Discrete Mathematics and Applications, Second Edition is intended for a one-semester course in discrete mathematics. Such a course is typically taken by mathematics, mathematics education, and computer science majors, usually in their sophomore year. Calculus is not a prerequisite to use this book.

Part one focuses on how to write proofs, then moves on to topics in number theory, employing set theory in the process. Part two focuses on computations, combinatorics, graph theory, trees, and algorithms.

  • Emphasizes proofs, which will appeal to a subset of this course market
  • Links examples to exercise sets
  • Offers edition that has been heavily reviewed and developed
  • Focuses on graph theory
  • Covers trees and algorithms


I Proofs

Logic and Sets

Statement Forms and Logical Equivalences

Set Notation


Set Operations and Identities

Valid Arguments

Basic Proof Writing

Direct Demonstration

General Demonstration (Part 1)

General Demonstration (Part 2)

Indirect Arguments

Splitting into Cases

Elementary Number Theory


Well-Ordering, Division, and Codes

Euclid's Algorithm and Lemma

Rational and Irrational Numbers

Modular Arithmetic and Encryption

Indexed by Integers

Sequences, Indexing, and Recursion

Sigma Notation

Mathematical Induction, An Introduction

Induction and Summations

Strong Induction

The Binomial Theorem


General Relations

Special Relations on Sets

Basics of Functions

Special Functions

General Set Constructions


II Combinatorics

Basic Counting

The Multiplication Principle

Permutations and Combinations

Addition and Subtraction


Applications of Combinations

Correcting for Overcounting

More Counting


Multinomial Coe□cients

Generating Functions

Counting Orbits

Combinatorial Arguments

Basic Graph Theory

Motivation and Introduction

Special Graphs




Directed Graphs and Markov Chains

Graph Properties


Euler Circuits

Hamiltonian Cycles

Planar Graphs

Chromatic Number

Trees and Algorithms


Search Trees

Weighted Trees

Analysis of Algorithms (Part 1)

Analysis of Algorithms (Part 2)

A Assumed Properties of Z and R

B Pseudocode

C Answers to Selected Exercises