Math Notation Flashcards
1
Q
≠
A
not equal sign
Inequality
5 ≠ 4
5 is not equal to 4
2
Q
=
A
equals sign
Equality
5 = 2+3
5 is equal to 2+3
3
Q
≈
A
approximately equal
approximation
x ≈ y means x is approximately equal to y
4
Q
>
A
inequality
greater than
5 > 4
5 is greater than 4
5
Q
A
inequality
less than
4 < 5
4 is less than 5
6
Q
≥
A
inequality
greater than or equal to
5 ≥ 4,
x ≥ y means x is greater than or equal to y
7
Q
≤
A
less than or equal to
4 ≤ 5,
x ≤ y means x is less than or equal to y
8
Q
( )
A
parentheses
calculate expression inside first
2 × (3+5) = 16
9
Q
[ ]
A
Brackets
calculate expression inside first
[(1+2)×(1+5)] = 18
10
Q
+
A
plus sign
Addition
1 + 1 = 2
11
Q
−
A
minus sign
Subtraction
2 − 1 = 1
12
Q
±
A
plus - minus
both plus and minus operations
3 ± 5 = 8 or -2
13
Q
*
A
Asterisk
Multiplication
2 * 3 = 6
14
Q
×
A
times sign
Multiplication
2 × 3 = 6
15
Q
⋅
A
multiplication dot
Multiplication
2 ⋅ 3 = 6
16
Q
÷
A
division sign / obelus
Division
6 ÷ 2 = 3
17
Q
/
A
division slash
Division
6 / 2 = 3
18
Q
—
A
horizontal line
division / fraction
19
Q
mod
A
Modulo
remainder calculation
7 mod 2 = 1
20
Q
.
A
Period
decimal point, decimal separator
2.56 = 2+56/100
21
Q
a^b
A
Caret
Exponent
2 ^ 3 = 8
22
Q
√a
A
square root
√a ⋅ √a = a
√9 = ±3
23
Q
3√a (3 superindex)
A
cube root
3√a ⋅ 3√a ⋅ 3√a = a
3√8 = 2
24
Q
n√a (n superindex)
A
“n-th root (radical)
for n=3, n√8 = 2”
25
%
Percent
1% = 1/100
10% × 30 = 3
26
‰
Per-mille
1‰ = 1/1000 = 0.1%
10‰ × 30 = 0.3
27
ppm
Per-million
1ppm = 1/1000000
10ppm × 30 = 0.0003
28
ppb
Per-billion
1ppb = 1/1000000000
10ppb × 30 = 3×10-7
29
∠
Angle
formed by two rays
∠ABC = 30°
30
°
Degree
1 turn = 360°
α = 60°
31
deg
Degree
1 turn = 360deg
α = 60deg
32
≅
congruent to
equivalence of geometric shapes and size
∆ABC≅ ∆XYZ
33
~ (geometry)
Similarity
same shapes, not same size
∆ABC~ ∆XYZ
34
Δ
Triangle
triangle shape
ΔABC≅ ΔBCD
35
|x-y|
Distance
distance between points x and y
| x-y | = 5
36
π
pi constant
π = 3.141592654…
c = π⋅d = 2⋅π⋅r
37
rad
Radians
radians angle unit
360° = 2π rad
38
c
Radians
radians angle unit
360° = 2π c
39
x
x variable
unknown value to find
when 2x = 4, then x = 2
40
≡
Equivalence
| identical to
41
≜
equal by definition
42
:=
equal by definition
43
~
approximately equal
weak approximation
11 ~ 10
44
≈
approximately equal
Approximation
sin(0.01) ≈ 0.01
45
∝
proportional to
y ∝ x when y = kx, k constant
46
∞
Lemniscate
| infinity symbol
47
≪
much less than
1 ≪ 1000000
48
≫
much greater than
1000000 ≫ 1
49
{ }
Braces
| set
50
⌊x⌋
floor brackets
rounds number to lower integer
⌊4.3⌋ = 4
51
⌈x⌉
ceiling brackets
rounds number to upper integer
⌈4.3⌉ = 5
52
x!
exclamation mark
Factorial
4! = 1*2*3*4 = 24
53
| x |
vertical bars
absolute value
| -5 | = 5
54
f (x)
```
function of x
maps values of x to f(x)
```
f (x) = 3x+5
55
(f ∘ g)
```
function composition
(f ∘ g) (x) = f (g(x))
```
f (x)=3x,g(x)=x-1 ⇒(f ∘ g)(x)=3(x-1)
56
(a,b)
```
open interval
(a,b) = {x | a < x < b}
```
x∈ (2,6)
57
[a,b]
closed interval
[a,b] = {x | a ≤ x ≤ b}
x ∈ [2,6]
58
∆
Delta
change / difference
∆t = t1 - t0
59
∑
Sigma
summation - sum of all values in range of series
∑ xi= x1+x2+...+xn
60
∑∑
Sigma
double summation
∑+∑
61
∏
capital pi
product - product of all values in range of series
∏ xi=x1∙x2∙...∙xn
62
e
Euler's number
e = 2.718281828…
e = lim (1+1/x)x , x→∞
63
γ
Euler-Mascheroni constant
| γ = 0.5772156649...
64
φ
golden ratio constant
65
·
Dot
scalar product
a · b
66
×
Cross
vector product
a × b
67
⊗
tensor product
tensor product of A and B
A ⊗ B
68
[ ]
Brackets
| matrix of numbers
69
|| x ||
double vertical bars
| norm
70
AT
Transpose
matrix transpose
(AT)ij = (A)ji
71
A -1
inverse matrix
72
dim(U)
Dimension
dimension of matrix A
dim(U) = 3
73
P(A)
probability function
probability of event A
P(A) = 0.5
74
P(A ⋂ B)
probability of events intersection
probability that of events A and B
P(A⋂B) = 0.5
75
P(A ⋃ B)
probability of events union
probability that of events A or B
P(A⋃B) = 0.5
76
P(A | B)
conditional probability function
probability of event A given event B occured
P(A | B) = 0.3
77
f (x) （probability)
probability density function (pdf)
P(a ≤ x ≤ b) = ∫ f (x) dx
78
F(x)
cumulative distribution function (cdf)
| F(x) = P(X≤ x)
79
μ
Mu
population mean
μ = 10
80
E(X)a
expectation value
expected value of random variable X
E(X) = 10
81
E(X | Y)
conditional expectation
expected value of random variable X given Y
E(X | Y=2) = 5
82
var(X)
Variance
variance of random variable X
var(X) = 4
83
σ2
Sigma (variation)
Variance
variance of random variable X
σ2 = 4
84
std(X)
standard deviation
standard deviation of random variable X
std(X) = 2
85
σX
standard deviation
standard deviation value of random variable X
σX = 2
86
x̃
Median
| middle value of random variable x
87
cov(X,Y)
Covariance
covariance of random variables X and Y
cov(X,Y) = 4
88
corr(X,Y)
Correlation
correlation of random variables X and Y
corr(X,Y) = 0.6
89
ρX,Y
Correlation
correlation of random variables X and Y
ρX,Y = 0.6
90
MR
Mid-range
| MR = (xmax+xmin)/2
91
Md
sample median
| half the population is below this value
92
Q1
lower / first quartile
| 25% of population are below this value
93
Q2
median / second quartile
| 50% of population are below this value = median of samples
94
Q3
upper / third quartile
| 75% of population are below this value
95
s 2
sample variance
population samples variance estimator
s 2 = 4
96
x-bar
sample mean
average / arithmetic mean
x-bar = (2+5+9) / 3 = 5.333
97
zx
standard score
zx = (x-xbar) / sx
98
s
sample standard deviation
population samples standard deviation estimator
s = 2
99
X ~
distribution of X
distribution of random variable X
X ~ N(0,3)
100
N(μ,σ2)
normal distribution
gaussian distribution
X ~ N(0,3)
101
U(a,b)
uniform distribution
equal probability in range a,b
X ~ U(0,3)
102
exp(λ)
exponential distribution
| f (x) = λe-λx , x≥0
103
λ
Lambda
104
gamma(c, λ)
gamma distribution
| f (x) = λ c xc-1e-λx / Γ(c), x≥0
105
χ 2(k)
chi-square distribution
| f (x) = xk/2-1e-x/2 / ( 2k/2 Γ(k/2) )
106
F (k1, k2)
F distribution
107
Bin(n,p)
binomial distribution
| f (k) = nCk pk(1-p)n-k
108
Poisson(λ)
Poisson distribution
| f (k) = λke-λ / k!
109
Geom(p)
geometric distribution
| f (k) = p(1-p) k
110
Bern(p)
Bernoulli distribution
111
n!
Factorial
n! = 1⋅2⋅3⋅...⋅n
5! = 1⋅2⋅3⋅4⋅5 = 120
112
nPk
Permutation
P(n,r)=n! (n−r)!
5P3 = 5! / (5-3)! = 60
113
nCk
Combination
| r! (n−r)!
114
{ }
Set
a collection of elements
```
A = {3,7,9,14},
B = {9,14,28}
```
115
A ∩ B
Intersection
objects that belong to set A and set B
A ∩ B = {9,14}
116
A ∪ B
Union
objects that belong to set A or set B
A ∪ B = {3,7,9,14,28}
117
A ⊆ B
Subset
A is a subset of B. set A is included in set B.
{9,14,28} ⊆ {9,14,28}
118
A ⊂ B
proper subset / strict subset
A is a subset of B, but A is not equal to B.
{9,14} ⊂ {9,14,28}
119
A ⊄ B
not subset
set A is not a subset of set B
{9,66} ⊄ {9,14,28}
120
A ⊇ B
Superset
A is a superset of B. set A includes set B
{9,14,28} ⊇ {9,14,28}
121
A ⊃ B
proper superset / strict superset
A is a superset of B, but B is not equal to A.
{9,14,28} ⊃ {9,14}
122
A ⊅ B
not superset
set A is not a superset of set B
{9,14,28} ⊅ {9,66}
123
A ⊅ B
not superset
set A is not a superset of set B
{9,14,28} ⊅ {9,66}
124
A - B
relative complement
objects that belong to A and not to B
```
A = {3,9,14},
B = {1,2,3},
A-B = {9,14}
```
125
A ∆ B
symmetric difference
objects that belong to A or B but not to their intersection
A = {3,9,14},
B = {1,2,3},
A ∆ B = {1,2,9,14}
126
A ⊖ B
symmetric difference
objects that belong to A or B but not to their intersection
A = {3,9,14},
B = {1,2,3},
A ⊖ B = {1,2,9,14}
127
∈
element of,
belongs to
set membership
A={3,9,14}, 3 ∈ A
128
∉
not element of
no set membership
A={3,9,14}, 1 ∉ A
129
(a,b) (Set theory symbols)
ordered pair
| collection of 2 elements
130
A×B
cartesian product
| set of all ordered pairs from A and B
131
```
|A|
#A
```
Cardinality
the number of elements of set A
A={3,9,14}, |A|=3
132
|
| Set theory symbols
vertical bar
such that
A={x|3
133
Ø
empty set
Ø = { }
C = {Ø}
134
∀
For All
| ∀x>1, x2>x
135
∴
Therefore
| a=b ∴ b=a
136
⋅ (Logic)
And
| x ⋅ y
137
&
Ampersand
and
x & y
138
(logic)+
Or
| x + y
139
| (logic)
vertical line
Or
x | y
140
⇒
implies
141
¬
not - negation
| ¬ x
142
⇔
Equivalent
| if and only if (iff)
143
∵
because / since
144
y '
Derivative
derivative - Lagrange's notation
(3x3)' = 9x2
145
y ''
second derivative
derivative of derivative
(3x3)'' = 18x
146
y(n)
nth derivative
(3x3)(3) = 18
147
∫
Integral
opposite to derivation
∫ f(x)dx
148
∫∫
double integral
integration of function of 2 variables
∫∫ f(x,y)dxdya
149
i
imaginary unit
i ≡ √-1
z = 3 + 2i
150
z*
complex conjugate
z = a+bi → z*=a-bi
z* = 3 - 2i
151
Re(z)
real part of a complex number
z = a+bi → Re(z)=a
Re(3 - 2i) = 3
152
Im(z)
imaginary part of a complex number
z = a+bi → Im(z)=b
Im(3 - 2i) = -2
153
| z |
absolute value/magnitude of a complex number
|z| = |a+bi| = √(a2+b2)
|3 - 2i| = √13
154
Α α
Alpha
155
Β β
Beta
156
Γ γ
Gamma
157
Δ δ
Delta
158
Ε ε
Epsilon
159
Ζ ζ
Zeta
160
Η η
Eta
161
Θ θ
Theta
162
Ι ι
Iota
163
Κ κ
Kappa
164
Λ λ
Lambda
165
Μ μ
Mu
166
Ν ν
Nu
167
Ξ ξ
Xi
168
Π π
Pi
169
Ρ ρ
Rho
170
Σ σ
Sigma
171
Τ τ
Tau
172
Υ υ
Upsilon
173
Φ φ
Phi
174
Χ χ
Chi
175
Ψ ψ
Psi
176
Ω ω
Omega
