IiI
Preface
and techniques
of
that chapter.
To
answer these questions students need to write long answers,
rather than just perfonn 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 100 in total) are
designed to be completed using existing software tools, such as programs that students or
instructors have written
or
mathematical computation packages such as Maple
or
Mathematica.
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
with Maple companion workbook 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 numbers and the integers, and illustrates how facts are proved directly from these axioms.
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 each chapter is provided in a
section at the end
of
the text. 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 within 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-tenn 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
instructor. A two-tenn introductory course can include all the optional mathematics sections
in
addition to the core sections. A course with a strong computer science emphasis can be taught
by covering some or all
of
the optional computer science sections.
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