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This book 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.
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Table of Contents

I Proofs Logic and Sets Statement Forms and Logical Equivalences Set Notation Quantifiers 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 Divisors 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 Relations General Relations Special Relations on Sets Basics of Functions Special Functions General Set Constructions Cardinality II Combinatorics Basic Counting The Multiplication Principle Permutations and Combinations Addition and Subtraction Probability Applications of Combinations Correcting for Overcounting More Counting Inclusion-Exclusion Multinomial Coecients Generating Functions Counting Orbits Combinatorial Arguments Basic Graph Theory Motivation and Introduction Special Graphs Matrices Isomorphisms Invariants Directed Graphs and Markov Chains Graph Properties Connectivity Euler Circuits Hamiltonian Cycles Planar Graphs Chromatic Number Trees and Algorithms Trees 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

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