\documentclass[11pt]{article}
\input{preamble.tex}

\begin{document}
\lecture{1}{Rafail Ostrosky}

\section{the first topic}
blah blah
\begin{theorem}
$xyz$
\end{theorem}

\begin{proof}
here are some calculations about $xyz$.
\end{proof}

\subsection{the first subtopic}
some more comments here.

\section{the second topic}

\subsection{the second part A}
some more comments here.

\subsection{the second part B}
some more comments here.

\end{document}


