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Schäffler, Stefan.

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Mathematics of information = theory and applications of Shannon-Wiener information /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Mathematics of information/ by Stefan Schäffler.
Reminder of title:	theory and applications of Shannon-Wiener information /
Author:	Schäffler, Stefan.
Published:	Berlin, Heidelberg :Springer Berlin Heidelberg : : 2024.,
Description:	xvii, 150 p. :ill., digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer Nature eBook
Subject:	Information theory in mathematics. -
Online resource:	https://doi.org/10.1007/978-3-662-69102-1
ISBN:	9783662691021

Mathematics of information = theory and applications of Shannon-Wiener information /
Schäffler, Stefan.

Mathematics of informationtheory and applications of Shannon-Wiener information /[electronic resource] :by Stefan Schäffler. - Berlin, Heidelberg :Springer Berlin Heidelberg :2024. - xvii, 150 p. :ill., digital ;24 cm. - Mathematics study resources,v. 92731-3832 ;. - Mathematics study resources ;v. 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.

ISBN: 9783662691021

Standard No.: 10.1007/978-3-662-69102-1doiSubjects--Topical Terms:

757432
Information theory in mathematics.

LC Class. No.: QA10.4 / .S33 2024

Dewey Class. No.: 519.2

Mathematics of information = theory and applications of Shannon-Wiener information /
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505 0 $a 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.
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