Symbol

Symbol Name

Example

=

equals

5 = 2+3

5 is equal to 2+3

≠

not equal to

5 ≠ 4

5 is not equal to 4

≈

approximately equal to

sin(0.01) ≈ 0.01,

x ≈ y means x is approximately equal to y

>

greater than

5 > 4

5 is greater than 4

<

less than

4 < 5

4 is less than 5

≥

greater than or equal to

5 ≥ 4,

x ≥ y means x is greater than or equal to y

≤

less than or equal to

4 ≤ 5,

x ≤ y means x is less than or equal to y

( )

parentheses

2 × (3+5) = 16

[ ]

brackets

[(1+2)×(1+5)] = 18

+

plus

1 + 1 = 2

−

minus

2 − 1 = 1

±

plus or minus

3 ± 5 = 8 and -2

*

multiply

2 * 3 = 6

×

times

2 × 3 = 6

⋅

multiply

2 ⋅ 3 = 6

÷

divided by

6 ÷ 2 = 3

/

Divided by, over

6 / 2 = 3

.

point

2.56 = 2+56/100

ab

to the power of

23 = 8

√a

square root

√9 = ±3

3√a

cube root

3√8 = 2

4√a

fourth root

4√16 = ±2

n√a

n-th root

for n=3, n√8 = 2

%

percent

10% × 30 = 3

ppm

part per million

10ppm × 30 = 0.0003

Symbol

Symbol Name

Example

∠

angle

∠ABC = 30°

∟

right angle

α = 90°

°

degree

α = 60°

deg

degree

60deg

′

Prime, minute

60°59′

″

double prime, second

60°59′22″

Line A B

AB

line segment A B

Ray A B

Arc A B

= 60°

⊥

perpendicular

AC ⊥ BC

| |

parallel

AB | | CD

Δ

triangle

ΔABC≅ ΔBCD

|x-y|

Distance from y to x

| x-y | = 5

π

pi constant

c = π⋅d = 2⋅π⋅r

rad

radians

360° = 2π rad

Symbol

Symbol Name

Example

x

variable

when 2x = 4, then x = 2

~

approximately equal

11 ~ 10

≈

approximately equal

sin(0.01) ≈ 0.01

∝

proportional to

y ∝ x when y = kx, k constant

∞

infinity

"to infinity and beyond"

≪

much less than

1 ≪ 1000000

≫

much greater than

1000000 ≫ 1

( )

parentheses

2 * (3+5) = 16

[ ]

brackets

[(1+2)*(1+5)] = 18

{ }

braces

x!

x factorial, exclamation mark

5! = 1⋅2⋅3⋅4⋅5 = 120

| x |

absolute value

| -5 | = 5

f (x)

function of x

f (x) = 3x+5

(f ∘ g)(x)

f of g of x

f (x)=3x,g(x)=x-1 ⇒(f ∘ g)(x)=3(x-1)

(a,b)

open interval

x∈ (2,6)

[a,b]

closed interval

x ∈ [2,6]

∆

delta

∆t = t1 - t0

∑

Sigma, summation

∑ xi= x1+x2+...+xn

e

Euler's number

e = lim (1+1/x)x , x→∞

e = 2.718281828...

π

pi constant

c = π⋅d = 2⋅π⋅r

π = 3.141592654...

Symbol

Symbol Name

Example

·

dot product, scalar product

a · b

×

Cross product, vector product

a × b

inner product, scalar product

[ ]

matrix

[2, 3]

( )

matrix

(2,3)

| A |

determinant of matrix A

det(A)

determinant of matrix A

AT

transpose

(AT)ij = (A)ji

A -1

inverse matrix

A A-1 = I

rank(A)

rank of matrix A

rank(A) = 3

dim(U)

dimension of matrix U

rank(U) = 3

Symbol

Symbol Name

Example

P(A)

probability of A

P(A) = 0.5

σ2

variance, sigma squared

σ2 = 4

std(X)

standard deviation of X

std(X) = 2

σX

standard deviation of x

σX  = 2

cov(X,Y)

Covariance of x and y

cov(X,Y) = 4

corr(X,Y)

correlation

corr(X,Y) = 0.6

ρX,Y

correlation

ρX,Y = 0.6

exp(λ)

exponential distribution

f (x) = λe-λx , x≥0

χ 2(k)

chi-square distribution

f (x) = xk/2-1e-x/2 / ( 2k/2 Γ(k/2) )

Symbol

Symbol Name

Example

&

and

x & y

∴

therefore

Symbol

Symbol Name

Example

limit

y '

derivative

(3x3)' = 9x2

y ''

second derivative

(3x3)'' = 18x

y(n)

nth derivative

(3x3)(3) = 18

derivative of y

d(3x3)/dx = 9x2

second derivative

d2(3x3)/dx2 = 18x

nth derivative

time derivative of y

second derivative

of y with respect to time

partial derivative

of f with respect to x

∂(x2+y2)/∂x = 2x

∫

integral

∫ f(x)dx

integral of f with respect to x

∫∫

double integral

∫∫ f(x,y)dxdy

∫∫∫

triple integral

∫∫∫ f(x,y,z)dxdydz

i

imaginary unit

z = 3 + 2i

i ≡ √-1

∇

gradient / divergence operator

∇f (x,y,z)

vector

δ

delta function

∞

infinity

1 / ∞ = 0

Chain Rule

f (x) = exp(x^2)

f '(x) = exp(x^2) (2x)

Α

α

Greek Letter Name

English Equivalent

Pronunciation

Upper Case

Lower Case

Α

α

Alpha

a

al-fa

Β

β

Beta

b

be-ta

Γ

γ

Gamma

g

ga-ma

Δ

δ

Delta

d

del-ta

Ε

ε

Epsilon

e

ep-si-lon

Θ

θ

Theta

th

te-ta

Κ

κ

Kappa

k

ka-pa

Λ

λ

Lambda

l

lam-da

Μ

μ

Mu

m

m-yoo

Ν

ν

Nu

n

noo

Π

π

Pi

p

pa-yee

Ρ

ρ

Rho

r

row

Σ

σ

Sigma

s

sig-ma

Τ

τ

Tau

t

ta-oo

Φ

φ

Phi

ph

f-ee

Χ

χ

Chi

ch

kh-ee

Ψ

ψ

Psi

ps

p-see

Ω

ω

Omega

o

o-me-ga