\documentclass[11pt]{article}

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\usepackage{fancyhdr}
\usepackage{amsmath,amssymb,amsthm,mathtools}
\usepackage{bm}
\usepackage{mathrsfs}
\usepackage{enumitem}
\usepackage{xcolor}
\usepackage{hyperref}
\usepackage[nameinlink,capitalise]{cleveref}
\usepackage{graphicx}
\usepackage{tikz}
\usepackage[ruled,vlined]{algorithm2e}

\newcommand{\coursename}{CSE 203A: Randomized Algorithms}
\newcommand{\semester}{Spring 2026}
\newcommand{\instructor}{Daniel M.\ Kane}

% ----------------------------------------------------------------
% SCRIBES: EDIT THESE FIELDS
% ----------------------------------------------------------------
\newcommand{\scribe}{(Scribe Name)}
\newcommand{\lecturenum}{(Lecture Number)}
\newcommand{\lecturedate}{(Lecture Date)}

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\chead{Lecture \lecturenum}
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\theoremstyle{definition}
\newtheorem{definition}[theorem]{Definition}
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\newcommand{\Var}{\mathrm{Var}}
\newcommand{\Prb}{\mathbb{P}}
\newcommand{\R}{\mathbb{R}}
\newcommand{\N}{\mathbb{N}}
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\begin{document}

\begin{center}
    {\LARGE \textbf{\coursename}}\\[0.5em]
    {\large \semester}\\[1em]
    \fbox{
        \begin{minipage}{0.95\textwidth}
            \vspace{0.5em}
            \textbf{Lecture \lecturenum:} Lecture Title Here\\
            \textbf{Date:} \lecturedate\\
            \textbf{Instructor:} \instructor\\
            \textbf{Scribe:} \scribe
            \vspace{0.5em}
        \end{minipage}
    }
\end{center}

\vspace{1em}

\section*{Lecture Overview}
Briefly summarize the main themes of the lecture in a few sentences. For example:
\begin{itemize}[itemsep=0.25em]
    \item What problem or model was introduced?
    \item What were the main results?
    \item What techniques or proof ideas appeared?
\end{itemize}


\section{Introduction}
Write a short introduction explaining where this lecture fits into the course.

For example, you might say:
\begin{quote}
In this lecture, we introduced randomized algorithms for approximate counting and discussed how concentration bounds help control the probability of error.
\end{quote}

\section{Brief Reminders about Previous Topics}

Briefly summarize any background from previous lectures that we need here.

\section{Main Lecture Content}

Put the lecture content here. Try to provide a moderately detailed summary of what was discussed along with the main points and motivation. You may want to break into further sections.

\paragraph{Algorithms}

If the lecture contains pseudocode, place it in an environment like this one:

\begin{algorithm}[H]
\DontPrintSemicolon
\KwIn{Input $x$}
\KwOut{Approximate solution}
Sample random bits\;
Compute a candidate solution using the random choices\;
\Return candidate\;
\caption{Generic Randomized Algorithm}
\end{algorithm}

\section{Further Remarks}
Include any of the following if relevant:
\begin{itemize}[itemsep=0.25em]
    \item historical context,
    \item connections to previous lectures,
    \item open questions mentioned in class,
    \item references for further reading.
\end{itemize}

\section{Summary}
End with a short recap of the most important takeaways from the lecture.


\begin{thebibliography}{9}
\bibitem{motwani-raghavan}
R. Motwani and P. Raghavan,
\emph{Randomized Algorithms},
Cambridge University Press, 1995.
\end{thebibliography}

\end{document}