The study of information by mathematical methods. Informally, information can be considered as the extent to which a message conveys what was previously unknown, and so is new or surprising. Mathematically, the rate at which information is conveyed from a source is identified with the entropy of the source (per second or per symbol). Although information theory is sometimes restricted to the entropy formulation of sources and channels, it may include coding theory, in which case the term is used synonymously with communication theory.