TY  - BOOK
AU  - Schäffler,Stefan
ED  - SpringerLink (Online service)
TI  - Mathematics of Information: Theory and Applications of Shannon-Wiener Information 
T2  - Mathematics Study Resources,
SN  - 9783662691021
AV  - QA273.A1-274.9 
PY  - 2024///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg, Imprint: Springer
KW  - Probabilities
KW  - Computer science
KW  - Mathematics
KW  - Quantum computers
KW  - Mathematical physics
KW  - Statistics 
KW  - Probability Theory
KW  - Mathematical Applications in Computer Science
KW  - Quantum Computing
KW  - Mathematical Physics
KW  - Statistics
N1  - 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
N2  - 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
UR  - https://doi.org/10.1007/978-3-662-69102-1
ER  -