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Discrete Mathematics, 8th edition

Published by Pearson (June 1, 2023) © 2023

  • 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

References

Hints and Solutions to Selected Exercises

Index

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