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When I read about Information Theory, for example on Wikipedia, I can never find statements that say if Information Theory is "real" Mathematics with underlying axioms, a notion of "proof beyond doubt" and such.

On the one hand I've read it's an engineering subject with a high level of abstraction (German Wikipedia) and "entropy" is a term used in thermodynamics, but on the other hand I recall reading proofs when seeking an answer to this question (didn't understand the least bit though) and it seems like Information Theory is a branch of probability theory (also, it's part of this website about math), but I'm still confused.

So, is Information Theory Mathematics?

Thanks in advance!

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  • $\begingroup$ There are entire Math books written on the subject, see amazon.com/Coding-Information-Theory-Graduate-Mathematics/dp/… . $\endgroup$ – Baby Dragon Dec 28 '14 at 21:02
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    $\begingroup$ Probability theory is the foundation of Information theory. This is a "theory" because Shannon defined the notion of "information entropy", and using probability theory, for instance, he proved the implications about the distribution of the information in a space and the "conection" wirh topological spaces. I think the Information theory has the same level of statistics, i.e., it's a branch of applied mathematics. $\endgroup$ – Cristhian Gz Dec 28 '14 at 21:03
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Yes, Information Theory is a branch of mathematics, although its practitioners are often found in departments of Electrical and Computer Engineering or Computer Science.

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Instead of mathematics, I would say it's probability/statistics. The basic idea, entropy, is defined in terms of the probability.

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    $\begingroup$ Probability is mathematics. Statistics is applied mathematics. $\endgroup$ – Yuval Filmus Dec 28 '14 at 21:30

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