### What's included

## Overview

*This title is part of the Pearson Modern Classics series. Pearson Modern Classics are acclaimed titles at a value price. Please visit www.pearsonhighered.com/math-classics-series for a complete list of titles.*

*An ever-increasing percentage of mathematic applications involve discrete rather than continuous models. Driving this trend is the integration of the computer into virtually every aspect of modern society. Intended for a one-semester introductory course, the strong algorithmic emphasis of Discrete Mathematics is independent of a specific programming language, allowing students to concentrate on foundational problem-solving and analytical skills. Instructors get the topical breadth and organizational flexibility to tailor the course to the level and interests of their students.*

## Table of contents

(Each Chapter concludes with "Historical Notes," "Supplementary Exercises," "Computer Projects," and "Suggested Readings.").

**1: An Introduction to Combinatorial Problems and Techniques**

Section 1.1 The Time to Complete a Project

Section 1.2 A Matching Problem

Section 1.3 A Knapsack Problem

Section 1.4 Algorithms and Their Efficiency

Historical Notes

Supplementary Exercises

Computer Projects

Suggested Readings

**2: Sets, Relations, and Functions**

Section 2.1 Set Operations

Section 2.2 Equivalence Relations

Section 2.3_ Partial Ordering Relations

Section 2.4 Functions

Section 2.5 Mathematical Induction

Section 2.6 Applications

Historical Notes

Supplementary Exercises

Computer Projects

Suggested Readings

**3: Coding Theory**

Section 3.1 Congruence

Section 3.2 The Euclidean Algorithm and Diophantine Equations

Section 3.3 The RSA Method

Section 3.4 Error-Detecting and Error-Correcting Codes

Section 3.5 Matrix Codes

Section 3.6 Matrix Codes That Correct All Single-Digit Errors

Historical Notes

Supplementary Exercises

Computer Projects

Suggested Readings

**4: Graphs**

Section 4.1 Graphs and Their Representations

Section 4.2 Paths and Circuits

Section 4.3 Shortest Paths and Distance

Section 4.4 Coloring a Graph

Section 4.5 Directed Graphs and Multigraphs

Historical Notes

Supplementary Exercises

Computer Projects

Suggested Readings

**5: Trees**

Section 5.1 Properties of Trees

Section 5.2 Spanning Trees

Section 5.3 Depth-First Search

Section 5.4 Rooted Trees

Section 5.5 Binary Trees and Traversals

Section 5.6 Optimal Binary Trees and Binary Search Trees

Historical Notes

Supplementary Exercises

Computer Projects

Suggested Readings

**6: Matching**

Section 6.1 Systems of Distinct Representatives

Section 6.2 Matchings in Graphs

Section 6.3 A Matching Algorithm

Section 6.4 Applications of the Algorithm

Section 6.5 The Hungarian Method

Historical Notes

Supplementary Exercises

Computer Projects

Suggested Readings

**7: Network Flows**

Section 7.1 Flows and Cuts

Section 7.2 A Flow Augmentation Algorithm

Section 7.3 The Max-Flow Min-Cut Theorem

Section 7.4 Flows and Matchings

Historical Notes

Supplementary Exercises

Computer Projects

Suggested Readings

**8: Counting Techniques**

Section 8.1 Pascal’s Triangle and the Binomial Theorem

Section 8.3 Permutations and Combinations

Section 8.4 Arrangements and Selections with Repetitions

Section 8.5 Probability

Section 8.6* The Principle of Inclusion-Exclusion

Section 8.7* Generating Permutations and r -Combinations

Historical Notes

Supplementary Exercises

Computer Projects

Suggested Readings

**9: Recurrence Relations and Generating Functions**

Section 9.1 Recurrence Relations

Section 9.2 The Method of Iteration

Section 9.3 Linear Difference Equations with Constant Coefficients

Section 9.4* Analyzing the Efficiency of Algorithms with Recurrence Relations

Section 9.5 Counting with Generating Functions

Section 9.6 The Algebra of Generating Functions

Historical Notes

Supplementary Exercises

Computer Projects

Suggested Readings

**10: Combinatorial Circuits and Finite State Machines**

Section 10.1 Logical Gates

Section 10.2 Creating Combinatorial Circuits

Section 10.3 Karnaugh Maps

Section 10.4 Finite State Machines

Historical Notes

Supplementary Exercises

Computer Projects

Suggested Readings

**Appendix A: An Introduction to Logic and Proof**

Section A.1 Statements and Connectives

Section A.2 Logical Equivalence

Section A.3 Methods of Proof

Historical Notes

Supplementary Exercises

Suggested Readings

**Appendix B Matrices**

**Historical Notes**

**Appendix C The Algorithms in This Book**

**Bibliography**

**Answers to odd-numbered exercises**

**Index**

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