typewriter.sty usage

test.tex

% !TeX program = lualatex

\documentclass{article}
\usepackage{amsmath}
\usepackage{typewriter}

\begin{document}
\title{Some math symbols}
\author{Ray D. Sameshima}

\maketitle

\section{Some equations}
\begin{equation}
E = mc^2
\end{equation}

\subsection{a text}
The quick brown fox jumps over the lazy dog.

\subsubsection{another test}
Unfortunately some mathematical symbols can not be used e.g., let me write
\begin{equation}
\verb|\forall n \in \mathbb{N}|
\end{equation} 
in equation:
\begin{equation}
\forall n \in \mathbb{N}.
\end{equation}

\verb|\pi| becomes \pi, but \verb|\sum, \prod| do not appear: $\sum, \prod$.

\end{document}

It was really aiming to emulate a typewriter and most (pre-electronic) typewriters would never have had those symbols... If you use the github version of the package, it's easier to change fonts: I used Lucida Console which has \sum and \prod and added a couple more definitions to get

Just changed the preamble to

\documentclass{article}
\usepackage{amsmath}

\newcommand\ttbasefont{lucon.ttf}
\usepackage{typewriter}
\def\forall{V\llap-}
\def\mathbb#1{\ifx N#1IN\else#1\fi}
\def\in{~in~}

\begin{document}