As in the first edition, the purpose of this book is to present an extensive range anddepth of topics in discrete mathematics and also work in a theme on how to do proofs.Proofs are introduced in the first chapter and continue throughout the book. Moststudents taking discrete mathematics are mathematics and computer science majors.Although the necessity of learning to do proofs is obvious for mathematics majors, itis also critical for computer science students to think logically. Essentially, a logicalbug-free computer program is equivalent to a logical proof, Also, it is assumed in thisbook that it is easier to use （or at least not misuse） an application if one understandswhy it works. With few exceptions, the book is self-contained. Concepts are developedmathematically before they are seen in an applied context.Additions and alterations in the second edition:
More coverage of proofs, especially in Chapter l. Added computer science applications, such as a greedy algorithm for coloring the nodes of a graph, a recursive algorithm for counting the number of nodes on a binary search tree, or an efficient algorithm for computing ab modn for very largevalues of a, b, and n.
An extensive increase in the number of problems in the first seven chapters.
More problems are included that involve proofs.
Additional material is included on matrices.
True-False questions at the end of each chapter.
Summary questions at the end of each chapter.
Functions and sequences are introduced earlier （in Chapter 2）.
Calculus is not required for any of the material in this book. College algebra isadequate for the basic chapters. However, although this book is self-contained, some ofthe remaining chapters require more mathematical maturity than do the basic chapters,so calculus is recommended more for giving maturity, than for any direct uses.
This book is intended for either a one- or two-term course in discrete mathematics.The first eight chapters of this book provide a foundation in discrete mathematicsand would be appropriate for a first-level course for freshmen or sophomores. Thesechapters are essentially independent, so that the instructor can pick the material he/shewishes to cover. The remainder of the book contains appropriate material for a secofidcourse in discrete mathematics. These chapters expand concepts introduced earlier andintroduce numerous advanced topics. Topics are explored from different points of viewto show how they may be used in different settings. The range of topics include:
Logic-Including truth tables, propositional logic, predicate calculus, circuits, induction, and proofs.
Set Theory-Including cardinality of sets, relations, partially ordered sets, congruence relations, graphs, directed graphs, and functions.
Algorithms-Including complexity of algorithms, search and sort algorithms, theEuclidean algorithm, Huffmans algorithm, Prims algorithms, Warshalls algorithm, the Ford-Fulkerson algorithm, the Floyd-Warshall algorithm, and Dijkstrasalgorithms.