Mathematics of Information
Theory and Applications of Shannon-Wiener Information
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Beschreibung
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.
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.
The translation was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content.
This book is a translation of an original German edition. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation.
Ausgehend vom Shannon-Wiener-Zugang zur mathematischen Informationstheorie beginnt das Buch mit einer Abgrenzung der Begriffe Nachricht und Information und der axiomatischen Zuordnung einer Informationsmenge zu einer Wahrscheinlichkeit. Im zweiten Teil werden abzählbare Wahrscheinlichkeitsräume untersucht, deren mittlere Informationsmenge zur Definition der Shannon-Entropie führt; dabei werden drei klassische Anwendungen der Shannon-Entropie in der statistischen Physik, der mathematischen Statistik und der Nachrichtentechnik vorgestellt, und es wird ein erster Einblick in den Bereich Quanteninformation gegeben. Der dritte Teil behandelt die informationstheoretische Analyse dynamischer Systeme.
Das Buch baut auf Bachelor-Wissen auf und legt großen Wert auf exakte Beweisführung.
Information Theory as a Mathematical Subdiscipline and Interface to Computer Science Exact Anchoring of the Concept of Information in Probability Theory Introduces Applications of Information Theory, Including Mathematical Statistics, Statistical Physics, and Communication Engineering
Autor*in
Stefan Schäffler
Themen in »Mathematics of Information«
Differential Entropy Dynamic Systems Quantum Computation Shannon Entropy Sufficient Statistics information and communication, circuits