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Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study. Number theory may be subdivided into several fields, according to the methods used and the type of questions investigated. These fields include analytic number theory, algebraic number theory, geometry of numbers, combinatorial number theory and computational number theory.
Number theory, long regarded as the purest of the pure sciences, has recently begun to find applications in cryptography. The recent invention of public-key cryptosystems, which are usually based on the difficulty of a particular number-theoretic computation, has encouraged research in number theory which is essentially applied.
Post graduate qualifications are required for this field.