To Papiro: Taking into account that the question was tagged with amsbook, i won't say that this is a duplicate of the numerous sectioning threads, as far as it questions the possibility to change the sectioning in a specific documentclass. The answer is clearly, that one can aplly the "standard" solutions using changectr or remreset.
Here, i'd like to point out, that remreset is also viable, because in this case (with amsbook) there is no need to redefine the regarding \the<cntr>. So the solution would look like:
\documentclass{amsbook}
\usepackage{remreset}
\makeatletter
\@removefromreset{section}{chapter}
\makeatother
\begin{document}
\chapter{First Test Chapter}
\section{First Test Section}
\section{Second Test Section}
\chapter{Second Test Chapter}
\section{Third Test Section}
\section{Fourth Test Section}
\end{document}