Mathem Mat hemati atical cal Sym Symbol bolss List of all ma math theemati matical cal symb symbols ols an andd si sign gnss - me mean aniing an andd ex exam ampl ples es..
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Basic math symbols Geometry symbols Algebra symbols Probability & statistics symbols Set theory symbols Logic symbols Calculus & analysis symbols Number symbols Greek symbols Roman numerals
Basic math symbols Symbol
Symbol Name
= ≠ ≈ > < ≥ ≤ () []
equals sign
+
plus sign
Meaning / definition equality
not equal sign
inequality
approximately equal
approximation
strict inequality
g r e at er t h an
strict inequality
less than
inequality
g r e a t e r t h an o r e qu al t o
inequality
less than or equal to
p a r e nt he s e s
calculate expression inside first
b r a c k et s
calculate expression inside first
addition
−
minus sign
±
plus - minus
both plus and minus operations
±
minus - plus
both minus and plus operations
*
asterisk
subtraction
multiplication
×
times sign
·
multiplication dot
÷
division sign / obelus
/
division slash
–
horizontal line
division / fraction
mod
modulo
remainder calculation
period
decimal point, decimal separator
ab a^b
power
exponent
caret
exponent
√a
square root
√a ∙ √a = a
3√a
cube root
3√a ∙ 3 √a
4√a
fourth root
4√
n√a
n-th root (radical)
.
multiplication
multiplication
division division
∙ 3√a = a
a ∙ 4√a ∙ 4√a ∙ 4√a = a
%
percent
1% = 1/100
‰
per-mille
1‰ = 1/1000 = 0.1%
ppm
per-million
1ppm = 1/1000000
ppb
per-billion
1ppb = 1/1000000000
ppt
per-trillion
1ppt = 10-12
Geometry symbols Symbol
∠
Symbol Name angle measured angle spherical angle
Meaning / definition formed by two rays
∟ ° deg
right angle
= 90°
degree
1 turn = 360°
degree
1 turn = 360deg
prime
arcminute, 1° = 60′
double prime
arcsecond, 1′ = 60″
line
infinite line
line segment
line from point A to point B
ray
line that start from point A
arc
arc from point A to point B
⊥
perpendicular
perpendicular lines (90° angle)
||
parallel
parallel lines
≅
congruent to
equivalence of geometric shapes and size
~ Δ
similarity
same shapes, not same size
triangle
triangle shape
distance
distance between points x and y
′ ″ AB
|x- y|
π = 3.141592654...
π
is the ratio between the
pi constant
circumference and diameter of a circle
rad
radians
radians angle unit
c
radians
radians angle unit
grad
gradians / gons
grads angle unit
g
gradians / gons
grads angle unit
Algebra symbols Symbol
x ≡ ≜
Symbol Name
Meaning / definition
x variable
unknown value to find
equivalence
identical to
equal by definition
equal by definition
:= ~ ≈ ∝
equal by definition
equal by definition
approximately equal
weak approximation
approximately equal
approximation
proportional to
proportional to
∞
lemniscate
infinity symbol
≪
much less than
much less than
≫
much greater than
much greater than
() [] {} ⌊ x⌋
parentheses
calculate expression inside first
brackets
calculate expression inside first
braces
set
floor brackets
rounds number to lower integer
⌈ x⌉
ceiling brackets
rounds number to upper integer
x! | x | f ( x)
exclamation mark
factorial
single vertical bar
absolute value
function of x
maps values of x to f(x)
( f ∘ g )
function composition
( f ∘ g ) ( x) = f ( g ( x))
(a,b) [a,b] ∆ ∆
open interval
(a,b) = { x | a < x < b}
closed interval
[a,b] = { x | a ≤ x ≤ b}
delta
change / difference
discriminant
Δ = b2 - 4ac
∑
sigma
summation - sum of all values in range of series
sigma
double summation
∏
capital pi
product - product of all values in range of series
e
e constant / Euler's number
e = 2.718281828...
γ
Euler-Mascheroni constant
γ = 0.527721566...
φ
golden ratio
golden ratio constant
∑∑
π = 3.141592654...
π
pi constant
is the ratio between the circumference and diameter of a circle
Linear Algebra Symbols Symbol
· × A⊗ B
Symbol Name
Meaning / definition
dot
scalar product
cross
vector product
tensor product
tensor product of A and B
inner product
[] () | A | det( A) || x ||
brackets
matrix of numbers
parentheses
matrix of numbers
determinant
determinant of matrix A
determinant
determinant of matrix A
double vertical bars
norm
AT
transpose
matrix transpose
A†
Hermitian matrix
matrix conjugate transpose
A*
Hermitian matrix
matrix conjugate transpose
A -1
inverse matrix
A A-1 = I
rank( A)
matrix rank
rank of matrix A
dim(U )
dimension
dimension of matrix A
Probability and statistics symbols Symbol
Symbol Name
Meaning / definition
P ( A)
probability function
probability of event A
P ( A ∩ B)
probability of events intersection
probability that of events A and B
P ( A ∪ B)
probability of events union
probability that of events A or B
conditional probability function
probability of event A given event B occured
probability density function (pdf)
P (a ≤ x ≤ b) = ∫ f ( x) dx
P ( A | B) f ( x)
F ( x)
cumulative distribution function (cdf)
F ( x) = P ( X ≤ x)
μ
population mean
mean of population values
E ( X )
expectation value
expected value of random variable X
conditional expectation
expected value of random variable X given Y
variance
variance of random variable X
variance
variance of population values
std ( X )
standard deviation
standard deviation of random variable X
σ X
standard deviation
standard deviation value of random variable X
median
middle value of random variable x
E ( X | Y ) var ( X )
σ2
cov( X ,Y )
covariance
covariance of random variables X and Y
corr ( X ,Y )
correlation
correlation of random variables X and Y
correlation
correlation of random variables X and Y
summation
summation - sum of all values in range of series
double summation
double summation
ρ X ,Y ∑
∑∑ Mo
mode
value that occurs most frequently in population
MR
mid-range
MR = ( xmax+ xmin)/2
sample median
half the population is below this value
Q1
lower / first quartile
25% of population are below this value
Q2
median / second quartile
50% of population are below this value = median of samples
Q3
upper / third quartile
75% of population are below this value
x
sample mean
average / arithmetic mean
sample variance
population samples variance estimator
s
sample standard deviation
population samples standard deviation estimator
z x
standard score
z x = ( x- x) / s x
distribution of X
distribution of random variable X
Md
s 2
X ~
N ( μ,σ 2)
normal distribution
gaussian distribution
U (a,b)
uniform distribution
equal probability in range a,b
exp(λ)
exponential distribution
f ( x) = λe- λx , x≥0
gamma distribution
f ( x) = λ c xc-1e- λx / Γ(c), x≥0
chi-square distribution
f ( x) = xk /2-1e- x/2 / ( 2 k/2 Γ(k /2) )
gamma(c, λ) χ 2 (k ) F (k 1 , k 2)
F distribution
Bin(n, p)
binomial distribution
f (k ) = nC k pk (1-p)n-k
Poisson(λ)
Poisson distribution
f (k ) = λk e- λ / k !
geometric distribution
f (k ) = p(1-p) k
Geom( p) HG( N , K ,n)
hyper-geometric distribution
Bern( p)
Bernoulli distribution
Combinatorics Symbols Symbol
Symbol Name
n!
factorial
n P k
permutation
Meaning / definition
n! = 1·2·3·...·n
nC k combination
Set theory symbols Symbol
Symbol Name
{}
Meaning / definition
set
a collection of elements
A∩B
intersection
objects that belong to set A and set B
A ∪ B
union
objects that belong to set A or set B
A ⊆ B
subset
subset has fewer elements or equal to the set
A ⊂ B
proper subset / strict subset
subset has fewer elements than the set
A ⊄ B
not subset
left set not a subset of right set
A ⊇ B
superset
set A has more elements or equal to the set B
A ⊃ B
set A has more elements than proper superset / strict superset set B
A ⊅ B
not superset
set A is not a superset of set B
power set
all subsets of A
power set
all subsets of A
equality
both sets have the same members
complement
all the objects that do not belong to set A
A\B
relative complement
objects that belong to A and not to B
A-B
relative complement
objects that belong to A and not to B
A∆B
symmetric difference
objects that belong to A or B but not to their intersection
A ⊖ B
symmetric difference
objects that belong to A or B but not to their intersection
a∈A
element of
set membership
x∉A (a,b)
not element of
no set membership
ordered pair
collection of 2 elements
A×B
cartesian product
set of all ordered pairs from A and B
2A
A=B
Ac
|A|
cardinality
the number of elements of set A
#A
cardinality
the number of elements of set A
aleph-null
infinite cardinality of natural numbers set
aleph-one
cardinality of countable ordinal numbers set
empty set
Ø={}
universal set
set of all possible values
Ø 0
natural numbers / whole numbers set (with zero)
0 = {0,1,2,3,4,...}
1
natural numbers / whole numbers set (without zero)
1 = {1,2,3,4,5,...}
integer numbers set
= {...-3,-2,-1,0,1,2,3,...}
rational numbers set
= { x | x=a/b, a,b∈ }
real numbers set
= { x | -∞ < x <∞}
complex numbers set
= { z | z=a+bi, -∞
Logic symbols Symbol
Symbol Name
Meaning / definition
and
and
^ & + ∨
caret / circumflex
and
ampersand
and
plus
or
reversed caret
or
| x' x ¬ ! ⊕
vertical line
or
single quote
not - negation
bar
not - negation
not
not - negation
exclamation mark
not - negation
circled plus / oplus
exclusive or - xor
~ ⇒ ⇔
tilde
negation
·
↔ ∀ ∃ ∄ ∴ ∵
implies equivalent
if and only if (iff)
equivalent
if and only if (iff)
for all there exists there does not exists
therefore because / since
Calculus & analysis symbols Symbol
Symbol Name limit
Meaning / definition limit value of a function represents a very small
ε
epsilon
number, near zero
e
e constant / Euler's number
e = 2.718281828...
derivative
derivative - Lagrange's notation
second derivative
derivative of derivative
nth derivative
n times derivation
derivative
derivative - Leibniz's notation
second derivative
derivative of derivative
nth derivative
n times derivation
time derivative
derivative by time - Newton's notation
time second derivative
derivative of derivative
derivative
derivative - Euler's notation
second derivative
derivative of derivative
y ' y ''
y(n)
D x y
D x2 y
partial derivative
∫
integral
opposite to derivation
∫∫
double integral
integration of function of 2 variables
∫∫∫
triple integral
integration of function of 3 variables
∮
closed contour / line integral
∯
closed surface integral
∰
closed volume integral
[a,b] (a,b) i z* z
closed interval
[a,b] = { x | a ≤ x ≤ b}
open interval
(a,b) = { x | a < x < b}
imaginary unit
i ≡ √-1
complex conjugate
z = a+bi → z*=a-bi
complex conjugate
z = a+bi → z = a-bi
∇
nabla / del
gradient / divergence operator
vector unit vector
x * y
δ ∞
convolution
y(t ) = x(t ) * h(t )
Laplace transform
F ( s) = { f (t )}
Fourier transform
X (ω) =
{ f (t )}
delta function lemniscate
infinity symbol
Numeral symbols Name
European
Roman
zero
0
one
1
I
two
2
II
three
3
III
four
4
IV
five
5
V
six
6
VI
seven
7
VII
eight
8
VIII
nine
9
IX
ten
10
X
eleven
11
XI
twelve
12
XII
thirteen
13
XIII
fourteen
14
XIV
fifteen
15
XV
sixteen
16
XVI
seventeen
17
XVII
eighteen
18
XVIII
nineteen
19
XIX
twenty
20
XX
Hebrew
thirty
30
XXX
forty
40
XL
fifty
50
L
sixty
60
LX
seventy
70
LXX
eighty
80
LXXX
ninety
90
XC
one hundred
100
C
Greek alphabet letters Greek Symbol Upper Case
Lower Case
Α Β Γ Δ Ε Ζ Η Θ Ι Κ Λ Μ Ν Ξ Ο Π Ρ
α β γ δ ε ζ η θ ι κ λ μ ν ξ ο π ρ
Greek Letter Name
English Equivalent
Alpha
al-fa
Beta
be-ta
Gamma
ga-ma
Delta
del-ta
Epsilon
ep-si-lon
Zeta
ze-ta
Eta
eh-ta
Theta
te-ta
Iota
io-ta
Kappa
ka-pa
Lambda
lam-da
Mu
m-yoo
Nu
noo
Xi
x-ee
Omicron
o-mee-c-ron
Pi
pa-yee
Rho
row
Σ Τ Υ Φ Χ Ψ Ω
σ τ υ φ χ ψ ω
Sigma
sig-ma
Tau
ta-oo
Upsilon
oo-psi-lon
Phi
f-ee
Chi
kh-ee
Psi
p-see
Omega
o-me-ga
Roman numerals Number
Roman numeral
0
not defined
1
I
2
II
3
III
4
IV
5
V
6
VI
7
VII
8
VIII
9
IX
10
X
11
XI
12
XII
13
XIII
14
XIV
15
XV
16
XVI
17
XVII
18
XVIII
19
XIX
20
XX
30
XXX
40
XL
50
L
60
LX
70
LXX
80
LXXX
90
XC
100
C
200
CC
300
CCC
400
CD
500
D
600
DC
700
DCC
800
DCCC
900
CM
1000
M
5000
V
10000
X
50000
L
100000
C
500000
D
1000000
M
See also Algebra symbols Geometry symbols Statistical symbols Logic symbols Set theory symbols Calculus & analysis symbols Number symbols Greek alphabet symbols Roman numerals
