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Discrete Structures for Computing
1. Logic and Proofs
1.1. Propositional Logic
1.2. Predicate Logic
1.3. Proofs
2. Sets and Relations
2.1. Sets and Set Theory
2.2. Relations
3. Basic Structures
3.1. Functions
3.2. Sequences and Series
3.3. Matrices
4. The Integers
4.1. Divisibility and Modular Arithmetic
4.2. Greatest Common Divisors and Primes
4.3. Solving Congruences
4.4. Integer Representations
4.5. Applications
5. Induction and Recursion
5.1. Induction
5.2. Recursion
5.3. Computer Program Verification
6. Combinatorics and Probability
6.1. Counting
6.2. Permutations and Combinations
6.3. Discrete Probability
7. Graph Theory
7.1. Graphs
7.2. Directed Graphs
7.3. Representing Graphs
7.4. Paths and Circuits
7.5. Applications
8. Glossary
Index
Symbols
|
A
|
B
|
C
|
D
|
E
|
F
|
G
|
H
|
I
|
L
|
M
|
N
|
O
|
P
|
Q
|
R
|
S
|
T
|
U
|
V
|
W
Symbols
\exists
\forall
A
antisymmetric
B
bijective
binary relation
binary tree height
bipartite graph
bound variable
C
cardinality
Cartesian product
clique
codomain
combination
comparable
complete bipartite graph
complete graph
composition
congruence class
congruent
conjecture
connected
connected component
consistent
contingency
contradiction
corollary
countably infinite
cover
cycle graph
D
DAG
directed acycling graph
directed graph
directed path
disjoint sets
divisible
domain
domain of definition
domain of discourse
E
empty set
equally-likely
equivalence class
equivalence relation
Euler circuit
Euler path
event
existential quantifier
experiment
F
finite set
free variable
G
genealized pigeon hole principle
graph
greatest common divisor
H
Hamilton circuit
Hamilton path
I
in-degree
injective
intersection
inverse function
isomorphic graphs
L
least common multiple
lemma
loop invariant
M
maximal
maximal clique
maximum
minimal
minimum
monotonic function
N
neighbourhood
non-decreasing
non-increasing
O
open formula
order of a graph
out-degree
P
partial function
partial order
partially ordered set
partition
path
permutation
pigeon hole principle
planar graph
poset
power set
predicate
predicate Logic
prime
product rule
proof
proper subgraph
proposition
(logic)
propositional formula
propositional function
propositional logic
Q
quantifier
R
range
rational number
recurrence relation
recursive definition
reflexive
relatively prime
rooted subtree
rooted tree
S
sample space
satisfiable
sequence
set intersection
set union
simple graph
singleton
string
strongly connected component
subgraph
subset
sum rule
surjective
symmetric
T
tautology
theorem
total
total order
totally ordered set
transitive
tree
trivial proof
truth assignment
tuple
U
uncountably infinite
underlying graph
union
univalent
universal quantifier
universal set
universe
V
vacuous proof
variable
W
weakly connected component
well-ordered
well-ordering principle
wheel graph