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My presentation has three parts about three different papers. I would like to number the theorems and propositions within each part (paper).

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Welcome to TeX.sx! Please add a minimal working example (MWE) that illustrates your required usage. It just helps in getting more accurate answers for your usage. –  Werner Oct 2 '12 at 20:53
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1 Answer

You can use the etoolbox package, to make the \part command reset the recounter(s):

\documentclass{beamer}
\usepackage{etoolbox}

\setbeamertemplate{theorems}[numbered]
\pretocmd{\part}{\setcounter{theorem}{0}}{}{}
\newtheorem{proposition}[theorem]{Proposition}

\begin{document}

\part{Test Part One}
\begin{frame}
\begin{theorem}
Test theorem in part one.
\end{theorem}
\begin{proposition}
Test proposition in part one.
\end{proposition}
\end{frame}    

\part{Test Part Two}
\begin{frame}
\begin{theorem}
Test theorem in part two.
\end{theorem}
\begin{proposition}
Test proposition in part two.
\end{proposition}
\end{frame}    

\end{document}

enter image description here

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