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Tables of Contents for Discrete Mathematics for Computing

Chapter/Section Title

Page #

Page Count

Preface

viii

List of symbols

x

Introduction

1

13

Modelling

1

4

Pseudocode

5

9

Exercise set 1

9

3

Chapter summary

12

2

Logic and proof

14

20

Propositions and logic

14

5

Predicates and quantifiers

19

2

Methods of proof

21

2

Mathematical induction

23

11

Exercise set 2

26

2

Chapter summary

28

1

Application: Correctness of algorithms

29

5

Set theory

34

22

Sets and set operations

34

6

The algebra of sets

40

2

Further properties of sets

42

14

Exercise set 3

47

2

Chapter summary

49

2

Application: Knowledge-based systems

51

5

Relations

56

21

Binary relations

56

5

Properties of relations

61

3

Equivalence relations and partial orders

64

13

Exercise set 4

68

2

Chapter summary

70

1

Application: Database management systems

71

6

Functions

77

24

Inverse relations and composition of relations

77

5

Functions

82

5

Inverse functions and composition of functions

87

3

The pigeonhole principle

90

11

Exercise set 5

93

3

Chapter summary

96

1

Application: Functional programming languages

97

4

Combinatorics

101

20

The addition and multiplication principles

101

2

Counting formulae

103

6

The binomial expansion

109

12

Exercise set 6

113

2

Chapter summary

115

1

Application: Efficiency of algorithms

116

5

Graphs

121

28

Graphs and terminology

121

6

Hamiltonian graphs

127

4

Trees

131

18

Exercise set 7

137

4

Chapter summary

141

2

Application: Sorting and searching

143

6

Directed graphs

149

21

Directed graphs

149

4

Paths in digraphs

153

4

Shortest paths

157

13

Exercise set 8

161

3

Chapter summary

164

1

Application: Communications networks

165

5

Boolean algebra

170

21

Boolean algebra

170

5

Karnaugh maps

175

4

Logic circuits

179

12

Exercise set 9

182

3

Chapter summary

185

1

Application: Designing a 2-bit adder

186

5

Solutions

191

41

Further reading

232

1

Index

233