Section numbering with chapter in amsbook

I'm using amsbook to write a report. I'm using \chapter{}s and \section{}s, and their numbering is fine. However, \section{}s are numbered sequentially inside each \chapter{}, but without the indication of the \chapter{}: basically, I'm getting Section 1 instead of1.1, and similarly Subsection 1 instead of 1.1.1.

How do I go about fixing this?

Answers

Write the following in the preamble:

\renewcommand{\thesection}{\thechapter.\arabic{section}}

alternate approach: in the preamble,
\numberwithin{section}{chapter}


but it doesn't carry along to subsections; for that you'd need
\numberwithin{subsection}{section}


etc.