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Starting with the Shannon-Wiener approach to mathematical information theory, allowing a mathematical "measurement" of an amount of information, the book begins by defining the terms message and information and axiomatically assigning an amount of information to a probability. The second part explores countable probability spaces, leading to the definition of Shannon entropy based on the average amount of information; three classical applications of Shannon entropy in statistical physics, mathematical statistics, and communication engineering are presented, along with an initial glimpse into the field of quantum information. The third part is dedicated to general probability spaces, focusing on the information-theoretical analysis of dynamic systems.
The book builds on bachelor-level knowledge and is primarily intended for mathematicians and computer scientists, placing a strong emphasis on rigorous proofs.
List of contents
Introduction - Symbols - List of figures - Part I Fundamentals. Message and information.- Information and chance.- Part II Countable systems. The entropy.- The maximum entropy principle.- Conditional probabilities.- Quantum information.- Part III General systems.- The entropy of partitions.- Stationary information sources.- Density functions and entropy.- Conditional expectations.- Literature.- Index.
About the author
Prof. Dr. Dr. Stefan Schäffler, University of the German Federal Armed Forces Munich, Faculty of Electrical Engineering and Information Technology, Chair of Mathematics and Operations Research.
