Page 13 - Discrete Mathematics and Its Applications

xii Preface

numbered exercises are provided at the back of the text. The solutions include proofs in which
most of the steps are clearly spelled out.

REVIEW QUESTIONS A set of review questions is provided at the end of each chapter.
These questions are designed to help students focus their study on the most important concepts
and techniques of that chapter. To answer these questions students need to write long answers,
rather than just perform calculations or give short replies.

SUPPLEMENTARY EXERCISE SETS Each chapter is followed by a rich and varied
set of supplementary exercises. These exercises are generally more difficult than those in the
exercise sets following the sections. The supplementary exercises reinforce the concepts of the
chapter and integrate different topics more effectively.

COMPUTER PROJECTS Each chapter is followed by a set of computer projects. The
approximately 150 computer projects tie together what students may have learned in computing
and in discrete mathematics. Computer projects that are more difficult than average, from both
a mathematical and a programming point of view, are marked with a star, and those that are
extremely challenging are marked with two stars.

COMPUTATIONS AND EXPLORATIONS A set of computations and explorations is
included at the conclusion of each chapter. These exercises (approximately 120 in total) are de-
signed to be completed using existing software tools, such as programs that students or instruc-
tors have written or mathematical computation packages such as Maple TM or Mathematica TM .
Many of these exercises give students the opportunity to uncover new facts and ideas through
computation. (Some of these exercises are discussed in the Exploring Discrete Mathematics
companion workbooks available online.)

WRITING PROJECTS Each chapter is followed by a set of writing projects. To do these
projects students need to consult the mathematical literature. Some of these projects are historical
in nature and may involve looking up original sources. Others are designed to serve as gateways
to new topics and ideas. All are designed to expose students to ideas not covered in depth in
the text. These projects tie mathematical concepts together with the writing process and help
expose students to possible areas for future study. (Suggested references for these projects can
be found online or in the printed Student’s Solutions Guide.)

APPENDIXES There are three appendixes to the text. The first introduces axioms for real
numbersandthepositiveintegers,andillustrateshowfactsareproveddirectlyfromtheseaxioms.
The second covers exponential and logarithmic functions, reviewing some basic material used
heavily in the course. The third specifies the pseudocode used to describe algorithms in this text.

SUGGESTED READINGS A list of suggested readings for the overall book and for each
chapter is provided after the appendices. These suggested readings include books at or below
the level of this text, more difficult books, expository articles, and articles in which discoveries
in discrete mathematics were originally published. Some of these publications are classics,
published many years ago, while others have been published in the last few years.

How to Use This Book

This text has been carefully written and constructed to support discrete mathematics courses
at several levels and with differing foci. The following table identifies the core and optional
sections. An introductory one-term course in discrete mathematics at the sophomore level can
be based on the core sections of the text, with other sections covered at the discretion of the