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How can I use two modes in emacs (markdown and auctex)?

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http://unix.stackexchange.com – When I edit markdown in emacs I use markdown-mode. However I often have to type some math formulas in the markdown file (processed by mathjax). However for those math parts markdown mode is not very comfortable. Is there a way to make emacs automatically switch to latex (auctex) mode (locally) when the point is between two $ signs for example ($\mathbb{R}$) or between two double $ signs for example $$ \begin{align} a = b \end{align} $$ ? (HowTos)