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Discrete Mathematics

by: Johnsonbaugh, Richard

Discrete Mathematics

by: Johnsonbaugh, Richard

ISBN 13:
9780130890085
ISBN 10:
0130890081
Edition: 5th
Format: Hardcover
Copyright: 01/01/2001
Publisher: Pearson College Div
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Summary

For one or two term introductory courses in discrete mathematics. This best-selling book provides an accessible introduction to discrete mathematics through an algorithmic approach that focuses on problem- solving techniques. This edition has woven techniques of proofs into the text as a running theme. Each chapter has a problem-solving corner that shows students how to attack and solve problems.

Preface

Logic and Proofs

(54)

Propositions

(5)

Conditional Propositions and Logical Equivalence

(7)

Quantifiers

(15)

Proofs

(8)

Resolution Proofs

(4)

Mathematical Induction

(14)

Problem-Solving Corner: Mathematical Induction

(2)

Notes

(1)

Chapter Review

(2)

Chapter Self-Test

(1)

Computer Exercises

(1)

The Language of Mathematics

(65)

Sets

(8)

Sequences and Strings

(7)

Number Systems

(6)

Relations

(8)

Problem-Solving Corner: Relations

(1)

Equivalence Relations

(7)

Problem-Solving Corner: Equivalence Relations

(2)

Matrices of Relations

(5)

Relational Databases

(4)

Functions

101

(19)

Notes

114

(1)

Chapter Review

114

(2)

Chapter Self-Test

116

(2)

Computer Exercises

118

(2)

Algorithms

120

(45)

Introduction

121

(1)

Notation for Algorithms

122

(6)

The Euclidean Algorithm

128

(4)

Recursive Algorithms

132

(6)

Complexity of Algorithms

138

(16)

Problem-Solving Corner: Design and Analysis of an Algorithm

152

(2)

Analysis of the Euclidean Algorithm

154

(3)

The RSA Public-Key Cryptosystem

157

(8)

Notes

160

(1)

Chapter Review

161

(1)

Chapter Self-Test

162

(2)

Computer Exercises

164

(1)

Counting Methods and the Pigeonhole Principle

165

(59)

Basic Principles

165

(9)

Problem-Solving Corner: Counting

172

(2)

Permutations and Combinations

174

(13)

Problem-Solving Corner: Combinations

185

(2)

Algorithms for Generating Permutations and Combinations

187

(5)

Introduction to Discrete Probability

192

(3)

Discrete Probability Theory

195

(11)

Generalized Permutations and Combinations

206

(5)

Binomial Coefficients and Combinatorial Identities

211

(5)

The Pigeonhole Principle

216

(8)

Notes

220

(1)

Chapter Review

220

(1)

Chapter Self-Test

221

(2)

Computer Exercises

223

(1)

Recurrence Relations

224

(39)

Introduction

224

(11)

Solving Recurrence Relations

235

(14)

Problem-Solving Corner: Recurrence Relations

246

(3)

Applications to the Analysis of Algorithms

249

(14)

Notes

260

(1)

Chapter Review

260

(1)

Chapter Self-Test

260

(1)

Computer Exercises

261

(2)

Graph Theory

263

(60)

Introduction

263

(11)

Paths and Cycles

274

(11)

Problem-Solving Corner: Graphs

284

(1)

Hamiltonian Cycles and the Traveling Salesperson Problem

285

(6)

A Shortest-Path Algorithm

291

(5)

Representations of Graphs

296

(5)

Isomorphisms of Graphs

301

(6)

Planar Graphs

307

(6)

Instant Insanity

313

(10)

Notes

317

(1)

Chapter Review

317

(2)

Chapter Self-Test

319

(2)

Computer Exercises

321

(2)

Trees

323

(67)

Introduction

323

(8)

Terminology and Characterizations of Trees

331

(6)

Problem-Solving Corner: Trees

336

(1)

Spanning Trees

337

(6)

Minimal Spanning Trees

343

(6)

Binary Trees

349

(6)

Tree Traversals

355

(6)

Decision Trees and the Minimum Time for Sorting

361

(6)

Isomorphism of Trees

367

(9)

Game Trees

376

(14)

Notes

384

(1)

Chapter Review

384

(1)

Chapter Self-Test

385

(4)

Computer Exercises

389

(1)

Network Models

390

(26)

Introduction

390

(6)

A Maximal Flow Algorithm

396

(8)

The Max Flow, Min Cut Theorem

404

(3)

Matching

407

(9)

Problem-Solving Corner: Matching

412

(1)

Notes

413

(1)

Chapter Review

414

(1)

Chapter Self-Test

414

(1)

Computer Exercises

415

(1)

Boolean Algebras and Combinatorial Circuits

416

(36)

Combinatorial Circuits

416

(7)

Properties of Combinatorial Circuits

423

(4)

Boolean Algebras

427

(7)

Problem-Solving Corner: Boolean Algebras

432

(2)

Boolean Functions and Synthesis of Circuits

434

(5)

Applications

439

(13)

Notes

447

(1)

Chapter Review

447

(1)

Chapter Self-Test

448

(2)

Computer Exercises

450

(2)

Automata, Grammars, and Languages

452

(37)

Sequential Circuits and Finite-State Machines

452

(6)

Finite-State Automata

458

(6)

Languages and Grammars

464

(8)

Nondeterministic Finite-State Automata

472

(7)

Relationships Between Languages and Automata

479

(10)

Notes

484

(1)

Chapter Review

485

(1)

Chapter Self-Test

486

(2)

Computer Exercises

488

(1)

Computational Geometry

489

(16)

The Closest-Pair Problem

489

(5)

A Lower Bound for the Closest-Pair Problem

494

(2)

An Algorithm to Compute the Convex Hull

496

(9)

Notes

503

(1)

Chapter Review

503

(1)

Chapter Self-Test

503

(1)

Computer Exercises

504

(1)

A Matrices

505

(4)

B Algebra Review

509

(12)

References

521

(6)

Hints and Solutions to Selected Exercises

527

(80)

Index

607

Amazon no longer offers textbook rentals. We do!

Discrete Mathematics

Discrete Mathematics

9780130890085

0130890081

Summary

Table of Contents

Supplemental Materials

Write a Review

Amazon no longer offers textbook rentals. We do!

Discrete Mathematics

Discrete Mathematics

9780130890085

0130890081

Summary

Table of Contents

Supplemental Materials

Write a Review

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