Dollar symbol typesetting

$a+b=b+a$
$a+b=b+a$

Superscript

$3x^2-x+2=0$
$3x^2-x+2=0\$

$3x^{20}-x+2=0$
$3x^{20}-x+2=0$

$3x^{3x^{20}-x+2=0}-x+2=0$
$3x^{3x^{20} - x + 2 = 0} - x + 2 = 0$

Subscript

$a0,a1,a2$
$a0,a1,a2$

$a_0,a_1,a_2...,a_{100}$
$a_0,a_1,a_2...,a_{100}$

trivial

$\circ$	$\circ$
$\boxed{a+b}$	$\boxed{a+b}$
$\mathbb{Z}$	$\mathbb{Z}$

The Greek letter

$\alpha$	$alpha$	$\Delta$	$\Delta$
$\beta$	$\beta$	$\Theta$	$\Theta$
$\gamma$	$\gamma$	$\Gamma$	$\Gamma$
$ϵ$	$\epsilon$
$\pi$	$\pi$	$\Pi$	$\Pi$
$\omega$	$\omega$	$\Omega$	$\Omega$

${\alpha }^3+{\beta }^2+\gamma =0$
$\alpha^3 + \beta^2 + \gamma = 0$

Mathematical functions

$\log$	$\log$
$\sin$	$\sin$
$\cos$	$\cos$
$\arcsin$	$\arcsin$
$\arccos$	$\arccos$
$\ln$	$\ln$
$\sqrt{2}$	$\sqrt2$
$\sqrt{2+\sqrt{2}}$	$\sqrt{2 + \sqrt{2}}$
$\sqrt[4]{x}$	$\sqrt[4]{x}$

$y={\log }_{2}x$
$y = \log_2 x$

$si{n}^{2}x+{\cos }^{2}x=1$
$sin^2 x + \cos^2 x = 1$

Common binary operators

$\cup$	$\cup$
$\cap$	$\cap$
$\vee$	$\vee$
$\wedge$	$\wedge$
$\oplus$	$\oplus$
$\pm$	$\pm$
$\mp$	$\mp$

Commonly used binary relations

$\le$	$\le$
$\ge$	$\ge$
$\ll$	$\ll$
$\equiv$	$\equiv$
$\subset$	$\subset$
$\supset$	$\supset$
$\subseteq$	$\sebseteq$
$\supseteq$	$\sepseteq$
$\approx$	$\approx$
$\in$	$\in$
$\ni$	$\ni$
$\notin$	$\notin$

Upper case number set

$\mathbb{Z}$
$\mathbb{Z}$

Universiade operator

$\sum$	$\sum$
$\int$	$\int$
$\oint$	$\oint$
$⨂$	$\bigotimes$

arrow

\nearrow	$\nearrow$
\swarrow	$\swarrow$
\searrow	$\searrow$
\nwarrow	$\nwarrow$

Fraction

$3/4$
$3/4$

$\frac{3}{4}$
$\frac{3}{4}$

Multiplication and division

$1\times 2=2$
$1 \times 2 = 2$

$9÷3=3$
$9 \div 3 = 3$

Formula size

$\csc \alpha =\frac{1}{\sin \alpha }$	$\csc\alpha = \scriptstyle\frac{1}{\sin\alpha}$
$\csc \alpha =\frac{1}{\sin \alpha }$	$\csc\alpha = \frac{1}{\sin\alpha}$
$\csc \alpha =\frac{1}{\sin \alpha }$	$\csc\alpha = \textstyle\frac{1}{\sin\alpha}$
$\csc \alpha =\frac{1}{\sin \alpha }$	$\csc\alpha = \displaystyle\frac{1}{\sin\alpha}$

Curly braces

$$F^{HLLC}=\{\begin{array}{rcl}{F}_L& & 0<S_L\\ F_L^{\ast }& & S_L\le 0<S_M\\ F_R^{\ast }& & S_M\le 0<S_R\\ F_R& & S_R\le 0\end{array}$$

$$ F^{HLLC}=\left\{
\begin{array}{rcl}
F_L       &      & {0      <      S_L}\\
F^*_L     &      & {S_L \leq 0 < S_M}\\
F^*_R     &      & {S_M \leq 0 < S_R}\\
F_R       &      & {S_R \leq 0}
\end{array} \right. $$

All kinds of brackets

$$\begin{array}{c}\begin{array}{cc}0& 1\\ 1& 0\end{array}\left(\begin{array}{cc}0& -i\\ i& 0\end{array}\right)\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right]\left\{\begin{array}{cc}1& 0\\ 0& -1\end{array}\right\}\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|\Vert \begin{array}{cc}i& 0\\ 0& -i\end{array}\Vert \end{array}$$

$$
\begin{gathered}
\begin{matrix} 0 & 1 \\ 1 & 0 \end{matrix}
\quad
\begin{pmatrix} 0 & -i \\ i & 0 \end{pmatrix}
\quad
\begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}
\quad
\begin{Bmatrix} 1 & 0 \\ 0 & -1 \end{Bmatrix}
\quad
\begin{vmatrix} a & b \\ c & d \end{vmatrix}
\quad
\begin{Vmatrix} i & 0 \\ 0 & -i \end{Vmatrix}
\end{gathered}
$$