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
Reviews for the first edition: 'I found the book interesting and entertaining … The level of difficulty of the material is well judged …' D. A. Stephens, The Statistician
'This text provides a blend of the traditional disciplines of probability theory and the relatively new field of information science in a well written manner … the author succeeds in introducing concepts of probability theory gently paced and user friendly as stated on page xi of the preface … The blend of probability theory and information science makes this an innovative text... The innovative blend of probability theory and information theory make this text a good choice for teachers wanting to present both a traditional background and modern ideas to their students.' Journal of the American Statistical Association
'Reviewing this book was a pleasure. Clearly the author is delighted by his subject and this attitude is communicated well … this is an excellent book which will make a stimulating text for Honours courses in probability for applied mathematicians, statisticians, physicists or engineers' John M. Halley, The Statistician
'… a nice introductory text for a modern course on basic facts in the theory of probability and information. The author always has in mind that many students, especially those specializing in informatics and/or technical sciences, do not often have a firm background in traditional mathematics. Therefore he attempts to keep the development of material gently paced and user-friendly.' EMS Newsletter
Product details
August 2008Hardback
9780521899048
250 pages
252 × 177 × 19 mm
0.73kg
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.
