Page 11 - Discrete Mathematics and Its Applications

x Preface

Graph Theory

A structured introduction to graph theory applications has been added.
More coverage has been devoted to the notion of social networks.
Applications to the biological sciences and motivating applications for graph isomor-
phism and planarity have been added.
Matchings in bipartite graphs are now covered, including Hall’s theorem and its proof.
Coverage of vertex connectivity, edge connectivity, and n-connectedness has been
added, providing more insight into the connectedness of graphs.

Enrichment Material

Many biographies have been expanded and updated, and new biographies of Bellman,
Bézout Bienyamé, Cardano, Catalan, Cocks, Cook, Dirac, Hall, Hilbert, Ore, and Tao
have been added.
Historical information has been added throughout the text.
Numerous updates for latest discoveries have been made.

Expanded Media

Extensive effort has been devoted to producing valuable web resources for this book.
Extra examples in key parts of the text have been provided on companion website.
Interactive algorithms have been developed, with tools for using them to explore topics
and for classroom use.
A new online ancillary, The Virtual Discrete Mathematics Tutor, available in fall 2012,
will help students overcome problems learning discrete mathematics.
A new homework delivery system, available in fall 2012, will provide automated home-
work for both numerical and conceptual exercises.
Student assessment modules are available for key concepts.
Powerpoint transparencies for instructor use have been developed.
A supplement Exploring Discrete Mathematics has been developed, providing extensive
support for using Maple TM or Mathematica TM in conjunction with the book.
An extensive collection of external web links is provided.

Features of the Book

ACCESSIBILITY This text has proved to be easily read and understood by beginning
students. There are no mathematical prerequisites beyond college algebra for almost all the
content of the text. Students needing extra help will find tools on the companion website for
bringing their mathematical maturity up to the level of the text. The few places in the book
where calculus is referred to are explicitly noted. Most students should easily understand the
pseudocode used in the text to express algorithms, regardless of whether they have formally
studied programming languages. There is no formal computer science prerequisite.
Each chapter begins at an easily understood and accessible level. Once basic mathematical
concepts have been carefully developed, more difficult material and applications to other areas
of study are presented.