\documentclass{sample}
\begin{document}
The following characters can be used for typing the source file:
\begin{center}
a-z

A-Z

0-9

+ = * / ( ) [ ]

, ; . ? ! : ` ' -
\end{center}

The following are used by LaTeX commands and therefore reserved:

\begin{center}
\# \$ \% \& \~ \_ \^{} \textbackslash \{ \} @ '' \textbar \textless \textgreater
\end{center}

In some cases, it may be necesary to enter text with \textbackslash text \{someText\} in order to build the correct layout. This is demonstrated in the next line.

\emph{Inline formulas} are enclosed with \textbackslash \$, for example typing:

\begin{center}
\textbackslash \$2\textbackslash textless \textbackslash textbar x \textbackslash textbar \textbackslash textgreater y\textbackslash \$
\end{center}

yields $2 < |x| > y$.

\emph{Displayed formulas} are enclosed in \textbackslash [ and \textbackslash ], as typsetted below:
\[
\lim_{x \to a} \frac{f(x) - f(a)}{x-a}
\]

Math symbols are invoked by command, e.g. \textbackslash infty and \textbackslash to: as $x \to \infty$. Many require arguments to produce:
\[
\frac{\sqrt{3}+7}{x + r}
\]

Note from this source that there are no blank lines before a displayed formula, only after. Formulas are styled according to the document class. Whitespace within a math environment (as denoted above) is mostly ignored. 

One can temporarily revert to regular text in a math environment with \textbackslash text\{something\}, for example $a + b \text{ is not the same as } a - b$. Again, check how spaces are not ignored in regular text (in the source) and therefore the extra space is required.
\end{document}