Ferland - Discrete Mathematics and Applications

This book is intended for a one- or two-semester course in discrete mathematics. Such a course is typically taken by mathematics, mathematics education, and computer science majors, usually in their sophomore year. Calculus is not a prerequisite to use this book. Consequently, even freshmen with sufficient maturity can use it. Additionally, the second half of the book can be used for an introductory course in combinatorics and graph theory. The basic organization of the book can be seen in Contents.

For those designing a one-semester course that covers the core material, the following sections accommodate this approach and make up half of the sections of this book.

A two-semester course may most naturally be set to follow

. That introduction is spread over three sections to mitigate the difficulties with induction proofs that many students experience.

In is on combinatorics and graph theory.

The Introduction is a single section that should take approximately one class to cover. Some users may even skip it or assign it as reading. However, it is included to emphasize the link between .

A conscious effort has been made to give suggestive names to the theorems in this book whenever reasonable, with the common names used whenever possible (e.g., the Rational Roots Theorem and the Binomial Theorem). Consequently, theorems may be referred to by name rather than by an unenlightening number. The names should remind the reader of the content of the theorem and hence reduce the amount of page flipping. The index gives page references when desired.

The more than 3600 exercises throughout this book have been purposefully structured. Students are provided a rich supply of straightforward exercises before they encounter those that stretch their thinking. Several exercises that are very much like the examples in the text are included. These provide the students with ample opportunity to sharpen their teeth before moving on to bigger prey. Beyond the exercises that reinforce the central concepts, there are many that explore further both the theory and applications of these concepts. Exercises that may be particularly challenging are marked with an asterisk ().

Solutions are provided in the back of the book for the odd-numbered exercises from each section and all of the exercises from the review sections. Consequently, a balance is maintained between the odd and even exercises. That is, each odd-numbered exercise is generally followed by a similar even-numbered exercise. Instructors wanting to assign homework without solution references can assign the even problems. Students can use the odd exercises to help them with the even ones. Note that an answer listed in the back may be more brief than that required by the exercise. In particular, exercises demanding proofs are often answered in the back with sketches. Students are expected to flesh out the answer given to obtain the answer requested.

Two appendices containing background material are also provided. In describes the pseudocode in which algorithms are presented throughout the book.