Discrete Mathematics 8th Edition by Richard Johnsonbaugh ISBN 9780131176874 0131176870

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ISBN 10: 0131176870
ISBN 13: 9780131176874
Author: Richard Johnsonbaugh

Discrete Mathematics 8th Edition Table of contents:

Chapter 1 SETS AND LOGIC

1.1 Sets

1.1 Problem-Solving Tips

1.1 Review Exercises

1.1 Exercises

1.2 Propositions

SOLUTION

1.2 Problem-Solving Tips

1.2 Review Exercises

1.2 Exercises

1.3 Conditional Propositions and Logical Equivalence

1.3 Problem-Solving Tips

1.3 Review Exercises

1.3 Exercises

1.4 Arguments and Rules of Inference

FIRST SOLUTION

SECOND SOLUTION

1.4 Problem-Solving Tips

1.4 Review Exercises

1.4 Exercises

1.5 Quantifiers

Rules of Inference for Quantified Statements

SOLUTION

SOLUTION

1.5 Problem-Solving Tips

1.5 Review Exercises

1.5 Exercises

1.6 Nested Quantifiers

SOLUTION

SOLUTION

SOLUTION

1.6 Problem-Solving Tips

1.6 Review Exercises

1.6 Exercises

Problem-Solving Corner Quantifiers

Problem

Attacking the Problem

Finding a Solution

Formal Solution

Summary of Problem-Solving Techniques

Exercises

Chapter 1 Notes

Chapter 1 Review

Section 1.1

Section 1.2

Section 1.3

Section 1.4

Section 1.5

Section 1.6

Chapter 1 Self-Test

Chapter 1 Computer Exercises

Chapter 2 PROOFS

2.1 Mathematical Systems, Direct Proofs, and Counterexamples

Direct Proofs

Disproving a Universally Quantified Statement

SOLUTION

2.1 Problem-Solving Tips

Some Common Errors

2.1 Review Exercises

2.1 Exercises

2.2 More Methods of Proof

Proof by Contradiction

SOLUTION

SOLUTION

SOLUTION

Proof by Contrapositive

SOLUTION

SOLUTION

Proof by Cases

SOLUTION

SOLUTION

Proofs of Equivalence

Existence Proofs

2.2 Problem-Solving Tips

2.2 Review Exercises

2.2 Exercises

Problem-Solving Corner Proving Some Properties of Real Numbers

Problem

Attacking the Problem

Finding a Solution

Formal Solution

Summary of Problem-Solving Techniques

Comments

Exercises

2.3 Resolution Proofs†

2.3 Problem-Solving Tips

2.3 Review Exercises

2.3 Exercises

2.4 Mathematical Induction

Principle of Mathematical Induction

SOLUTION

Basis Step (n = 1)

Inductive Step

SOLUTION

Basis Step (n = 0)

Inductive Step

SOLUTION

Basis Step (n = 1)

Inductive Step

Basis Step (k = 1)

Inductive Step

SOLUTION

2.4 Problem-Solving Tips

2.4 Review Exercises

2.4 Exercises

Basis Step (n = 1)

Inductive Step

Problem-Solving Corner Mathematical Induction

Problem

Attacking the Problem

Finding a Solution

Formal Solution

Basis Step (n = 0)

Inductive Step

Summary of Problem-Solving Techniques

Comments

Exercises

2.5 Strong Form of Induction and the Well-Ordering Property

Strong Form of Mathematical Induction

SOLUTION

Basis Steps (n = 4, n = 5)

Inductive Step

SOLUTION

Basis Step (n = 1)

Inductive Step

SOLUTION

SOLUTION

Basis Step (n = 1)

Inductive Step

Well-Ordering Property

2.5 Problem-Solving Tips

2.5 Review Exercises

2.5 Exercises

Basis Step (n = 3)

Inductive Step

Chapter 2 Notes

Chapter 2 Review

Section 2.1

Section 2.2

Section 2.3

Section 2.4

Section 2.5

Chapter 2 Self-Test

Chapter 2 Computer Exercises

Chapter 3 FUNCTIONS, SEQUENCES, AND RELATIONS

3.1 Functions

3.1 Problem-Solving Tips

3.1 Review Exercises

3.1 Exercises

Problem-Solving Corner Functions

Problem

Attacking the Problem

Finding a Solution

Formal Solution

Summary of Problem-Solving Techniques

3.2 Sequences and Strings

3.2 Problem-Solving Tips

3.2 Review Exercises

3.2 Exercises

3.3 Relations

SOLUTION

3.3 Problem-Solving Tips

3.3 Review Exercises

3.3 Exercises

3.4 Equivalence Relations

SOLUTION

SOLUTION

3.4 Problem-Solving Tips

3.4 Review Exercises

3.4 Exercises

Problem-Solving Corner Equivalence Relations

Problem

Attacking the Problem

Finding a Solution

Summary of Problem-Solving Techniques

Comments

3.5 Matrices of Relations

3.5 Problem-Solving Tips

3.5 Review Exercises

3.5 Exercises

3.6 Relational Databases†

SOLUTION

SOLUTION

3.6 Problem-Solving Tips

3.6 Review Exercises

3.6 Exercises

Chapter 3 Notes

Chapter 3 Review

Section 3.1

Section 3.2

Section 3.3

Section 3.4

Section 3.5

Section 3.6

Chapter 3 Self-Test

Chapter 3 Computer Exercises

Chapter 4 ALGORITHMS

4.1 Introduction

4.1 Problem-Solving Tips

4.1 Review Exercises

4.1 Exercises

4.2 Examples of Algorithms

Searching

Sorting

Time and Space for Algorithms

4.2 Problem-Solving Tips

4.2 Review Exercises

4.2 Exercises

4.3 Analysis of Algorithms

4.3 Problem-Solving Tips

4.3 Review Exercises

4.3 Exercises

Basis Step

Inductive Step

Problem-Solving Corner Design and Analysis of an Algorithm

Problem

Attacking the Problem

Finding a Solution

Formal Solution

Summary of Problem-Solving Techniques

Comments

Exercises

4.4 Recursive Algorithms

Solution

4.4 Problem-Solving Tips

4.4 Review Exercises

4.4 Exercises

Chapter 4 Notes

Chapter 4 Review

Section 4.1

Section 4.2

Section 4.3

Section 4.4

Chapter 4 Self-Test

Chapter 4 Computer Exercises

Chapter 5 INTRODUCTION TO NUMBER THEORY

5.1 Divisors

SOLUTION

5.1 Problem-Solving Tips

5.1 Review Exercises

5.1 Exercises

5.2 Representations of Integers and Integer Algorithms

5.2 Problem-Solving Tips

5.2 Review Exercises

5.2 Exercises

5.3 The Euclidean Algorithm

SOLUTION

Analysis of the Euclidean Algorithm

A Special Result

Computing an Inverse Modulo an Integer

5.3 Problem-Solving Tips

5.3 Review Exercises

5.3 Exercises

Problem-Solving Corner Making Postage

Problem

Attacking the Problem

Finding a Solution

Formal Solution

Summary of Problem-Solving Techniques

Exercise

5.4 The RSA Public-Key Cryptosystem

5.4 Review Exercises

5.4 Exercises

Chapter 5 Notes

Chapter 5 Review

Section 5.1

Section 5.2

Section 5.3

Section 5.4

Chapter 5 Self-Test

Chapter 5 Computer Exercises

Chapter 6 COUNTING METHODS AND THE PIGEONHOLE PRINCIPLE

6.1 Basic PrinciplesInclusion-Exclusion Principle

SOLUTION

6.1 Problem-Solving Tips

6.1 Review Exercises

6.1 Exercises

Problem-Solving Corner Counting

Problem

Attacking the Problem

Finding Another Solution

Formal Solution

Summary of Problem-Solving Techniques

6.2 Permutations and Combinations

6.2 Problem-Solving Tips

6.2 Review Exercises

6.2 Exercises

Problem-Solving Corner Combinations

Problem

Attacking the Problem

Finding a Solution

Formal Solution

Summary of Problem-Solving Techniques

Comments

Exercises

6.3 Generalized Permutations and Combinations

6.3 Problem-Solving Tips

6.3 Review Exercises

6.3 Exercises

6.4 Algorithms for Generating Permutations and Combinations

6.4 Review Exercises

6.4 Exercises

6.5 Introduction to Discrete Probability †

6.5 Review Exercises

6.5 Exercises

6.6 Discrete Probability Theory †

Formulas

SOLUTION

SOLUTION

SOLUTION

Conditional Probability

SOLUTION

Independent Events

SOLUTION

SOLUTION

Pattern Recognition and Bayes’ Theorem

SOLUTION

SOLUTION

6.6 Review Exercises

6.6 Exercises

6.7 Binomial Coefficients and Combinatorial Identities

6.7 Review Exercises

6.7 Exercises

6.8 The Pigeonhole Principle

6.8 Review Exercises

6.8 Exercises

Chapter 6 Notes

Chapter 6 Review

Section 6.1

Section 6.2

Section 6.3

Section 6.4

Section 6.5

Section 6.6

Section 6.7

Section 6.8

Chapter 6 Self-Test

Chapter 6 Computer Exercises

Chapter 7 RECURRENCE RELATIONS

7.1 Introduction

SOLUTION

SOLUTION

7.1 Problem-Solving Tips

7.1 Review Exercises

7.1 Exercises

7.2 Solving Recurrence Relations

7.2 Problem-Solving Tips

7.2 Review Exercises

7.2 Exercises

7.3 Applications to the Analysis of Algorithms

7.3 Review Exercises

7.3 Exercises

7.4 The Closest-Pair Problem†

SOLUTION

7.4 Review Exercises

7.4 Exercises

Chapter 7 Notes

Chapter 7 Review

Section 7.1

Section 7.2

Section 7.3

Section 7.4

Chapter 7 Self-Test

Chapter 7 Computer Exercises

Chapter 8 GRAPH THEORY

8.1 Introduction

SOLUTION

SOLUTION

8.1 Problem-Solving Tips

8.1 Review Exercises

8.1 Exercises

8.2 Paths and Cycles

SOLUTION

SOLUTION

SOLUTION

Corollary 8.2.22

8.2 Review Exercises

8.2 Exercises

8.3 Hamiltonian Cycles and the Traveling Salesperson Problem

SOLUTION

SOLUTION

8.3 Problem-Solving Tips

8.3 Review Exercises

8.3 Exercises

8.4 A Shortest-Path Algorithm

Algorithm 8.4.1 Dijkstra’s Shortest-Path Algorithm

SOLUTION

8.4 Review Exercises

8.4 Exercises

Algorithm 8.4.6

8.5 Representations of Graphs

8.5 Review Exercises

8.5 Exercises

8.6 Isomorphisms of Graphs

Corollary 8.6.5

SOLUTION

8.6 Review Exercises

8.6 Exercises

8.7 Planar Graphs

SOLUTION

SOLUTION

8.7 Review Exercises

8.7 Exercises

8.8 Instant Insanity†

SOLUTION

8.8 Review Exercises

8.8 Exercises

Chapter 8 Notes

Chapter 8 Review

Section 8.1

Section 8.2

Section 8.3

Section 8.4

Section 8.5

Section 8.6

Section 8.7

Section 8.8

Chapter 8 Self-Test

Chapter 8 Computer Exercises

Chapter 9 TREES

9.1 Introduction

Algorithm 9.1.9

SOLUTION

9.1 Review Exercises

9.1 Exercises

9.2 Terminology and Characterizations of Trees

9.2 Problem-Solving Tips

9.2 Review Exercises

9.2 Exercises

9.3 Spanning Trees

SOLUTION

Algorithm 9.3.6

Algorithm 9.3.7

SOLUTION

SOLUTION

Algorithm 9.3.10

9.3 Problem-Solving Tips

9.3 Review Exercises

9.3 Exercises

9.4 Minimal Spanning Trees

Algorithm 9.4.3

SOLUTION

9.4 Review Exercises

9.4 Exercises

9.5 Binary Trees

SOLUTION

Algorithm 9.5.10

9.5 Review Exercises

9.5 Exercises

9.6 Tree Traversals

Algorithm 9.6.1

SOLUTION

Algorithm 9.6.3 Inorder Traversal

SOLUTION

Algorithm 9.6.5

SOLUTION

9.6 Review Exercises

9.6 Exercises

9.7 Decision Trees and the Minimum Time for Sorting

9.7 Review Exercises

9.7 Exercises

9.8 Isomorphisms of Trees

Algorithm 9.8.13

9.8 Review Exercises

9.8 Exercises

9.9 Game Trees†

SOLUTION

SOLUTION

9.9 Review Exercises

9.9 Exercises

Chapter 9 Notes

Chapter 9 Review

Section 9.1

Section 9.2

Section 9.3

Section 9.4

Section 9.5

Section 9.6

Section 9.7

Section 9.8

Section 9.9

Chapter 9 Self-Test

Chapter 9 Computer Exercises

Chapter 10 NETWORK MODELS

10.1 Introduction

SOLUTION

SOLUTION

10.1 Review Exercises

10.1 Exercises

10.2 A Maximal Flow Algorithm

SOLUTION

10.2 Review Exercises

10.2 Exercises

10.3 The Max Flow, Min Cut Theorem

10.3 Review Exercises

10.3 Exercises

10.4 Matching

SOLUTION

Chapter 11 BOOLEAN ALGEBRAS AND COMBINATORIAL CIRCUITS

11.1 Combinatorial Circuits

SOLUTION

SOLUTION

11.1 Review Exercises

11.1 Exercises

11.2 Properties of Combinatorial Circuits

SOLUTION

SOLUTION

11.2 Review Exercises

11.2 Exercises

11.3 Boolean Algebras

11.3 Review Exercises

11.3 Exercises

11.4 Boolean Functions and Synthesis of Circuits

SOLUTION

SOLUTION

11.4 Review Exercises

11.4 Exercises

11.5 Applications

11.5 Review Exercises

11.5 Exercises

Chapter 11 Notes

Chapter 11 Review

Section 11.1

Section 11.2

Section 11.3

Section 11.4

Section 11.5

Chapter 11 Self-Test

Chapter 11 Computer Exercises

Chapter 12 AUTOMATA, GRAMMARS, AND LANGUAGES

12.1 Sequential Circuits and Finite-State Machines

12.1 Review Exercises

12.1 Exercises

12.2 Finite-State Automata

Algorithm 12.2.10

12.2 Review Exercises

12.2 Exercises

12.3 Languages and Grammars

12.3 Review Exercises

12.3 Exercises

12.4 Nondeterministic Finite-State Automata

SOLUTION

SOLUTION

12.4 Review Exercises

12.4 Exercises

12.5 Relationships Between Languages and Automata

12.5 Review Exercises

12.5 Exercises

Chapter 12 Notes

Chapter 12 Review

Section 12.1

Section 12.2

Section 12.3

Section 12.4

Section 12.5

Chapter 12 Self-Test

Chapter 12 Computer Exercises

Appendix A MATRICES

Exercises

Appendix B ALGEBRA REVIEW

Grouping

Fractions

Exponents

Factoring

Solving a Quadratic Equation

SOLUTION

Inequalities

Exercises

Appendix C PSEUDOCODE

Exercises

REFERENCES

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Tags: Richard Johnsonbaugh, Discrete Mathematics