Math symbol examples:
${\big Delta}, \Theta, \Lambda, \Xi, \Pi, \Sigma, \Upsilon, \Phi, \Psi, \Omega$
Inline math (math in lines of text): $\mathbf{X}[k+1]=A\mathbf {X}[k]+B\mathbf{u}[k]$
Some text here and some inline math $ \left(\, \sum_{k=1}^n a_k b_k \right)^{\!\!2} \le \left(\, \sum_{k=1}^n a_k^2 \right) \left(\, \sum_{k=1}^n b_k^2 \right)$
Diplayed math (centered without surrounding text on the line): $$\mathbf{X}[k+1]=A\mathbf {X}[k]+B\mathbf{u}[k]$$ \[ x\left( x-1\right) =x^{2}-x \]
Some text here and some diplayed math $$ \left(\, \sum_{k=1}^n a_k b_k \right)^{\!\!2} \le \left(\, \sum_{k=1}^n a_k^2 \right) \left(\, \sum_{k=1}^n b_k^2 \right)$$
Aligned equations: \begin{eqnarray} mA &=&nA^{2} \label{LemmaEquationArray} \\ mA-nA^{2} &=&0 \\ A\left( m-nA\right) &=&0 \end{eqnarray}
Dollar sign \$ is $\backslash$\$
(backslash symbol followed by dollarsign with no spaces between).
Backslash $\backslash$ is \$ $\backslash$backslash\$
(dollarsign then backslash symbol then word backslash then dollarsign, all with no spaces between).