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Discrete Mathematics

by: Johnsonbaugh, Richard

Discrete Mathematics

by: Johnsonbaugh, Richard

ISBN 13:
9780135182420
ISBN 10:
0135182425
Edition: 4th
Format: Hardcover
Copyright: 07/01/1996
Publisher: Pearson College Div
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Summary

Mild revision of top selling text. This text has the best coverage of topics in computer science. New edition features new Mathematician's Corner which is found in each chapter and shows students how to do proofs.

1 LOGIC AND PROOFS

(62)

1.1 Propositions

(6)

1.2 Conditional Propositions and Logical Equivalence

(10)

1.3 Quantifiers

(16)

1.4 Proofs

(8)

1.5 Resolution Proofs

(4)

1.6 Mathematical Induction

(10)

Problem-Solving Corner: Mathematical Induction

(3)

Notes

(1)

Chapter Review

(2)

Chapter Self-Test

(2)

2 THE LANGUAGE OF MATHEMATICS

(79)

2.1 Sets

(9)

2.2 Sequences and Strings

(11)

2.3 Number Systems

(7)

2.4 Relations

(13)

Problem-Solving Corner: Relations

102

(2)

2.5 Equivalence Relations

104

(10)

Problem-Solving Corner: Equivalence Relations

111

(3)

2.6 Matrices of Relations

114

(4)

2.7 Relational Databases

118

(7)

2.8 Functions

125

(11)

Notes

136

(1)

Chapter Review

137

(2)

Chapter Self-Test

139

(3)

3 ALGORITHMS

142

(55)

3.1 Introduction

143

(1)

3.2 Notation for Algorithms

144

(7)

3.3 The Euclidean Algorithms

151

(6)

3.4 Recursive Algorithms

157

(9)

3.5 Complexity of Algorithms

166

(20)

Problem-Solving Corner: Design and Analysis of an Algorithm

182

(4)

3.6 Analysis of the Euclidean Algorithm

186

(3)

3.7 The RSA Public-Key Cryptosystem

189

(4)

Notes

193

(1)

Chapter Review

193

(1)

Chapter Self-Test

194

(3)

4 COUNTING METHODS AND THE PIGEONHOLE PRINCIPLE

197

(59)

4.1 Basic Principles

197

(13)

Problem-Solving Corner: Counting

207

(3)

4.2 Permutations and Combinations

210

(18)

Problem-Solving Corner: Combinations

225

(3)

4.3 Algorithms for Generating Permutations and Combinations

228

(7)

4.4 Generalized Permutations and Combinations

235

(7)

4.5 Binomial Coefficients and Combinatorial Identities

242

(6)

4.6 The Pigeonhole Principle

248

(5)

Notes

253

(1)

Chapter Review

253

(1)

Chapter Self-Test

254

(2)

5 RECURRENCE RELATIONS

256

(48)

5.1 Introduction

256

(14)

5.2 Solving Recurrence Relations

270

(17)

Problem-Solving Corner: Recurrence Relations

284

(3)

5.3 Applications to the Analysis of Algorithms

287

(15)

Notes

302

(1)

Chapter Review

302

(1)

Chapter Self-Test

302

(2)

6 GRAPH THEORY

304

(72)

6.1 Introduction

305

(11)

6.2 Paths and Cycles

316

(15)

Problem-Solving Corner: Graphs

330

(1)

6.3 Hamiltonian Cycles and the Traveling Salesperson Problem

331

(7)

6.4 A Shortest-Path Algorithm

338

(6)

6.5 Representations of Graphs

344

(6)

6.6 Isomorphisms of Graphs

350

(9)

6.7 Planar Graphs

359

(7)

6.8 Instant Insanity

366

(5)

Notes

371

(1)

Chapter Review

371

(1)

Chapter Self-Test

372

(4)

7 TREES

376

(79)

7.1 Introduction

377

(8)

7.2 Terminology and Characterizations of Trees

385

(7)

Problem-Solving Corner: Trees

390

(2)

7.3 Spanning Trees

392

(8)

7.4 Minimal Spanning Trees

400

(8)

7.5 Binary Trees

408

(7)

7.6 Tree Traversals

415

(7)

7.7 Decision Trees and the Minimum Time for Sorting

422

(7)

7.8 Isomorphisms of Trees

429

(11)

7.9 Game Trees

440

(10)

Notes

450

(1)

Chapter Review

450

(1)

Chapter Self-Test

451

(4)

8 NETWORK MODELS AND PETRI NETS

455

(45)

8.1 Network Models

456

(6)

8.2 A Maximal Flow Algorithm

462

(11)

8.3 The Max Flow, Min Cut Theorem

473

(5)

8.4 Matching

478

(8)

Problem-Solving Corner: Matching

484

(2)

8.5 Petri Nets

486

(10)

Notes

496

(1)

Chapter Review

497

(1)

Chapter Self-Test

498

(2)

9 BOOLEAN ALGEBRAS AND COMBINATORIAL CIRCUITS

500

(46)

9.1 Combinatorial Circuits

500

(9)

9.2 Properties of Combinatorial Circuits

509

(7)

9.3 Boolean Algebras

516

(8)

Problem-Solving Corner: Boolean Algebras

522

(2)

9.4 Boolean Functions and Synthesis of Circuits

524

(7)

9.5 Applications

531

(11)

Notes

542

(1)

Chapter Review

542

(1)

Chapter Self-Test

543

(3)

10 AUTOMATA, GRAMMARS, AND LANGUAGES

546

(47)

10.1 Sequential Circuits and Finite-State Machines

546

(8)

10.2 Finite-State Automata

554

(8)

10.3 Languages and Grammars

562

(11)

10.4 Nondeterministic Finite-State Automata

573

(9)

10.5 Relationships Between Languages and Automata

582

(7)

Notes

589

(1)

Chapter Review

590

(1)

Chapter Self-Test

590

(3)

11 COMPUTATIONAL GEOMETRY

593

(17)

11.1 The Closest-Pair Problem

593

(5)

11.2 A Lower Bound for the Closest-Pair Problem

598

(3)

11.3 An Algorithm to Compute the Convex Hull

601

(7)

Notes

608

(1)

Chapter Review

609

(1)

Chapter Self-Test

609

(1)

APPENDIX: MATRICES

610

(5)

REFERENCES

615

(6)

HINTS AND SOLUTIONS TO SELECTED EXERCISES

621

(66)

INDEX

687

Amazon no longer offers textbook rentals. We do!

Discrete Mathematics

Discrete Mathematics

9780135182420

0135182425

Summary

Table of Contents

Supplemental Materials

Write a Review

Amazon no longer offers textbook rentals. We do!

Discrete Mathematics

Discrete Mathematics

9780135182420

0135182425

Summary

Table of Contents

Supplemental Materials

Write a Review

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