04176nam a22006015i 4500 978-3-662-69102-1 DE-He213 20251030112646.0 cr nn 008mamaa 240723s2024 gw | s |||| 0|eng d 9783662691021 978-3-662-69102-1 10.1007/978-3-662-69102-1 doi QA273.A1-274.9 PBT bicssc PBWL bicssc MAT029000 bisacsh PBT thema PBWL thema Schäffler, Stefan. author. aut http://id.loc.gov/vocabulary/relators/aut 81152 Mathematics of Information [electronic resource] : Theory and Applications of Shannon-Wiener Information / by Stefan Schäffler. 1st ed. 2024. Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2024. XVII, 150 p. 27 illus. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Mathematics Study Resources, 2731-3832 ; 9 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. 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. Probabilities. 65724 Computer science Mathematics. 64041 Quantum computers. 65955 Mathematical physics. Statistics . 65982 Probability Theory. 67428 Mathematical Applications in Computer Science. 65518 Quantum Computing. 64754 Mathematical Physics. Statistics. 65982 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783662691014 Printed edition: 9783662691038 Mathematics Study Resources, 2731-3832 ; 9 81153 https://doi.org/10.1007/978-3-662-69102-1 ZDB-2-SMA ZDB-2-SXMS 61854 61854