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Susanna Epp's "Discrete Mathematics with Applications" provides a clear introduction to discrete mathematics. Renowned for her lucid, accessible prose, Epp explains complex, abstract concepts with clarity and precision. This book presents not only the major themes of discrete mathematics, but also the reasoning that underlies mathematical thought. Students develop the ability to think abstractly as they study the ideas of logic and proof. While learning about such concepts as logic circuits and computer addition, algorithm analysis, recursive thinking, computability, automata, cryptography, and combinatorics, students discover that the ideas of discrete mathematics underlie and are essential to the science and technology of the computer age. Overall, Epp's emphasis on reasoning provides students with a strong foundation for computer science and upper-level mathematics courses.

Speaking Mathematically
Variables
The Language of Sets
The Language of Relations and Functions
The Language of Graphs
The Logic of Compound Statements
Logical Form and Logical Equivalence
Conditional Statements
Valid and Invalid Arguments
Application: Digital Logic Circuits
Application: Number Systems and Circuits for Addition
The Logic of Quantified statements
Predicates and Quantified Statements I
Predicates and Quantified Statements II
Statements with Multiple Quantifiers
Arguments with Quantified Statements
Elementary Number theory and Methods of Proof
Direct Proof and Counterexample I: Introduction
Direct Proof and Counterexample II: Writing Advice
Direct Proof and Counterexample III: Rational Numbers
Direct Proof and Counterexample IV: Divisibility
Direct Proof and Counterexample V: Division into Cases and the Quotient-Remainder Theorem
Direct Proof and Counterexample VI: Floor and Ceiling
Indirect Argument: Contradiction and Contraposition
Indirect Argument: Two Famous Theorems
Application: The Handshake Theorem
Application: Algorithms
Sequences, Mathematical Induction, and Recursion
Sequences
Mathematical Induction I: Proving Formulas
Mathematical Induction II: Applications
Strong Mathematical Induction and the Well-Ordering Principle for the Integers
Application: Correctness of Algorithms
Defining Sequences Recursively
Solving Recurrence Relations by Iteration
Second-Order Linear Homogeneous Recurrence Relations with Constant Coefficients
General Recursive Definitions and Structural Induction
Set Theory
Set Theory: Definitions and the Element Method of Proof
Properties of Sets
Disproofs and Algebraic Proofs
Boolean Algebras, Russell’s Paradox, and the Halting Problem
Properties of Functions
Functions Defined on General Sets
One-to-One, Onto, and Inverse Functions
Composition of Functions
Cardinality with Applications to Computability
Properties of Relations
Relations on Sets
Reflexivity, Symmetry, and Transitivity
Equivalence Relations
Modular Arithmetic with Applications to Cryptography
Partial Order Relations
Counting and Probability
Introduction to Probability
Possibility Trees and the Multiplication Rule
Counting Elements of Disjoint Sets: The Addition Rule
The Pigeonhole Principle
Counting Subsets of a Set: Combinations
r-Combinations with Repetition Allowed
Pascal’s Formula and the Binomial Theorem
Probability Axioms and Expected Value
Conditional Probability, Bayes’ Formula, and Independent Events
Theory of graphs and Trees
Trails, Paths, and Circuits
Matrix Representations of Graphs
Isomorphisms of Graphs
Trees: Examples and Basic Properties
Rooted Trees
Spanning Trees and a Shortest Path Algorithm
Analysis of Algorithm Efficiency
Real-Valued Functions of a Real Variable and Their Graphs
Big-O, Big-Omega, and Big-Theta Notations
Application: Analysis of Algorithm Efficiency I
Exponential and Logarithmic Functions: Graphs and Orders
Application: Analysis of Algorithm Efficiency II
Regular Expressions and Finite-State Automata
Formal Languages and Regular Expressions
Finite-State Automata
Simplifying Finite-State Automata
Appendix A: Properties of the real Numbersp
Appendix B: Solutions and Hints to Selected Exercises