"A Mathematical Theory of Communication" is an article by

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

Claude E. Shannon published in '' Bell System Technical Journal'' in 1948. It was renamed ''The Mathematical Theory of Communication'' in the 1949 book of the same name, a small but significant title change after realizing the generality of this work. It became one of the most cited scientific articles and gave rise to the field of

information theory Information theory is the scientific study of the quantification (science), quantification, computer data storage, storage, and telecommunication, communication of information. The field was originally established by the works of Harry Nyquist a ...

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'' (), which was published as a

paperback A paperback (softcover, softback) book is one with a thick paper or paperboard cover, and often held together with adhesive, glue rather than stitch (textile arts), stitches or Staple (fastener), staples. In contrast, hardcover (hardback) book ...

in 1963 (). The book contains an additional article by

Warren Weaver Warren Weaver (July 17, 1894 – November 24, 1978) was an American scientist, mathematician, and science administrator. He is widely recognized as one of the pioneers of machine translation and as an important figure in creating support for scien ...

, providing an overview of the theory for a more general audience.

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 In signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The '' IEEE Transactions on Signal Processing' ...

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 In information theory, the entropy of a random variable is the average level of "information", "surprise", or "uncertainty" inherent to the variable's possible outcomes. Given a discrete random variable X, which takes values in the alphabet \ ...

and redundancy, and introduced the term

bit The bit is the most basic unit of information in computing and digital communications. The name is a portmanteau of binary digit. The bit represents a logical state with one of two possible values. These values are most commonly represente ...

(which Shannon credited to

John Tukey John Wilder Tukey (; June 16, 1915 – July 26, 2000) was an American mathematician and statistician, best known for the development of the fast Fourier Transform (FFT) algorithm and box plot. The Tukey range test, the Tukey lambda distributi ...

) as a unit of information. It was also in this paper that the

Shannon–Fano coding In the field of data compression, Shannon–Fano coding, named after Claude Shannon and Robert Fano, is a name given to two different but related techniques for constructing a prefix code based on a set of symbols and their probabilities (estimat ...

technique was proposed – a technique developed in conjunction with

Robert Fano Roberto Mario "Robert" Fano (11 November 1917 – 13 July 2016) was an Italian-American computer scientist and professor of electrical engineering and computer science at the Massachusetts Institute of Technology. He became a student and working ...

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(PDF) "A Mathematical Theory of Communication" by C. E. Shannon
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Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher le ...

Khan Academy video about "A Mathematical Theory of Communication"
{{DEFAULTSORT:Mathematical Theory of Communication 1963 non-fiction books Information theory Computer science books Mathematics books Mathematics papers Works originally published in American magazines 1948 documents Works originally published in science and technology magazines Texts related to the history of the Internet Claude Shannon

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