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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