BASIC MATH SYMBOLS

Symbol	Symbol Name	Meaning / definition	Example
≠	not equal sign	inequality	5 ≠ 4
=	equals sign	equality	5 = 2+3
<	strict inequality	less than	4 < 5
>	strict inequality	greater than	5 > 4
≤	inequality	less than or equal to	4 ≤ 5
≥	inequality	greater than or equal to	5 ≥ 4
[ ]	brackets	calculate expression inside first	[(1+2)*(1+5)] = 18
( )	parentheses	calculate expression inside first	2 × (3+5) = 16
−	minus sign	subtraction	2 − 1 = 1
+	plus sign	addition	1 + 1 = 2
∓	minus – plus	both minus and plus operations	3 ∓ 5 = -2 and 8
±	plus – minus	both plus and minus operations	3 ± 5 = 8 and -2
×	times sign	multiplication	2 × 3 = 6
*	asterisk	multiplication	2 * 3 = 6
÷	division sign / obelus	division	6 ÷ 2 = 3
∙	multiplication dot	multiplication	2 ∙ 3 = 6
–	horizontal line	division / fraction
/	division slash	division	6 / 2 = 3
mod	modulo	remainder calculation	7 mod 2 = 1
ab	power	exponent	23 = 8
.	period	decimal point, decimal separator	2.56 = 2+56/100
√a	square root	√a · √a = a	√9 = ±3
a^b	caret	exponent	2 ^ 3 = 8
4√a	fourth root	4√a · 4√a · 4√a · 4√a = a	4√16 = ±2
3√a	cube root	3√a · 3√a · 3√a = a	3√8 = 2
%	percent	1% = 1/100	10% × 30 = 3
n√a	n-th root (radical)		for n=3, n√8 = 2
ppm	per-million	1 ppm = 1/1000000	10ppm × 30 = 0.0003
‰	per-mille	1‰ = 1/1000 = 0.1%	10‰ × 30 = 0.3
ppt	per-trillion	1ppt = 10-12	10ppt × 30 = 3×10-10
ppb	per-billion	1 ppb = 1/1000000000	10 ppb × 30 = 3×10-7

Calculus & Analysis Symbols

Symbol	Symbol Name	Meaning / definition	Example
ε	epsilon	represents a very small number, near zero	ε → 0
$\underset{x\to a}{lim}$	limit	limit value of a function	$\underset{x\to a}{lim}(3x+1)=3\times a+1=3a+1$
y ‘	derivative	derivative – Lagrange’s notation	${\left(5x^3\right)}^{\prime }=15x^2$
e	e constant / Euler’s number	e = 2.718281828…	e = lim (1+1/x)x , x→∞
y(n)	nth derivative	n times derivation	nth derivative of $3x^n=3n(n-1)(n-2)\dots .\left(2\right)\left(1\right)=3n!$
y ”	second derivative	derivative of derivative	$\left(4x^3\right)”=24x$
$\frac{d^{2}y}{d{x}^2}$	second derivative	derivative of derivative	$\frac{d^2}{d{x}^2}(6x^3+x^2+3x+1)=36x+1$
dy/dx	derivative	derivative – Leibniz’s notation	$\frac{d}{dx}\left(5x\right)=5$
$\frac{d^{n}y}{d{x}^n}$	nth derivative	n times derivation
$\ddot{y}=\frac{d^{2}y}{d{t}^2}$	Second derivative of time	derivative of derivative
$\dot{y}$	Single derivative of time	derivative by time – Newton’s notation
$D^{2}x$	second derivative	derivative of derivative
Dx	derivative	derivative – Euler’s notation
∫	integral	opposite to derivation
$\frac{af(x,y)}{ax}$	partial derivative		∂(x2+y2)/∂x = 2x
∭	triple integral	integration of function of 3 variables
∬	double integral	integration of function of 2 variables
∯	closed surface integral
∮	closed contour / line integral
[a,b]	closed interval	[a,b] = {x | a ≤ x ≤ b}
∰	closed volume integral
(a,b)	open interval	(a,b) = {x | a < x < b}
z*	complex conjugate	z = a+bi → z*=a-bi	z* = 3 + 2i
i	imaginary unit	i ≡ √-1	z = 3 + 2i
∇	nabla / del	gradient / divergence operator	∇f (x,y,z)
z	complex conjugate	z = a+bi → z = a–bi	z = 3 + 2i
$\vec{x}$	vector	$\vec{V}=x\hat{i}+y\hat{j}+z\hat{k}$
x * y	convolution	y(t) = x(t) * h(t)
∞	lemniscate	infinity symbol
δ	delta function