Mathematics of Information
Mathematics of Information: Theory and Applications of Shannon-Wiener Information
English | 2024 | ISBN: 3662691019 | 167 Pages | PDF EPUB (True) | 16 MB
English | 2024 | ISBN: 3662691019 | 167 Pages | PDF EPUB (True) | 16 MB
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.