The author's intent in writing this book is to cover in descriptive terms a good part of the mathematics that bears upon computer programming and, in some cases, upon computer design. We are not concerned with the substantial body of mathematics relevant to the uses of the computer but restrict the discussion to those subjects that have implications to the fundamental nature of the computing process.
The appropriate subject areas—mathematical logic and foundations, computability and recursive function theory, formal linguistics, and automata theory—are vast, with a rapidly growing body of literature that has been undoubtedly stimulated by the sweeping role of the computer. This book does not provide a treatment of these topics that adheres to the very highest standards of mathematical rigor and abstract formalism. It is not primarily intended for serious students of mathematics in advanced undergraduate or graduate courses devoted to these subjects, where a more formal and complete development might be desirable. It is possible, however, that such students may find in the sequel a perspective or an emphasis that is different from that which might appear in a more formal coverage of these topics.