Algorithmics: The Spirit of Computing

Abstract

AbstractThe fundamental notion of an algorithm is presented here, the focus being on its traditional, “symbol-based” conception. A carefully selected set of formal models of an algorithm and universal computer is then presented in a non-traditional and novel manner. These and other formal models are the theoretical foundation for the discipline of computer science, which was developed by mathematical logicians during the 1930s, before the advent of the electronic, digital computer in the mid-1940s. During the early days of the ensuing computer revolution, numerical computation was paramount, and its practical foundation was the finite-precision, floating-point model. This model was developed by numerical analysts, who played a leading role in the creation of the computer science discipline, and it is described in detail. The basic concept of a symbol-based algorithm led to the much broader conception of algorithmic systems for computation, for example, neural, quantum, and natural, as is briefly itemized in the concluding section. The metaphorical phrase, “under the rubric of algorithm,” refers to the overarching umbrella of modern computer science.