About the Text--Epp's 4th edition/Discrete Mathematics with Applications

• Chapter 1: Speaking Mathematically
• 1.1 Variables
• 1.2 The Language of Sets
• 1.3 The Langage ofRelations and Functions
• Chapter 2: The Logic of Compound Statements
• 2.1 Logical Form and Logical Equivalence
• 2.2 Conditional Statements
• 2.3 Valid and Invalid Arguments
• 2.4 Application: Digital Logic Circuits
• 2.5 Application: Number Systems and Circuits for Addition
• Chapter 3:  The Logic of Quantified Statements
• 3.1 Predicate and Quantified Statements I
• 3.2 Predicates and Quantified Statements II
• 3.3 Statements with Multiple Quantifiers
• 3.4 Arguments with Quantified Statements
• Chapter 4:  Elementary Number Theory and Methods of Proof
• 4.1 Direct Proof and Counterexample I: Introduction
• 4.2 Direct Proof and Counterexample II: Rational Numbers
• 4.3 Direct Proof and Counterexample III: Divisibility
• 4.4 Direct Proof and Counterexample IV: Division into Cases and the Quotent-Remainder Theorem
• 4.5 Direct Proof and Counterexample V: Floor and Ceiling
• 4.6 Indirect Argument: Contradiction and Contraposition
• 4.7 Indirect Argument: Two Classical Theorems
• 4.8 Application: Algorithm
• Chapter 5: Sequences: Mathematical Induction, and Recursion
• 5.1 Sequences
• 5.2 Mathematical Induction I
• 5.3 Mathematical Induction II
• 5.4 Strong Mathematical Induction and the Well-Ordering Principle for the Integers
• 5.5 Applicaiton: Correctness of Algortithms
• 5.6 Defining Sequences Recursively
• 5.7 Solving Recurrence Relations by Iteration
• 5.8 Second-Order Linear Homogenous Recurrence Relations
• 5.9 General Recursive Definitions and Structural Induction
• Chapter 6: Set Theory
• 6.1 Set Theory: Definitions and the Element Method of Proof
• 6.2 Properties of Sets
• 6.3 Disproofs and Algebraic Proofs
• 6.4 Boolean Algebras, Russell's Paradox, and the Halting Problem
• Chapter 7: Functions
• 7.1 Functions Defined on General Sets
• 7.2 One-to-One and Onto, Inverse Functions
• 7.3 Composition of Functions
• 7.4 Cardinality with Applications to Computability
• Chapter 8: Relations
• 8.1 Relations on Sets
• 8.2 Reflexivity, Symmetry, and Transitivity
• 8.3 Equivalence Relations
• 8.4 Modular Arithmetic with Applications to Cryptography
• 8.5 Partial Order Relations
• Chapter 9: Counting and Probability
• 9.1 Introduction
• 9.2 Possibility Trees and the Multplication Rule
• 9.3 Counting Elements of Disjoint Sets: The Addition Rule
• 9.4 The Pigeonhole Principle
• 9.5 Counting Subsets of a Set: Combinations
• 9.6 r-Combinations with Repetition Allowed
• 9.7 Pascal's Formula and the Binomial Theorem
• 9.8 Probability Axioms and Exprected Value
• 9.9 Conditional Probability, Byes' Formula, and Independent Events
• Chapter 10: Grphs and Trees
• 10.1 Graphs: Defintions and Basic Properties
• 10.2 Trails, Paths, and Circuits
• 10.3 Matrix Representations of Graphs
• 10.4 Isomorphisms of Graphs
• 10.5 Trees
• 10.6 Rooted Trees
• 10.7 Spanning Trees and Shortedst Paths
• Chapter 11: Analysisy of Algorithm Efficiency
• 11.1 Real-Valued Functions of a Real Variable and Their Graphs
• 11.2 Ο-, Ω-, and Θ-Notations
• 11.3 Application: Analysis of Algorithm Effciency I
• 11.4 Expoential and Logarithmic Functions: Graphs and Orders
• 11.5 Application: Analysis of Algorithm Effciency II
• Chpater 12: Regular Expressions and Finite-State Automata
• 12.1 Formal Languages and Regular Expressions
• 12.2 Finite-State Automata
• 12.3 Simplifying Finte-State Automata

• Applets through the author's homepage link.
• Errata: check this errata for possible errors in your book.
• Find-the-mistakes and their solutions.
• Some math conventions,  induction formats,  proof tips, ...
• Chapter reviews: ch01, ch02, ch03, ch04, ch05, ch06, ch07, ch08, ch09, ch10, ch11, ch12. 
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• An interesting example: application of logic (through the  link).