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Discrete Mathematics with Applications, 4th Edition Discrete Mathematics with Applications, 4th Edition
Chapter 1
Speaking Mathematically
| 1.1 | Variables | Exercise Set | p.5 |
| 1.2 | The Language of Sets | Test Yourself | p.12 |
| Exercise Set | p.13 | ||
| 1.3 | The Language of Relations and Functions | Exercise Set | p.21 |
Chapter 2
The Logic Of Compound Statements
| 2.1 | Logical Form and Logical Equivalence | Exercise Set | p.37 |
| 2.2 | Conditional Statements | Exercise Set | p.49 |
| 2.3 | Valid and Invalid Arguments | Exercise Set | p.61 |
| 2.4 | Application: Digital Logic Circuits | Exercise Set | p.76 |
| 2.5 | Application: Number Systems and Circuits for Addition | Exercise Set | p.94 |
Chapter 3
The Logic Of Quantified Statements
| 3.1 | Predicates and Quantified Statements I | Exercise Set | p.106 |
| 3.2 | Predicates and Quantified Statements II | Exercise Set | p.115 |
| 3.3 | Statements with Multiple Quantifiers | Exercise Set | p.129 |
| 3.4 | Arguments with Quantified Statements | Exercise Set | p.142 |
Chapter 4
Elementary Number Theory And Methods Of Proof
| 4.1 | Direct Proof and Counterexample I: Introduction | Exercise Set | p.161 |
| 4.2 | Direct Proof and Counterexample II: Rational Numbers | Exercise Set | p.168 |
| 4.3 | Direct Proof and Counterexample III: Divisibility | Exercise Set | p.177 |
| 4.4 | Direct Proof and Counterexample IV: Division into Cases and the Quotient-Remainder Theoerem | Exercise Set | p.189 |
| 4.5 | Direct Proof and Counterexample V: Floor and Ceiling | Exercise Set | p.197 |
| 4.6 | Indirect Argument: Contradiction and Contraposition | Exercise Set | p.205 |
| 4.7 | Indirect Argument: Two Classical Theorems | Exercise Set | p.212 |
| 4.8 | Application: Algorithms | Exercise Set | p.225 |
Chapter 5
Sequences, Mathematical Induction, And Recursion
| 5.1 | Sequences | Exercise Set | p.242 |
| 5.2 | Mathematical Induction I | Exercise Set | p.256 |
| 5.3 | Mathematical Induction II | Exercise Set | p.266 |
| 5.4 | Strong Mathematical Induction and the Well-Ordering Principle for the Integers | Exercise Set | p.277 |
| 5.5 | Application: Correctness of Algorithms | Exercise Set | p.288 |
| 5.6 | Defining Sequences Recursively | Exercise Set | p.302 |
| 5.7 | Solving Recurrence Relations by Iteration | Exercise Set | p.314 |
| 5.8 | Second-Order Linear Homogenous Recurrence Relations with Constant Coefficients | Exercise Set | p.326 |
| 5.9 | General Recursive Definitions and Structural Induction | Exercise Set | p.334 |
Chapter 6
Set Theory
| 6.1 | Set Theory: Definitions and the Element Method of Proof | Exercise Set | p.349 |
| 6.2 | Properties of Sets | Exercise Set | p.364 |
| 6.3 | Disproofs, Algebraic Proofs, and Boolean Algebras | Exercise Set | p.372 |
| 6.4 | Boolean Algebras, Russell's Paradox, and the Halting Problem | Exercise Set | p.381 |
Chapter 7
Functions
| 7.1 | Functions Defined on General Sets | Exercise Set | p.393 |
| 7.2 | One-to-One and Onto, Inverse Functions | Exercise Set | p.413 |
| 7.3 | Composition of Functions | Exercise Set | p.426 |
| 7.4 | Cardinality with Applications to Computability | Exercise Set | p.439 |
Chapter 8
Relations
| 8.1 | Relations on Sets | Exercise Set | p.448 |
| 8.2 | Reflexivity, Symmetry, and Transtivity | Exercise Set | p.458 |
| 8.3 | Equivalence Relations | Exercise Set | p.475 |
| 8.4 | Modular Arithmetic with Applications to Cryptography | Exercise Set | p.496 |
| 8.5 | Partial Order Relations | Exercise Set | p.513 |
Chapter 9
Counting And Probability
| 9.1 | Introduction | Exercise Set | p.523 |
| 9.2 | Possibility Trees and the Multiplication Rule | Exercise Set | p.536 |
| 9.3 | Counting Elements of Disjoint Sets: The Addition Rule | Exercise Set | p.549 |
| 9.4 | The Pigeonhole Principle | Exercise Set | p.563 |
| 9.5 | Counting Subsets of a Set: Combinations | Exercise Set | p.581 |
| 9.6 | r-Combinations with Repetition Allowed | Exercise Set | p.590 |
| 9.7 | Pascal's Formula and the Binomial Theorem | Exercise Set | p.603 |
| 9.8 | Probability Axioms and Expected Value | Exercise Set | p.610 |
| 9.9 | Conditional Probability, Bayes' Formula, and Independent Events | Exercise Set | p.622 |
Chapter 10
Graphs And Trees
| 10.1 | Graphs: Definitions and Basic Properties | Exercise Set | p.639 |
| 10.2 | Trails, Paths, and Circuits | Exercise Set | p.657 |
| 10.3 | Matrix Representations of Graphs | Exercise Set | p.673 |
| 10.4 | Isomorphisms of Graphs | Exercise Set | p.681 |
| 10.5 | Trees | Exercise Set | p.693 |
| 10.6 | Rooted Trees | Exercise Set | p.700 |
| Exercise Set | p.715 |
Chapter 11
Analysis Of Algorithm Efficiency
| 11.1 | Real-Valued Functions of a Real Variable and Their Graphs | Exercise Set | p.724 |
| 11.2 | O-, Ω-, and Θ-Notations | Exercise Set | p.736 |
| 11.3 | Application: Analysis of Algorithm Efficiency I | Exercise Set | p.748 |
| 11.4 | Exponential and Logarithmic Functions: Graphs and Orders | Exercise Set | p.762 |
| 11.5 | Application: Analysis of Algorithm Efficiency II | Exercise Set | p.777 |
Chapter 12
Regular Expressions And Finite-State Automata
| 12.1 | Formal Languages and Regular Expressions | Exercise Set | p.789 |
| 12.2 | Finite-State Automata | Exercise Set | p.805 |
| 12.3 | Simplifying Finite-State Automata | Exercise Set | p.818 |
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