Page 8 - Discrete Mathematics and Its Applications

Preface

n writing this book, I was guided by my long-standing experience and interest in teaching
Idiscrete mathematics. For the student, my purpose was to present material in a precise,
readable manner, with the concepts and techniques of discrete mathematics clearly presented
and demonstrated. My goal was to show the relevance and practicality of discrete mathematics
to students, who are often skeptical. I wanted to give students studying computer science all of
the mathematical foundations they need for their future studies. I wanted to give mathematics
students an understanding of important mathematical concepts together with a sense of why
these concepts are important for applications. And most importantly, I wanted to accomplish
these goals without watering down the material.
For the instructor, my purpose was to design a flexible, comprehensive teaching tool using
proven pedagogical techniques in mathematics. I wanted to provide instructors with a package
of materials that they could use to teach discrete mathematics effectively and efficiently in the
most appropriate manner for their particular set of students. I hope that I have achieved these
goals.
I have been extremely gratified by the tremendous success of this text. The many improve-
ments in the seventh edition have been made possible by the feedback and suggestions of a large
number of instructors and students at many of the more than 600 North American schools, and
at any many universities in parts of the world, where this book has been successfully used.
This text is designed for a one- or two-term introductory discrete mathematics course taken
by students in a wide variety of majors, including mathematics, computer science, and engineer-
ing. College algebra is the only explicit prerequisite, although a certain degree of mathematical
maturity is needed to study discrete mathematics in a meaningful way. This book has been de-
signed to meet the needs of almost all types of introductory discrete mathematics courses. It is
highly flexible and extremely comprehensive. The book is designed not only to be a successful
textbook, but also to serve as valuable resource students can consult throughout their studies
and professional life.

Goals of a Discrete Mathematics Course

A discrete mathematics course has more than one purpose. Students should learn a particular
set of mathematical facts and how to apply them; more importantly, such a course should teach
students how to think logically and mathematically. To achieve these goals, this text stresses
mathematical reasoning and the different ways problems are solved. Five important themes
are interwoven in this text: mathematical reasoning, combinatorial analysis, discrete structures,
algorithmic thinking, and applications and modeling. A successful discrete mathematics course
should carefully blend and balance all five themes.

1. Mathematical Reasoning: Students must understand mathematical reasoning in order to
read, comprehend, and construct mathematical arguments. This text starts with a discussion
of mathematical logic, which serves as the foundation for the subsequent discussions of
methods of proof. Both the science and the art of constructing proofs are addressed. The
technique of mathematical induction is stressed through many different types of examples
of such proofs and a careful explanation of why mathematical induction is a valid proof
technique.

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