B 74-27 Program Test Methods

Computer Science bears approximately the same relationship to computers as Aerodynamics bears to sailboats. It describes how they work but has little impact on their design which is based almost entirely on intuition strengthened and controlled by experience. However, one day, the Wright brothers of the "ultra-computer" will get to their Kitty Hawk and Computer Science will come into its own. In preparation for that day stands the present volume. It is an excellent mathematics textbook written by an experienced teacher. The text is intended as an introduction to discrete mathematics for computer science and engineering undergraduates. Professor Stone develops his subject from elementary logic through linear finite-state machines. The first chapter is essentially a review of sets, functions and algebraic structures which the author has found recently to be familiar to most of his students. Chapter two then introduces groups and completes the foundations for the rest of the book. The main thrust of development proceeds via sequential machines and a chapter on rings and fields before reaching the final chapter on linear finite-state machines. The author has then added almost as an afterthought a chapter on Boolean algebra. The book derives from a course which the author has taught many times, and the impression comes through that he taught it rather well. The material is presented with a well balanced mixture of informal, expository text with formal mathematical statement. He has recognized that a definition is not an explanation and must be put into context if it is to be properly understood by most students. Each section begins with an informal introduction which sets the stage for the formal development. Many contexts are set by posing meaningful problems which the student is invited to solve before and after studying the mathematical material. The author has used diagrams liberally and to good effect. Each section of every chapter ends with a set of exercises. One minor point of occasional confusion lies in the fact that both diagrams and exercises use the same numbering scheme. An ample bibliography is supplied and referred to only by author and date (year) and not by irritating reference numbers. The title of this book refers to the application of discrete structures and includes a chapter on applications. But the author has had to try very hard to come up with any significant examples. Probably the most significant examples occur in the discussion of feedback shift registers, and of the three presented there, only one really