Numbered sections in unnumbered chapters + ToC

Question

I want to have numbered sections in an unnumbered chapter.

This is my code:

\documentclass{book}

\begin{document}

\tableofcontents

\chapter*{Introduction}
\addcontentsline{toc}{chapter}{Introduction}
\section{First numbered section in unnumbered chapter}
\section{Second numbered section in unnumbered chapter}

\chapter{First numbered chapter}
\section{First numbered section in numbered chapter}

\end{document}

This is a preview of the compiled Table of Contents:

As you can see the numbered sections have leading zeroes in the Table of Contents. How can I delete the leading zeros? Of course I want to achieve the same in the actuel text.

Thank you

Answer 1

Temporarily change the definition of \thesection (no guarantee this won't break anything...)

\documentclass{book}

\begin{document}

\tableofcontents

\chapter*{Introduction}
\addcontentsline{toc}{chapter}{Introduction}

\begingroup
\makeatletter
\renewcommand\thesection{\@arabic\c@section}
\makeatother
\section{First numbered section in unnumbered chapter}
\section{Second numbered section in unnumbered chapter}
\endgroup

\chapter{First numbered chapter}
\section{First numbered section in numbered chapter}

\end{document}