Review of Applied Number Theory

Abstract

Number theory (or the theory of numbers [1]) starts from elementary (not necessarily simple and easy, and in fact, it is often very hard) number theory and grows up with analytic number theory (including additive and multiplicative number theory), algebraic number theory, geometric number theory (including arithmetic algebraic geometry), combinatorial number theory, computational number theory (including algorithmic number theory), to name just a few. Applied number theory, on the other hand, is involved in the application of various branches of number theory to a wide range of areas including, e.g., physics, chemistry, biology, graphics, arts, music, and particularly computing and digital communications [2]. Number theory was once viewed as the purest of the pure mathematics, with little application to other areas. However, with the advent of modern computers and digital communications, number theory becomes increasingly important and applicable to many areas ranging from natural sciences, engineering to social sciences.