Page 20 - Discrete Mathematics and Its Applications

To the Student xix

percentage of the exercises require original thought. This is intentional. The material discussed
in the text provides the tools needed to solve these exercises, but your job is to successfully
apply these tools using your own creativity. One of the primary goals of this course is to learn
how to attack problems that may be somewhat different from any you may have previously
seen. Unfortunately, learning how to solve only particular types of exercises is not sufficient for
success in developing the problem-solving skills needed in subsequent courses and professional
work. This text addresses many different topics, but discrete mathematics is an extremely diverse
and large area of study. One of my goals as an author is to help you develop the skills needed
to master the additional material you will need in your own future pursuits.

THE EXERCISES I would like to offer some advice about how you can best learn discrete
mathematics (and other subjects in the mathematical and computing sciences).You will learn the
most by actively working exercises. I suggest that you solve as many as you possibly can. After
working the exercises your instructor has assigned, I encourage you to solve additional exercises
such as those in the exercise sets following each section of the text and in the supplementary
exercises at the end of each chapter. (Note the key explaining the markings preceding exercises.)

Key to the Exercises
no marking A routine exercise
∗
A difficult exercise
∗∗
An extremely challenging exercise
An exercise containing a result used in the book (Table 1 on the
following page shows where these exercises are used.)
(Requires calculus ) An exercise whose solution requires the use of limits or concepts
from differential or integral calculus
The best approach is to try exercises yourself before you consult the answer section at the
end of this book. Note that the odd-numbered exercise answers provided in the text are answers
only and not full solutions; in particular, the reasoning required to obtain answers is omitted in
these answers. The Student’s Solutions Guide, available separately, provides complete, worked
solutions to all odd-numbered exercises in this text. When you hit an impasse trying to solve an
odd-numbered exercise, I suggest you consult the Student’s Solutions Guide and look for some
guidance as to how to solve the problem. The more work you do yourself rather than passively
reading or copying solutions, the more you will learn. The answers and solutions to the even-
numbered exercises are intentionally not available from the publisher; ask your instructor if you
have trouble with these.

WEB RESOURCES You are strongly encouraged to take advantage of additional re-
sources available on the Web, especially those on the companion website for this book found
at www.mhhe.com/rosen. You will find many Extra Examples designed to clarify key concepts;
Self Assessments for gauging how well you understand core topics; Interactive Demonstration
Applets exploring key algorithms and other concepts; a Web Resources Guide containing an
extensive selection of links to external sites relevant to the world of discrete mathematics; extra
explanations and practice to help you master core concepts; added instruction on writing proofs
and on avoiding common mistakes in discrete mathematics; in-depth discussions of important
applications; and guidance on utilizing Maple TM software to explore the computational aspects
of discrete mathematics. Places in the text where these additional online resources are available
are identified in the margins by special icons. You will also find (after fall 2012) the Virtual
Discrete Mathematics Tutor, an on-line resource that provides extra support to help you make
the transition from lower level courses to discrete mathematics. This tutorial should help answer
many of your questions and correct errors that you may make, based on errors other students
using this book, have made. For more details on these and other online resources, see the
description of the companion website immediately preceding this “To the Student” message.