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Titlebook: Mathematics of Information; Theory and Applicati Stefan Schäffler Textbook 2024 The Editor(s) (if applicable) and The Author(s), under excl

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发表于 2025-3-21 19:07:46 | 显示全部楼层 |阅读模式
书目名称Mathematics of Information
副标题Theory and Applicati
编辑Stefan Schäffler
视频video
概述Information Theory as a Mathematical Subdiscipline and Interface to Computer Science.Exact Anchoring of the Concept of Information in Probability Theory.Introduces Applications of Information Theory,
丛书名称Mathematics Study Resources
图书封面Titlebook: Mathematics of Information; Theory and Applicati Stefan Schäffler Textbook 2024 The Editor(s) (if applicable) and The Author(s), under excl
描述.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..
出版日期Textbook 2024
关键词Differential Entropy; Dynamic Systems; Quantum Computation; Shannon Entropy; Sufficient Statistics; infor
版次1
doihttps://doi.org/10.1007/978-3-662-69102-1
isbn_softcover978-3-662-69101-4
isbn_ebook978-3-662-69102-1Series ISSN 2731-3824 Series E-ISSN 2731-3832
issn_series 2731-3824
copyrightThe Editor(s) (if applicable) and The Author(s), under exclusive license to Springer-Verlag GmbH, DE
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发表于 2025-3-21 21:40:34 | 显示全部楼层
The Entropyther hand, we cannot predict an outcome exactly when conducting the experiment, but only with a certain probability. The last section described such an experiment by examining a specific point in a German text to see what character is there. We based this on an alphabet of 30 different characters; t
发表于 2025-3-22 02:45:55 | 显示全部楼层
Conditional Probabilitieslity . as the probability of the event . given that the event . definitely occurs (conditional probability). One has, so to speak, reduced the set of possible outcomes Ω to the set .. If now . applies, it follows that .; in this case, the probability for . is not affected by the reduction of the set
发表于 2025-3-22 06:50:18 | 显示全部楼层
The Entropy of Partitionsre is no surjective mapping . (in symbols: .). It would now be obvious to demand the properties (P1)–(P3) for a probability measure . even when there are uncountably many results in Ω. Unfortunately, it turns out that for uncountable Ω there are no useful mappings . of this kind (see for example [Wa
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Conditional Expectationsitical in the discrete probability spaces considered. In order to now be able to investigate the question of sufficient statistics within the framework of general probability spaces, a generalization of the previously considered conditional probabilities is necessary. Starting from a probability spa
发表于 2025-3-22 21:52:03 | 显示全部楼层
e University of Antwerp (Belgium), 05-11 September 1993. It was held for the third time in Antwerp at the conference center of UIA, after successful meetings in 1979 and 1987 and an almost yearly tradition since the early 70‘s. The following figures illustrate the growing number of participants and
发表于 2025-3-23 03:43:25 | 显示全部楼层
Cuyt at the University of Antwerp (Belgium), 05-11 September 1993. It was held for the third time in Antwerp at the conference center of UIA, after successful meetings in 1979 and 1987 and an almost yearly tradition since the early 70‘s. The following figures illustrate the growing number of partici
发表于 2025-3-23 08:11:51 | 显示全部楼层
Stefan SchäfflerCuyt at the University of Antwerp (Belgium), 05-11 September 1993. It was held for the third time in Antwerp at the conference center of UIA, after successful meetings in 1979 and 1987 and an almost yearly tradition since the early 70‘s. The following figures illustrate the growing number of partici
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