Information theory

Information theory is a discipline in applied mathematics involving the quantification of data with the goal of enabling as much data as possible to be reliably stored on a medium and/or communicated over a channel. The measure of data, known as information entropy, is usually expressed by the average number of bits needed for storage or communication. For example, if a daily weather description has 3 bits of entropy, then, over enough days, we can describe daily weather with an average of approximately 3 bits per day (each bit being a 0 or a 1).
Applications of fundamental topics of information theory include ZIP files (lossless data compression), MP3s (lossy data compression), and DSL (channel coding). The field is at the crossroads of mathematics, statistics, computer science, physics, neurobiology, and electrical engineering. Its impact has been crucial to success of the Voyager missions to deep space, the invention of the CD, the feasibility of mobile phones, the development of the Internet, the study of linguistics and of human perception, the understanding of black holes, and numerous other fields.