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010   $a9783662691021$b(electronic bk.)
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024 7 $a10.1007/978-3-662-69102-1
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101 0 $aeng
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200 10$aMathematics of Information $eTheory and Applications of Shannon-Wiener Information /$fby Stefan Schäffler
205   $a1st ed. 2024.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2024.
215   $a1 online resource (154 pages)
225 1 $aMathematics Study Resources,$x2731-3832 ;$v9
311 08$aPrint version: Schäffler, Stefan Mathematics of Information Berlin, Heidelberg : Springer Berlin / Heidelberg,c2024 9783662691014 
327   $aIntroduction - 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.
330   $aStarting with the Shannon-Wiener approach to mathematical information theory, allowing a mathematical "measurement" of an amount of information, the book begins by defining the terms message and information and axiomatically assigning an amount of information to a probability. The second part explores countable probability spaces, leading to the definition of Shannon entropy based on the average amount of information; three classical applications of Shannon entropy in statistical physics, mathematical statistics, and communication engineering are presented, along with an initial glimpse into the field of quantum information. The third part is dedicated to general probability spaces, focusing on the information-theoretical analysis of dynamic systems. The book builds on bachelor-level knowledge and is primarily intended for mathematicians and computer scientists, placing a strong emphasis on rigorous proofs. Prof. Dr. Dr. Stefan Schäffler, University of the German Federal Armed Forces Munich, Faculty of Electrical Engineering and Information Technology, Chair of Mathematics and Operations Research. The translation was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content. This book is a translation of an original German edition. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation.
410  0$aMathematics Study Resources,$x2731-3832 ;$v9
606   $aProbabilities
606   $aComputer science$xMathematics
606   $aQuantum computers
606   $aMathematical physics
606   $aStatistics
606   $aProbability Theory
606   $aMathematical Applications in Computer Science
606   $aQuantum Computing
606   $aMathematical Physics
606   $aStatistics
615  0$aProbabilities.
615  0$aComputer science$xMathematics.
615  0$aQuantum computers.
615  0$aMathematical physics.
615  0$aStatistics.
615 14$aProbability Theory.
615 24$aMathematical Applications in Computer Science.
615 24$aQuantum Computing.
615 24$aMathematical Physics.
615 24$aStatistics.
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