ENGLISH

Mathematics of Information: Theory and Applications of Shannon-Wiener Information

By Stefan Schäffler

Book information

Publisher
Springer
Year
2024
ISBN
3662691019, 9783662691014, 9783662691021
DOI
10.1007/978-3-662-69102-1
ISSN
2731-3824
LCC
Q360
Language
english
Format
EPUB
Filesize
12 MB (12829669 bytes)
Series
Mathematics Study Resources, 9
Edition
1
Pages
xvii, 150\0
Orientation
no
Paginated
no
Scanned
portrait
Time added
2024-07-24 11:56:51
Differential Entropy; Dynamic Systems; Quantum Com

Description

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.

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