\documentclass{article}[12pt]

\usepackage{lipsum}
\usepackage{multicol}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage[USenglish]{babel}
\usepackage[stretch=10,shrink=10]{microtype}
\usepackage[left=1.3in,
            right=1.3in,
            top=1in,
            bottom=1in,
            footskip=.5in]{geometry}
\setlength{\columnsep}{0.4in}

\renewcommand{\rmdefault}{zpltlf}
\usepackage{newpxtext}
% will mess up embeded symbols
% \usepackage{newpxmath}

\title{The hard mode}
\author{krasjet}
\date{}

\begin{document}
\begin{multicols}{2}
[
  \maketitle
]

\section{Section One}

\lipsum[2-3]

\section{Section $1 + 1 = 2$}

\lipsum[2-1]
\begin{align*}
  x^2 + 2 = 4
\end{align*}
\lipsum[2-1]

\subsection{Subsection Two.One}
\lipsum[2-5]

\section*{$\mathrm{e}^{\ln(3)}$}

\setcounter{section}{3}
\setcounter{subsection}{0}

\lipsum[1-2]

\subsection{Subsection $\mathrm{e}^{\ln(3)}$.1, with looo\-ooooooooong title}
\lipsum[2-5]

\subsection{$\mathbb{S}$ubsection Three.Two, another long title}
\lipsum[1-1]

\subsection{Subsection Three.Three}
\lipsum[2-3]

\section{The $x \to \infty$ End}

\lipsum[2-2]

\end{multicols}

\end{document}
