\documentclass{article}
\usepackage{textcase}
\usepackage{cite}
\begin{document}
\section{\MakeTextUppercase{Uppercase}}\label{intro}

\subsection{Text and math interleaved}

\MakeTextUppercase{abc\ae\ \( a = b \) and $\alpha \neq a$
or even \ensuremath{x=y} and $\ensuremath{x=y}$}

\subsection{Refs and cites}

\MakeTextUppercase{%
Text in section~\ref{intro}, about \cite[pp 2--4]{bbb}}

\MakeTextUppercase{%
Text \cite{bbb} and \cite{ccc}}

{\renewcommand\citeform{\MakeUppercase}\MakeTextUppercase{%
Text \cite{bbb} and \cite{ccc}}}

\subsection{Nested with NoCaseChange}

\MakeTextUppercase{%
Text \NoCaseChange{More Text} yet more text}

\subsection{NoCaseChange and tabular}

\MakeTextUppercase{%
Text \NoCaseChange{\begin{tabular}{ll}}%
table&stuff\\goes&here
\NoCaseChange{\end{tabular}}
More text}

\subsection{Nested brace groups}

\MakeTextUppercase{a b {c $d$} $e$}

\subsection{Environment protection}

\MakeTextUppercase{...\NoCaseChange{\begin{center}} ...inner...\NoCaseChange{\end{center}}...}

% ----
\section{\MakeTextLowercase{Lowercase}}

\MakeTextLowercase{THIS WAS WRITTEN UPPER, SHOULD APPEAR LOW}

\begin{thebibliography}{9}

\bibitem{bbb} Something numeric
\bibitem[David Carlisle 1997]{ccc} Something textual
\end{thebibliography}

\end{document}