Capitalizing mathematical parts in section mark

You can switch out \MakeUppercase for \MakeTextUppecase which skips math mode:

\documentclass{book}
\usepackage[overload]{textcase}
\begin{document}
    \section{$n+2=N$}
\end{document}

You can manually protect single characters (or a range in which everything is lowercase) by using \lowercase:

\documentclass{book}
\begin{document}
  \section{$\lowercase{n+n-n}+2=N$}
\end{document}