Ultimate Crash Course for STEM Majors

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ALGEBRA

Symbol	Meaning	Example
$=$	Equal	$0=0$
$\ne$	Not equal	$1\ne0$
$\pm$	Plus or Minus	$x=\pm a \Rightarrow x=a \text{ or } x=-a$
$\mp$	Minus or Plus	$x=\mp a \Rightarrow x=-a \text{ or } x=a$
$\iff$	If and only if	$p\Rightarrow q \text{ and } q\Rightarrow p \iff p\Leftrightarrow q$
$\Rightarrow$	Implies	$p\Rightarrow q$
$\lt$	Less than	$latex x-a<0 \Rightarrow x
$\le$	Less than equal	$x-a\le0 \Rightarrow x\le a$
$\ge$	Greater than equal	$x-a\ge0 \Rightarrow x\ge a$
$>$	Greater than	$x-a>0 \Rightarrow x>a$
$\times$	Times	$2\times3=6$
* or $\cdot$	Multiplication	$2*3=6 \text{ or } 2\cdot3=6$
(…)(…)	Multiplication	$(2)(3)=6$
[…](…)	Multiplication	$=6$
[…][…]	Multiplication	$[2][3]=6$
$\infty$	Infinity	Never ends
$\Delta$	Displacement or change of	$\Delta x = x-x_0$
$\sum$	Summation	$\sum_{n=1}^{3} a_n x^n = a_1x + a_2x^2 + a_3x^3$
$\theta$	Theta – reserved for angles	$\theta=\frac{\pi}{4}=45^\circ$
$f(x)$	Function of x	$f(x)=x^n+\dots$
$f(x,y)$	Function of x and y	$f(x,y)=(xy)^n+\dots$
$\in$	Element of	$latex x\in[a,b) \text{ means } a\le x
$\forall$	For all	$\forall x$
$\therefore$	Therefore	$x-a=0 \Rightarrow x=a$
$\equiv$	Equivalent	$latex (-2,3)\equiv -2
(,)	Open interval	$latex (-2,3)\equiv -2
[,]	Closed interval	$[2,3]\equiv 2\le x\le3$
$\subset$	Proper subset	$A\subset B$
$\subseteq$	Subset (equal)	$A\subseteq B \Rightarrow A=B$
$\cup$	Union	$\{1,2,3\}\cup\{3,4,5\}=\{1,2,3,4,5\}$
$\cap$	Intersection	$\{1,2,3\}\cap\{3,4,5\}=\{3\}$
$\mathbb{R}$	Real numbers	$(-\infty,\infty)$
$P(x_0,y_0)$	Point	$(1,f(1))$