Algorithms: Main Ideas and Applications

The theory of algorithms not only answers philosophical questions but also is applicable to practical computing, as well as to software and hardware design. This text presents exact mathematical formulations of major concepts and facts of the theory of algorithms in a unified way. Precise mathematical statements are given, together with their underlying motivations, philosophical interpretations and historical developments, starting with Frege, Hilbert and Borel through Goedel and Turing up to Kolmogorov's results of 1950-1980. It is divided into two parts. The first part outlines the fundamental discoveries of the general theory of algorithms. Numerous applications are discussed in the second part. The concept of probabilistic algorithms is presented in the appendix. This work should be of interest to mathematicians, computer scientists, engineers and to everyone who uses algorithms.