/w illus. 3 tables 240 exercises
Available
Table of Contents
- Preface to the first edition
- Preface to the second edition
- 1. Introduction
- 2. Combinatorics
- 3. Sets and measures
- 4. Probability
- 5. Discrete random variables
- 6. Information and entropy
- 7. Communication
- 8. Random variables with probability density functions
- 9. Random vectors
- 10. Markov chains and their entropy
- Exploring further
- Appendix 1. Proof by mathematical induction
- Appendix 2. Lagrange multipliers
- Appendix 3. Integration of exp (-½x²)
- Appendix 4. Table of probabilities associated with the standard normal distribution
- Appendix 5. A rapid review of Matrix algebra
- Selected solutions
- Index.
