國立虎尾科技大學 |

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

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Mathematics of information/ by Stefan Schäffler.
其他題名:	theory and applications of Shannon-Wiener information /
作者:	Schäffler, Stefan.
出版者:	Berlin, Heidelberg :Springer Berlin Heidelberg : : 2024.,
面頁冊數:	xvii, 150 p. :ill., digital ; : 24 cm.;
Contained By:	Springer Nature eBook
標題:	Mathematical Physics. -
電子資源:	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 ;4..

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:

786661
Mathematical Physics.

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

Dewey Class. No.: 519.2

Mathematics of information = theory and applications of Shannon-Wiener information /
LDR:03199nam a2200373 a 4500 001 1134271
003 DE-He213
005 20240723130741.0
006 m d
007 cr nn 008maaau
008 241213s2024 gw s 0 eng d
020 $a 9783662691021 $q (electronic bk.)
020 $a 9783662691014 $q (paper)
024 7 $a 10.1007/978-3-662-69102-1 $2 doi
035 $a 978-3-662-69102-1
040 $a GP $c GP
041 1 $a eng $h ger
050 4 $a QA10.4 $b .S33 2024
072 7 $a PBT $2 bicssc
072 7 $a PBWL $2 bicssc
072 7 $a MAT029000 $2 bisacsh
072 7 $a PBT $2 thema
072 7 $a PBWL $2 thema
082 0 4 $a 519.2 $2 23
090 $a QA10.4 $b .S296 2024
100 1 $a Schäffler, Stefan. $3 1455655
240 1 0 $a Mathematik der Information. $l English
245 1 0 $a Mathematics of information $h [electronic resource] : $b theory and applications of Shannon-Wiener information / $c by Stefan Schäffler.
260 $a Berlin, Heidelberg : $c 2024. $b Springer Berlin Heidelberg : $b Imprint: Springer,
300 $a xvii, 150 p. : $b ill., digital ; $c 24 cm.
490 1 $a Mathematics study resources, $x 2731-3832 ; $v v. 9
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.
520 $a 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.
650 2 4 $a Mathematical Physics. $3 786661
650 2 4 $a Quantum Computing. $3 883739
650 2 4 $a Mathematical Applications in Computer Science. $3 815331
650 1 4 $a Probability Theory. $3 1366244
650 0 $a Statistics. $3 556824
650 0 $a Distribution (Probability theory) $3 527721
650 0 $a Information theory in mathematics. $3 1106176
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
830 0 $a Mathematics study resources ; $v 4. $3 1408225
856 4 0 $u https://doi.org/10.1007/978-3-662-69102-1
950 $a Mathematics and Statistics (SpringerNature-11649)