Page 12 - Discrete Mathematics and Its Applications

Preface xi

FLEXIBILITY This text has been carefully designed for flexible use. The dependence
of chapters on previous material has been minimized. Each chapter is divided into sections of
approximately the same length, and each section is divided into subsections that form natural
blocks of material for teaching. Instructors can easily pace their lectures using these blocks.

WRITING STYLE The writing style in this book is direct and pragmatic. Precise mathe-
matical language is used without excessive formalism and abstraction. Care has been taken to
balance the mix of notation and words in mathematical statements.

MATHEMATICAL RIGOR AND PRECISION All definitions and theorems in this text
are stated extremely carefully so that students will appreciate the precision of language and
rigor needed in mathematics. Proofs are motivated and developed slowly; their steps are all
carefully justified. The axioms used in proofs and the basic properties that follow from them
are explicitly described in an appendix, giving students a clear idea of what they can assume in
a proof. Recursive definitions are explained and used extensively.

WORKED EXAMPLES Over 800 examples are used to illustrate concepts, relate different
topics, and introduce applications. In most examples, a question is first posed, then its solution
is presented with the appropriate amount of detail.

APPLICATIONS The applications included in this text demonstrate the utility of discrete
mathematics in the solution of real-world problems. This text includes applications to a wide va-
riety of areas, including computer science, data networking, psychology, chemistry, engineering,
linguistics, biology, business, and the Internet.

ALGORITHMS Results in discrete mathematics are often expressed in terms of algo-
rithms; hence, key algorithms are introduced in each chapter of the book. These algorithms
are expressed in words and in an easily understood form of structured pseudocode, which is
described and specified in Appendix 3. The computational complexity of the algorithms in the
text is also analyzed at an elementary level.

HISTORICAL INFORMATION The background of many topics is succinctly described
in the text. Brief biographies of 83 mathematicians and computer scientists are included as foot-
notes. These biographies include information about the lives, careers, and accomplishments of
these important contributors to discrete mathematics and images, when available, are displayed.
In addition, numerous historical footnotes are included that supplement the historical in-
formation in the main body of the text. Efforts have been made to keep the book up-to-date by
reflecting the latest discoveries.

KEY TERMS AND RESULTS A list of key terms and results follows each chapter. The
key terms include only the most important that students should learn, and not every term defined
in the chapter.

EXERCISES There are over 4000 exercises in the text, with many different types of
questions posed. There is an ample supply of straightforward exercises that develop basic skills,
a large number of intermediate exercises, and many challenging exercises. Exercises are stated
clearly and unambiguously, and all are carefully graded for level of difficulty. Exercise sets
contain special discussions that develop new concepts not covered in the text, enabling students
to discover new ideas through their own work.
∗
Exercises that are somewhat more difficult than average are marked with a single star ;
those that are much more challenging are marked with two stars ∗∗ . Exercises whose solutions
require calculus are explicitly noted. Exercises that develop results used in the text are clearly
identified with the right pointing hand symbol . Answers or outlined solutions to all odd-