Basic Symbols
Symbol Symbol Meaning
= equality
inequality
approximation
> greater than
< less than
greater than or equal to
greater than or equal to
( ) calculate expression inside first
subtraction
± both plus and minus operations
± both minus and plus operations
*|×|⋅ multiplication
÷|/|— division/fraction
. decimal point, decimal separator
ab|a^b exponent
√a square root
3√a cube root
% percent
per-mille
Geometry Symbols
Symbol Symbol Meaning
angle, formed by two rays
*= 90°
° 1 turn = 360°
deg 1 turn = 360 deg
arcminute, 1° = 60′
arcsecond, 1′ = 60″
AB line from point A to point B
perpendicular lines (90° angle)
parallel lines
equivalence of geometric shapes and size
~ same shapes, not same size
Δ triangle shape
|x-y| distance between points x and y
π Ratio between the circumference and diameter of a circle
Algebra Symbols
Symbol Symbol Meaning
x unknown value to find
identical to
equal by definition
:= equal by definition
~ weak approximation
approximation
proportional to
infinity symbol
much less than
much greater than
( ) calculate expression inside first
[ ] calculate expression inside first
{ } set
⌊x⌋ rounds number to lower integer
⌈x⌉ rounds number to upper integer
x! factorial
| x | absolute value
f (x) maps values of x to f(x)
(f ∘ g) function composition, (f ∘ g) (x) = f (g(x))
(a,b) open interval, (a,b) = {x | a < x < b}
[a,b] closed interval, [a,b] = {x | a ≤ x ≤ b}
change / difference
discriminant, Δ = b2 - 4ac
summation - sum of all values in range of series
∑∑ double summation
product - product of all values in range of series
e Euler's number, e = 2.718281828...
γ Euler-Mascheroni constant, γ = 0.5772156649...
φ golden ratio constant
π π = 3.141592654...
Linear Algebra Symbols
Symbol Symbol Meaning
· scalar product
× vector product
A⊗B tensor product of A and B
[ ] matrix of numbers
( ) matrix of numbers
| A | determinant of matrix A
det(A) determinant of matrix A
|| x || norm
AT matrix transpose
A† matrix conjugate transpose
A* matrix conjugate transpose
A -1 inverse matrix, A A-1 = I
rank(A) rank of matrix A
dim(U) dimension of matrix A
Probability / Statistics Symbols
Symbol Symbol Meaning
P(A) probability function
P(A ⋂ B) probability of events intersection
P(A ⋃ B) probability of events union
P(A | B) conditional probability function
f (x) probability density function (pdf)
F(x) cumulative distribution function (cdf)
μ population mean
E(X) expectation value
E(X | Y) conditional expectation
var(X) variance
σ2 variance
std(X) standard deviation
σX standard deviation
cov(X,Y) covariance
corr(X,Y) correlation
ρX,Y correlation
summation
∑∑ double summation
Mo mode
MR mid-range
Md sample median
Q1 lower / first quartile
Q2 median / second quartile
Q3 upper / third quartile
x sample mean
s 2 sample variance
s sample standard deviation
zx standard score
X ~ distribution of X
N(μ,σ2) normal distribution
U(a,b) uniform distribution
exp(λ) exponential distribution
gamma(c, λ) gamma distribution
χ 2(k) chi-square distribution
F (k1, k2) F distribution
Bin(n,p) binomial distribution
Poisson(λ) Poisson distribution
Geom(p) geometric distribution
HG(N,K,n) hyper-geometric distribution
Bern(p) Bernoulli distribution
Combinatorics Symbols
Symbol Symbol Meaning
n! factorial
nPk permutation
nCk combination
Set Theory Symbols
" "
Symbol Symbol Meaning
{ } set
A ∩ B intersection
A ∪ B union
A ⊆ B subset
A ⊂ B proper subset / strict subset
A ⊄ B not subset
A ⊇ B superset
A ⊃ B proper superset / strict superset
A ⊅ B not superset
2A power set
A = B equality
Ac complement
A \ B relative complement
A - B relative complement
A ∆ B symmetric difference
A ⊖ B symmetric difference
a∈A element of, belongs to
Logic Symbols
Symbol Symbol Meaning
and
^ caret / circumflex (and)
& ampersand (and)
+ plus (or)
reversed caret (or)
| vertical line (or)
x' single quote (not - negation)
x 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 Meaning
ε epsilon
e e constant / Euler's number
y ' derivative
y '' second derivative
y(n) nth derivative
Dx y derivative
Dx2y second derivative
integral
∫∫ double integral
∫∫∫ triple integral
closed contour / line integral
closed surface integral
closed volume integral
[a,b] closed interval
(a,b) open interval
i imaginary unit
z* complex conjugate
z complex conjugate
Re(z) real part of a complex number
Im(z) imaginary part of a complex number
| z | absolute value/magnitude of a complex number
arg(z) argument of a complex number
nabla / del
x * y convolution
δ delta function
lemniscate