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| Discrete Mathematics and Its Applications, Fifth Edition | |
| The Foundations: Logic and Proof, Sets, and Functions | |
| Logic | |
| Propositional Equivalences | |
| Predicates and Quantifiers | |
| Nested Quantifiers | |
| Methods of Proof | |
| Sets | |
| Set Operations | |
| Functions | |
| The Fundamentals: Algorithms, the Integers, and Matrices | |
| Algorithms | |
| The Growth of Functions | |
| Complexity of Algorithms | |
| The Integers and Division | |
| Applications of Number Theory | |
| Matrices | |
| Mathematical Reasoning, Induction, and Recursion | |
| Proof Strategy | |
| Sequences and Summations | |
| Mathematical Induction | |
| Recursive Definitions and Structural Induction | |
| Recursive Algorithms | |
| Program Correctness | |
| Counting | |
| The Basics of Counting | |
| The Pigeonhole Principle | |
| Permutations and Combinations | |
| Binomial Coefficients | |
| Generalized Permutations and Combinations | |
| Generating Permutations and Combinations | |
| Discrete Probability | |
| An Introduction to Discrete Probability | |
| Probability Theory | |
| Expected Value and Variance | |
| Advanced Counting Techniques | |
| Recurrence Relations | |
| Solving Recurrence Relations | |
| Divide-and-Conquer Algorithms and Recurrence Relations | |
| Generating Functions | |
| Inclusion-Exclusion | |
| Applications of Inclusion-Exclusion | |
| Relations | |
| Relations and Their Properties | |
| n-ary Relations and Their Applications | |
| Representing Relations | |
| Closures of Relations | |
| Equivalence Relations | |
| Partial Orderings | |
| Graphs | |
| Introduction to Graphs | |
| Graph Terminology | |
| Representing Graphs and Graph Isomorphism | |
| Connectivity | |
| Euler and Hamilton Paths | |
| Shortest-Path Problems | |
| Planar Graphs | |
| Graph Coloring | |
| Trees | |
| Introduction to Trees | |
| Applications of Trees | |
| Tree Traversal | |
| Spanning Trees | |
| Minimum Spanning Trees | |
| Boolean Algebra | |
| Boolean Functions | |
| Representing Boolean Functions | |
| Logic Gates | |
| Minimization of Circuits | |
| Modeling Computation | |
| Languages and Grammars | |
| Finite-State Machines with Output | |
| Finite-State Machines with No Output | |
| Language Recognition | |
| Turing Machines | |
| Appendixes | |
| Exponential and Logarithmic Functions | |
| Pseudocode | |
| Table of Contents provided by Publisher. All Rights Reserved. |
