LaTeX tip #7

If you want to reset the numbering of theorems each time you change sections and you want to reset the numbering of notes each time you change chapters, the preamble would contain these lines:

\makeatletter

\renewcommand{\thetheorem}{\thesection.\arabic{theorem}}

\@addtoreset{theorem}{section}

\renewcommand{\thenote}{\thesection.\arabic{theorem}}

\@addtoreset{note}{chapter}

\makeatother

More on the same topic: Tips of MacKichan Software, Inc. and Using the amsthm Package