diff --git a/math_commands.tex b/math_commands.tex
index da669ee..477f790 100644
--- a/math_commands.tex
+++ b/math_commands.tex
@@ -53,8 +53,8 @@
 \def\Partref#1{Part~\ref{#1}}
 \def\twopartref#1#2{parts \ref{#1} and \ref{#2}}
 
-\def\ceil#1{\lceil #1 \rceil}
-\def\floor#1{\lfloor #1 \rfloor}
+\DeclarePairedDelimiter{\ceil}{\lceil}{\rceil}
+\DeclarePairedDelimiter{\floor}{\lfloor}{\rfloor}
 \def\1{\bm{1}}
 \newcommand{\train}{\mathcal{D}}
 \newcommand{\valid}{\mathcal{D_{\mathrm{valid}}}}
diff --git a/notation_example.tex b/notation_example.tex
index 3b9928f..207cb80 100644
--- a/notation_example.tex
+++ b/notation_example.tex
@@ -42,6 +42,7 @@
 \usepackage{multirow}
 \usepackage{colortbl}
 \usepackage{booktabs}
+\usepackage{mathtools}
 % This allows us to cite chapters by name, which was useful for making the
 % acknowledgements page
 \usepackage{nameref}