There are certain rules that one must abide by in order to create a
successful sequel. -- Randy Meeks, from the trailer to Scream 2 While we
may not follow the precise rules that Mr. Meeks had in mind for s-
cessful sequels, we have made a number of changes to the text in this
second edition. In the new edition, we continue to introduce new topics
with concrete - amples, we provide complete proofs of almost every
result, and we preserve the book'sfriendlystyle andlivelypresentation,
interspersingthetextwith occasional jokes and quotations. The rst two
chapters, on graph theory and combinatorics, remain largely independent,
and may be covered in either order. Chapter 3, on in nite combinatorics
and graphs, may also be studied independently, although many readers
will want to investigate trees, matchings, and Ramsey theory for nite
sets before exploring these topics for in nite sets in the third
chapter. Like the rst edition, this text is aimed at upper-division
undergraduate students in mathematics, though others will nd much of
interest as well. It assumes only familiarity with basic proof
techniques, and some experience with matrices and in nite series. The
second edition offersmany additionaltopics for use in the classroom or
for independentstudy. Chapter 1 includesa new sectioncoveringdistance
andrelated notions in graphs, following an expanded introductory
section. This new section also introduces the adjacency matrix of a
graph, and describes its connection to important features of the graph.
