Discrete Mathematics, 2nd edition

Book Preface

This book is designed for an introductory course in discrete mathematics for the prospective computer scientist, applied mathematician, or engineer who would like to learn how the ideas apply to computer science. The choice of topicsand the depth and breadth of coverage-reflects the desire to provide students with the foundations needed to successfully complete courses in undergraduate computer science programs. The book is the outgrowth of a course at Portland State University that has evolved over twenty years from a course for upperdivision students into a course for sophomores.

The book can be read by anyone with a good background in high school mathematics; therefore, it could also be used at the freshman level or at the advanced high school level. Although the book is intended for future computer scientists, applied mathematicians, or engineers, it may also be suitable for a wider audience. For example, it could be used in courses for students who intend to teach discrete mathematics in high school.

This book differs in several ways from current books about discrete mathematics. It presents an elementary and unified introduction to a collection of topics that previously have not been available in a single source. A major feature of the book is the unification of the material so that it doesn’t fragment into a vast collection of seemingly unrelated ideas. This is accomplished through organization and focus.

The book is organized more along the lines of technique than on a subjectby- subject basis. The focus throughout the book is on the computation and construction of objects. Therefore, many traditional topics are dispersed throughout the text to places where they fit naturally with the techniques under discussion. For example, to read about properties of-and techniques for processingnatural numbers, lists, strings, graphs, or trees, it’s necessary to look in the index or scan the table of contents to find the several places where they are found.