Discrete Mathematics,8th edition

• Richard Johnsonbaugh DePaul University
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Discrete Mathematics, 8th Edition is an accessible introduction that helps to develop your mathematical maturity. Ample opportunities to practice, apply and demonstrate conceptual understanding are provided. Exercise sets feature a large number of applications, especially to computer science. Worked examples provide ready reference as you work. The text models various problem-solving techniques in detail, then encourages you to practice these techniques; it also emphasizes how to read and write proofs. Many proofs are illustrated with annotated figures and/or motivated by special Discussion sections. URLs throughout direct you to relevant applications, extensions, and computer programs.

1. Sets and Logic

• 1.1 Sets
• 1.2 Propositions
• 1.3 Conditional Propositions and Logical Equivalence
• 1.4 Arguments and Rules of Inference
• 1.5 Quantifiers
• 1.6 Nested Quantifiers
• Problem-Solving Corner: Quantifiers

2. Proofs

• 2.1 Mathematical Systems, Direct Proofs, and Counterexamples
• 2.2 More Methods of Proof
• Problem-Solving Corner: Proving Some Properties of Real Numbers
• 2.3 Resolution Proofs
• 2.4 Mathematical Induction
• Problem-Solving Corner: Mathematical Induction
• 2.5 Strong Form of Induction and the Well-Ordering Property

3. Functions, Sequences, and Relations

• 3.1 Functions
• Problem-Solving Corner: Functions
• 3.2 Sequences and Strings
• 3.3 Relations
• 3.4 Equivalence Relations
• Problem-Solving Corner: Equivalence Relations
• 3.5 Matrices of Relations
• 3.6 Relational Databases

4. Algorithms

• 4.1 Introduction
• 4.2 Examples of Algorithms
• 4.3 Analysis of Algorithms
• Problem-Solving Corner: Design and Analysis of an Algorithm
• 4.4 Recursive Algorithms

5. Introduction to Number Theory

• 5.1 Divisors
• 5.2 Representations of Integers and Integer Algorithms
• 5.3 The Euclidean Algorithm
• Problem-Solving Corner: Making Postage
• 5.4 The RSA Public-Key Cryptosystem

6. Counting Methods and the Pigeonhole Principle

• 6.1 Basic Principles
• Problem-Solving Corner: Counting
• 6.2 Permutations and Combinations
• Problem-Solving Corner: Combinations
• 6.3 Generalized Permutations and Combinations
• 6.4 Algorithms for Generating Permutations and Combinations
• 6.5 Introduction to Discrete Probability
• 6.6 Discrete Probability Theory
• 6.7 Binomial Coefficients and Combinatorial Identities
• 6.8 The Pigeonhole Principle

7. Recurrence Relations

• 7.1 Introduction
• 7.2 Solving Recurrence Relations
• Problem-Solving Corner: Recurrence Relations
• 7.3 Applications to the Analysis of Algorithms

8. Graph Theory

• 8.1 Introduction
• 8.2 Paths and Cycles
• Problem-Solving Corner: Graphs
• 8.3 Hamiltonian Cycles and the Traveling Salesperson Problem
• 8.4 A Shortest-Path Algorithm
• 8.5 Representations of Graphs
• 8.6 Isomorphisms of Graphs
• 8.7 Planar Graphs
• 8.8 Instant Insanity

9. Trees

• 9.1 Introduction
• 9.2 Terminology and Characterizations of Trees
• Problem-Solving Corner: Trees
• 9.3 Spanning Trees
• 9.4 Minimal Spanning Trees
• 9.5 Binary Trees
• 9.6 Tree Traversals
• 9.7 Decision Trees and the Minimum Time for Sorting
• 9.8 Isomorphisms of Trees
• 9.9 Game Trees

10. Network Models

• 10.1 Introduction
• 10.2 A Maximal Flow Algorithm
• 10.3 The Max Flow, Min Cut Theorem
• 10.4 Matching
• Problem-Solving Corner: Matching

11. Boolean Algebras and Combinatorial Circuits

• 11.1 Combinatorial Circuits
• 11.2 Properties of Combinatorial Circuits
• 11.3 Boolean Algebras
• Problem-Solving Corner: Boolean Algebras
• 11.4 Boolean Functions and Synthesis of Circuits
• 11.5 Applications

12. Automata, Grammars, and Languages

• 12.1 Sequential Circuits and Finite-State Machines
• 12.2 Finite-State Automata
• 12.3 Languages and Grammars
• 12.4 Nondeterministic Finite-State Automata
• 12.5 Relationships Between Languages and Automata

13. Computational Geometry

• 13.1 The Closest-Pair Problem
• 13.2 An Algorithm to Compute the Convex Hull

Appendices

• A. Matrices
• B. Algebra Review
• C. Pseudocode

Index

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