Discrete Mathematics with Applications, 2nd Ed. Susanna S. Epp

1. 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

2. THE LOGIC OF QUANTIFIED STATEMENTS
Predicates and Quantified Statements / Predicates and Quantified Statements / Arguments with Quantified Statements

3. ELEMENTARY NUMBER THEORY AND METHODS OF PROOF
Direct Proof and Counterexample I: Introduction / Direct Proof and Counterexample II: Rational Numbers / Direct Proof and Counterexample III: Divisibility / Direct Proof and Counterexample IV: Division into Cases and the Quotient-Remainder Theorem / Direct Proof and Counterexample V: Floor and Ceiling / Indirect Argument: Contradiction and Contraposition / Two Classical Theorems / Application: Algorithms

4. SEQUENCES AND MATHEMATICAL INDUCTION
Sequences / Mathematical Induction I / Mathematical Induction II / Strong Mathematical Induction and the Well-Ordering Principle / Application: Correctness of Algorithms

5. SET THEORY
Basic Definitions of Set Theory / Properties of Sets / The Empty Set, Partitions , Power Sets, and Boolean Algebras / Russell's Paradox and the Halting Problem

6.COUNTING
Counting and Probability / Possibility Trees and the Multiplication Rule / Counting Elements of Disjoint Sets: The Addition Rule / counting Subsets of a Set: Combinations / R-Combinations with Repetition Allowed / The Algebra of Combination s / The Binomial Theorem

7.FUNCTIONS
Functions Defined on General Sets / Application: Finite-State Automata / One-to- One and Onto, Inverse Functions / Applications: The Pigeonhole Principle / Composition of Functions / Cardinality with Applications to Computability

8. RECURSION
Recursively Defined Sequences / Solving Recurrence Relations by Iteration / Second-Order Linear Homogeneous Recurrence Relations with Constant Coefficients / General Recursive Definitions

9. O-NOTATION AND THE EFFICIENCY OF ALGORITHMS
Real-Valued Functions of a Real Variable and Their Graphs / O-Notation / Application: Efficiency of Algorithms I / Exponential and Logarithmic Functions: Graphs and Orders / Application: Efficiency of Algorithms II

10. RELATIONS
Relations on Sets / Reflexivity, Symmetry, and Transitivity / Equivalence Relations / Application: Simplifying Finite-State Automata / Partial Order Relations

11. GRAPHS AND TREES
Graphs: An Introduction / Paths and Circuits / Matrix Representations of Graphs / Isomorphisms of Graphs / Trees / Spanning Trees