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| Preface | |
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| Acknowledgements | |
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| To The Student | |
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| Introduction | |
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| What Is Discrete Mathematics? | |
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| The Stable Marriage Problem | |
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| Other Examples | |
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| Exercises | |
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| Chapter Review | |
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| Sets, Logic, and Boolean Algebras | |
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| Sets | |
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| Logic in Daily Life | |
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| Propositional Logic | |
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| Logical Equivalence and Rules of Inference | |
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| Boolean Algebras | |
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| Predicate Logic | |
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| Quick Check Solutions | |
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| Chapter Review | |
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| Proof | |
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| Introduction to Mathematical Proof | |
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| Elementary Number Theory: Fuel for Practice | |
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| Proof Strategies | |
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| Applications of Elementary Number Theory | |
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| Mathematical Induction | |
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| Creating Proofs: Hints and Suggestions | |
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| Quick Check Solutions | |
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| Chapter Review | |
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| Algorithms | |
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| Expressing Algorithms | |
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| Measuring Algorithm Efficiency | |
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| Pattern Matching | |
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| The Halting Problem | |
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| Quick Check Solutions | |
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| Chapter Review | |
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| Counting | |
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| Permutations and Combinations | |
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| Combinatorial Proofs | |
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| Pigeon-Hole Principle | |
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| Inclusion-Exclusion | |
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| Quick Check Solutions | |
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| Chapter Review | |
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| Finite Probability Theory | |
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| The Language of Probabilities | |
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| Conditional Probabilities and Independent Events | |
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| Counting and Probability | |
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| Expected Value | |
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| The Binomial Distribution | |
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| Bayes's Theorem | |
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| Quick Check Solutions | |
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| Recursion | |
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| Recursive Algorithms | |
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| Recurrence Relations | |
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| Big-2and Recursive Algorithms: The Master Theorem | |
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| Generating Functions | |
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| The Josephus Problem | |
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| Quick Check Solutions | |
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| Chapter Review | |
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| Combinatorics | |
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| Partitions, Occupancy Problems, Stirling Numbers | |
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| Latin Squares | |
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| Finite Projective Planes | |
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| Balanced Incomplete Block Designs | |
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| The Knapsack Problem | |
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| Error-Correcting Codes | |
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| Distinct Representatives, Ramsey Numbers | |
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| Quick Check Solutions | |
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| Chapter Review | |
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| Formal Models in Computer Science | |
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| Information | |
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| Finite-State Machines | |
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| Formal Languages | |
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| Regular Expressions | |
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| The Three Faces of Regular | |
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| A Glimpse at More Advanced Topics | |
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| Quick Check Solutions | |
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| Chapter Review | |
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| Graphs | |
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| Terminology | |
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| Connectivity and Adjacency | |
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| Euler and Hamilton | |
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| Representation and Isomorphism | |
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| The Big Theorems: Planarity, Euler, Polyhedra, Chromatic Number | |
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| Directed Graphs and Weighted Graphs | |
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| Quick Check Solutions | |
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| Chapter Review | |
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| Trees | |
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| Terminology, Counting | |
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| Traversal, Searching, and Sorting | |
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| More Applications of Trees | |
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| Spanning Trees | |
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| Quick Check Solutions | |
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| Chapter Review | |
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| Functions, Relations, Databases, and Circuits | |
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| Functions and Relations | |
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| Equivalence Relations, Partially Ordered Sets | |
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| n-ary Relations and Relational Databases | |
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| Boolean Functions and Boolean Expressions | |