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020 _a9783662691021
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024 7 _a10.1007/978-3-662-69102-1
_2doi
050 4 _aQA273.A1-274.9
072 7 _aPBT
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072 7 _aMAT029000
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_2thema
100 1 _aSchäffler, Stefan.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_981152
245 1 0 _aMathematics of Information
_h[electronic resource] :
_bTheory and Applications of Shannon-Wiener Information /
_cby Stefan Schäffler.
250 _a1st ed. 2024.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2024.
300 _aXVII, 150 p. 27 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aMathematics Study Resources,
_x2731-3832 ;
_v9
505 0 _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.
520 _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.
650 0 _aProbabilities.
_965724
650 0 _aComputer science
_xMathematics.
_964041
650 0 _aQuantum computers.
_965955
650 0 _aMathematical physics.
650 0 _aStatistics .
_965982
650 1 4 _aProbability Theory.
_967428
650 2 4 _aMathematical Applications in Computer Science.
_965518
650 2 4 _aQuantum Computing.
_964754
650 2 4 _aMathematical Physics.
650 2 4 _aStatistics.
_965982
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783662691014
776 0 8 _iPrinted edition:
_z9783662691038
830 0 _aMathematics Study Resources,
_x2731-3832 ;
_v9
_981153
856 4 0 _uhttps://doi.org/10.1007/978-3-662-69102-1
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