Page 9 - Discrete Mathematics and Its Applications

viii Preface

2. Combinatorial Analysis: An important problem-solving skill is the ability to count or enu-
merate objects. The discussion of enumeration in this book begins with the basic techniques
of counting. The stress is on performing combinatorial analysis to solve counting problems
and analyze algorithms, not on applying formulae.
3. Discrete Structures: A course in discrete mathematics should teach students how to work
with discrete structures, which are the abstract mathematical structures used to represent
discrete objects and relationships between these objects. These discrete structures include
sets, permutations, relations, graphs, trees, and finite-state machines.
4. Algorithmic Thinking: Certain classes of problems are solved by the specification of an
algorithm. After an algorithm has been described, a computer program can be constructed
implementing it. The mathematical portions of this activity, which include the specification
of the algorithm, the verification that it works properly, and the analysis of the computer
memory and time required to perform it, are all covered in this text.Algorithms are described
using both English and an easily understood form of pseudocode.
5. Applications and Modeling: Discrete mathematics has applications to almost every conceiv-
able area of study. There are many applications to computer science and data networking
in this text, as well as applications to such diverse areas as chemistry, biology, linguistics,
geography, business, and the Internet. These applications are natural and important uses of
discrete mathematics and are not contrived. Modeling with discrete mathematics is an ex-
tremely important problem-solving skill, which students have the opportunity to develop by
constructing their own models in some of the exercises.

Changes in the Seventh Edition

Although the sixth edition has been an extremely effective text, many instructors, including
longtime users, have requested changes designed to make this book more effective. I have
devoted a significant amount of time and energy to satisfy their requests and I have worked hard
to find my own ways to make the book more effective and more compelling to students.
The seventh edition is a major revision, with changes based on input from more than 40
formal reviewers, feedback from students and instructors, and author insights. The result is a
new edition that offers an improved organization of topics making the book a more effective
teaching tool. Substantial enhancements to the material devoted to logic, algorithms, number
theory, and graph theory make this book more flexible and comprehensive. Numerous changes
in the seventh edition have been designed to help students more easily learn the material.
Additional explanations and examples have been added to clarify material where students often
have difficulty. New exercises, both routine and challenging, have been added. Highly relevant
applications, including many related to the Internet, to computer science, and to mathematical
biology, have been added. The companion website has benefited from extensive development
activity and now provides tools students can use to master key concepts and explore the world
of discrete mathematics, and many new tools under development will be released in the year
following publication of this book.
I hope that instructors will closely examine this new edition to discover how it might meet
their needs. Although it is impractical to list all the changes in this edition, a brief list that
highlights some key changes, listed by the benefits they provide, may be useful.

More Flexible Organization
Applications of propositional logic are found in a new dedicated section, which briefly
introduces logic circuits.
Recurrence relations are now covered in Chapter 2.
Expanded coverage of countability is now found in a dedicated section in Chapter 2.