\usepackage[capitalize,noabbrev]{cleveref}
\begin{lemma}\label{foo}
Bar
\end{lemma}then \cref{foo} gives Lemma x.y in the
PDF. Moreover, if we were to promote the lemma to a theorem,
then cref automatically changes the references accordingly,
of course.
overfull hboxes (in the bibliography, for instance).
mathtools package\DeclarePairedDelimiter{\abs}{\lvert}{\rvert}
allows you to write
\abs{x} instead of
\lvert x \rvert and even better,
\abs*{\frac{x}{y}}
\abs[\Big]{\frac{x}{y}} instead of
\left\lvert \frac{x}{y} \right\rvert
\Big\lvert \frac{x}{y} \Big\rvert.
\(...\) for inline math\(...\) rather than $...$
improves error messages. Besides, it makes more sense to have separate
opening and closing tags, just like you do for other LaTeX environments.