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