Front Cover -- Discrete Mathematicswith Applications -- Copyright Page -- Table of Contents -- Preface -- A Word to the Student -- Chapter 1. The Language of Logic -- 1.1 Propositions -- 1.2 Logical Equivalences -- 1.3 Quantifiers -- 1 .4 Arguments (optional) -- 1.5 Proof Methods -- Chapter Summary -- Review Exercises -- Supplementary Exercises -- Computer Exercises -- Exploratory Writing Projects -- Enrichment Readings -- Chapter 2. The Language of Sets -- 2.1 The Concept of a Set -- 2.2 Operations with Sets -- 2.3 Computer Operations with Sets (optional) -- 2.4 The Cardinality of a Set -- 2.5 Recursively Defined Sets -- Chapter Summary -- Review Exercises -- Supplementary Exercises -- Computer Exercises -- Exploratory Writing Projects -- Enrichment Readings -- Chapter 3. Functions and Matrices -- 3.1 The Concept of a Function -- 3.2 Special Functions -- 3.3 Properties of Functions -- 3.4 The Pigeonhole Principle -- 3.5 Composition of Functions -- 3.6 Sequences and the Summation Notation -- 3.7 Matrices -- Chapter Summary -- Review Exercises -- Supplementary Exercises -- Computer Exercises -- Exploratory Writing Projects -- Enrichment Readings -- Chapter 4. Induction and Algorithms -- 4.1 The Division Algorithm -- 4.2 Divisibility Properties -- 4.3 Nondecimal Bases -- 4.4 Mathematical Induction -- 4.5 Algorithm Correctness -- 4.6 The Growth of Functions -- 4 .7 Complexities of Algorithms (optional) -- Chapter Summary -- Review Exercises -- Supplementary Exercises -- Computer Exercises -- Exploratory Writing Projects -- Enrichment Readings -- Chapter 5. Recursion -- 5.1 Recursively Defined Functions -- 5.2 Solving Recurrence Relations -- 5.3 Solving Recurrence Relations Revisited -- 5.4 Generating Functions -- 5.5 Recursive Algorithms -- 5.6 Correctness of Recursive Algorithms -- 5.7 Complexities of Recursive Algorithms (optional).

Chapter Summary -- Review Exercises -- Supplementary Exercises -- Computer Exercises -- Exploratory Writing Projects -- Enrichment Readings -- Chapter 6. Combinatorics and Discrete Probability -- 6.1 The Fundamental Counting Principles -- 6.2 Permutations -- 6.3 Derangements -- 6.4 Combinations -- 6.5 Permutations and Combinations with Repetitions -- 6.6 The Binomial Theorem -- 6.7 The Generalized Inclusion-Exclusion Principle (GIEP) (optional) -- 6.8 Discrete Probability (optional) -- 6.9 Additional Topics in Probability (optional) -- Chapter Summary -- Review Exercises -- Supplementary Exercises -- Computer Exercises -- Exploratory Writing Projects -- Enrichment Readings -- Chapter 7. Relations -- 7.1 Boolean Matrices -- 7.2 Relations and Digraphs -- 7.3 Computer Representations of Relations (optional) -- 7.4 Properties of Relations -- 7.5 Operations on Relations -- 7.6 The Connectivity Relation (optional) -- 7.7 Transitive Closure (optional) -- 7.8 Equivalence Relations -- 7.9 Partial and Total Orderings -- Chapter Summary -- Review Exercises -- Supplementary Exercises -- Computer Exercises -- Exploratory Writing Projects -- Enrichment Readings -- Chapter 8. Graphs -- 8.1 Graphs -- 8.2 Computer Representations of Graphs (optional) -- 8.3 Isomorphic Graphs -- 8.4 Paths, Cycles, and Circuits -- 8.5 Eulerian and Hamiltonian Graphs -- 8.6 Planar Graphs -- 8.7 Graph Coloring -- Chapter Summary -- Review Exercises -- Supplementary Exercises -- Computer Exercises -- Exploratory Writing Projects -- Enrichment Readings -- Chapter 9. Trees -- 9.1 Trees -- 9.2 Spanning trees -- 9.3 Minimal Spanning Trees -- 9.4 Rooted Trees -- 9.5 Binary Trees -- 9.6 Binary Search Trees -- 9.7 Huffman Trees (optional) -- 9.8 Decision Trees (optional) -- Chapter Summary -- Review Exercises -- Supplementary Exercises -- Computer Exercises -- Exploratory Writing Projects.

Enrichment Readings -- Chapter 10. Digraphs -- 10.1 Digraphs -- 10.2 Dags -- 10.3 Weighted Digraphs -- Chapter Summary -- Review Exercises -- Supplementary Exercises -- Computer Exercises -- Exploratory Writing Projects -- Enrichment Readings -- Chapter 11. Formal Languages and Finite-State Machines -- 11.1 Formal Languages -- 11.2 Grammars -- 11.3 Finite-State Automata -- 11.4 Finite-State Machines -- 11.5 Deterministic Finite-State Automata and Regular Languages -- 11.6 Nondeterministic Finite-State Automata -- 11.7 Automata and Regular Languages -- Chapter Summary -- Review Exercises -- Supplementary Exercises -- Computer Exercises -- Exploratory Writing Projects -- Enrichment Readings -- Chapter 12. Boolean Algebra and Combinatorial Circuits -- 12.1 Boolean Algebra -- 12.2 Boolean functions -- 12.3 Logic Gates -- 12.4 Combinatorial Circuits -- 12.5 Minimization of Combinatorial Circuits -- 12.6 Don't Care Conditions -- Chapter Summary -- Review Exercises -- Supplementary Exercises -- Computer Exercises -- Exploratory Writing Projects -- Enrichment Readings -- Appendix A -- A.1 ASCII Character Set -- A.2 Determinants -- A.3 Exponential and Logarithmic Functions -- A.4 Generating Permutations and Combinations -- A.5 The Multinomial Theorem -- A.6 The Greek Alphabet -- A.7 Web Sites -- References -- Solutions to Odd-Numbered Exercises -- Credits -- Index -- List of Biographical Sketches -- Application Index -- Alogrithms Index -- List of Symbols.