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{{Short description|1948 article on theory of communication by Claude Shannon}}
"'''A Mathematical Theory of Communication'''" is an article by [[Biography:Mathematician|mathematician]] Claude E. Shannon published in ''[[Engineering:Bell System Technical Journal|Bell System Technical Journal]]'' in 1948.<ref name="Shannon_1948_1"/><ref name="Shannon_1948_2"/><ref>{{cite book| 
title=Information Theory: Tracts in Pure & Applied Mathematics|
last=Ash|
first=Robert B.|
location=New York|
publisher=John Wiley & Sons Inc|
year=1966|
isbn=0-470-03445-9}}</ref><ref>{{Cite book|
title=Information Theory and Network Coding| url=https://archive.org/details/informationtheor00yeun| url-access=limited|
last=Yeung|
first=Raymond W.|
year=2008|
publisher=Springer|
isbn=978-0-387-79233-0|
chapter=The Science of Information| pages=[https://archive.org/details/informationtheor00yeun/page/n18 1]–4|
doi=10.1007/978-0-387-79234-7_1}}</ref> It was renamed '''''The Mathematical Theory of Communication''''' in the 1949 book of the same name,<ref name="Shannon_1949"/> a small but significant title change after realizing the generality of this work. It has tens of thousands of citations which is rare for a scientific article and gave rise to the field of [[Information theory|information theory]]. ''Scientific American'' referred to the paper as the "Magna Carta of the Information Age".<ref>{{Cite web |last=Goodman |first=Rob |last2=Soni |first2=Jimmy |date=2018 |title=Genius in Training |url=https://alumni.umich.edu/michigan-alum/genius-in-training/ |access-date=2023-10-31 |website=Alumni Association of the University of Michigan |language=en-US}}</ref>

==Publication==
The article was the founding work of the field of information theory. It was later published in 1949 as a book titled ''The Mathematical Theory of Communication'' ({{ISBN|0-252-72546-8}}), which was published as a paperback in 1963 ({{ISBN|0-252-72548-4}}). The book contains an additional article by [[Biography:Warren Weaver|Warren Weaver]], providing an overview of the theory for a more general audience.

==Contents==
[[File:Shannon communication system.svg|thumb|right|343px|Shannon's diagram of a general [[Social:Communications system|communications system]], showing the process by which a message sent becomes the message received (possibly corrupted by noise)]]
This work is known for introducing the concepts of [[Engineering:Channel capacity|channel capacity]] as well as the [[Noisy-channel coding theorem|noisy channel coding theorem]].

Shannon's article laid out the basic elements of communication:
*An information source that produces a message
*A transmitter that operates on the message to create a signal which can be sent through a channel
*A channel, which is the medium over which the signal, carrying the information that composes the message, is sent
*A receiver, which transforms the signal back into the message intended for delivery
*A destination, which can be a person or a machine, for whom or which the message is intended

It also developed the concepts of information entropy and [[Redundancy (information theory)|redundancy]], and introduced the term [[Bit|bit]] (which Shannon credited to [[Biography:John Tukey|John Tukey]]) as a unit of information. It was also in this paper that the [[Shannon–Fano coding]] technique was proposed – a technique developed in conjunction with [[Biography:Robert Fano|Robert Fano]].

==References==
{{Reflist|refs=
<ref name="Shannon_1948_1">{{cite journal |author-last=Shannon |author-first=Claude Elwood |title=A Mathematical Theory of Communication |journal=[[Engineering:Bell System Technical Journal|Bell System Technical Journal]] |volume=27 |issue=3 |pages=379–423 |date=July 1948 |doi=10.1002/j.1538-7305.1948.tb01338.x |hdl=11858/00-001M-0000-002C-4314-2 |url=http://cm.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf |archive-url=https://web.archive.org/web/19980715013250/http://cm.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf |url-status=dead |archive-date=1998-07-15 |quote=The choice of a logarithmic base corresponds to the choice of a unit for measuring information. If the base 2 is used the resulting units may be called binary digits, or more briefly ''[[Bit|bit]]s'', a word suggested by J. W. Tukey.|hdl-access=free }}</ref>
<ref name="Shannon_1948_2">{{cite journal |author-last=Shannon |author-first=Claude Elwood |title=A Mathematical Theory of Communication |journal=[[Engineering:Bell System Technical Journal|Bell System Technical Journal]] |volume=27 |issue=4 |pages=623–656 |date=October 1948 |doi=10.1002/j.1538-7305.1948.tb00917.x |hdl=11858/00-001M-0000-002C-4314-2|hdl-access=free }}</ref>
<ref name="Shannon_1949">{{cite book |author-last1=Shannon |author-first1=Claude Elwood |author-first2=Warren |author-last2=Weaver |author-link2=Warren Weaver |title=The Mathematical Theory of Communication |publisher=University of Illinois Press |date=1949 |isbn=0-252-72548-4 |url=http://cm.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf |archive-url=https://web.archive.org/web/19980715013250/http://cm.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf |url-status=dead |archive-date=1998-07-15}}</ref>
}}

== External links ==
* [https://people.math.harvard.edu/~ctm/home/text/others/shannon/entropy/entropy.pdf (PDF) "A Mathematical Theory of Communication" by C. E. Shannon] (reprint with corrections) hosted by the [http://math.harvard.edu/ Harvard Mathematics Department], at [[Organization:Harvard University|Harvard University]]
** Original publications: {{Cite book |url=https://archive.org/details/sim_att-technical-journal_1948-07_27_3/page/n2/ |title=The Bell System Technical Journal 1948-07: Vol 27 Iss 3 |date=1948-07-01 |publisher=AT & T Bell Laboratories |others=Internet Archive |pages=379-423 |language=en}}, {{Cite book |url=https://archive.org/details/sim_att-technical-journal_1948-10_27_4/page/623/ |title=The Bell System Technical Journal 1948-10: Vol 27 Iss 4 |date=1948-10-01 |publisher=AT & T Bell Laboratories |others=Internet Archive |pages=623-656 |language=en}}
* [https://www.khanacademy.org/computing/computer-science/informationtheory/moderninfotheory/v/a-mathematical-theory-of-communication Khan Academy video about "A Mathematical Theory of Communication"]

{{DEFAULTSORT:Mathematical Theory of Communication}}
[[Category:Information theory]]
[[Category:Computer science books]]
[[Category:Mathematics books]]

{{Sourceattribution|A Mathematical Theory of Communication}}