Probability and Information: An Integrated Approach

ISBN-13: 9780521727884 / Angielski / Miękka / 2008 / 290 str.

David Applebaum

Opis

This new and updated textbook is an excellent way to introduce probability and information theory to students new to mathematics, computer science, engineering, statistics, economics, or business studies. Only requiring knowledge of basic calculus, it begins by building a clear and systematic foundation to probability and information. Classic 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. Newly covered for this edition is modern material on Markov chains and their entropy. 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.

Recenzje

'… 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

Spis treści

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.