Algorithms and Automatic Computing Machines

ALTHOUGH ALGORITHMS have been known and used since antiquity, the theory of algorithms has been developed almost entirely in the twentieth century. Fundamental to the theory is the question of algorithmic solvability and unsolvability. In defining rigorously the term algorithm the author considers the close relation between algorithms and computing machines. Indeed, he proves the algorithmic unsolvability of several problems using a special type of computing machine called the Turing machine. The reader will need no specific information from other branches of mathematics beyond intermediate algebra to be able to read the book. However, he will have to be able to follow a rather complex train of logical thought. References to several of the topics discussed are given in the Bibliography.