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\begin{document}

\lecture{Lecture 1: Algebraic Graph Algorithms}{September 14, 2021}{Instructor:\hspace{0.08cm}\emph{Josh Alman }}{\emph{YOUR NAME}}

\section{Introduction}

The class is about algebraic algorithms for graph problems...

\section{Course Topics}
\textbullet{} Matrix Multiplication  \\
....


\section{Problem: All-Pairs Shortest Paths}

In this problem, we have to...



\begin{claim}
$T(n) = O(n^{\log_2 7})$.
\end{claim}
\begin{proof}
  The proof is by induction...
\end{proof}

\end{document}
