\documentclass[a4paper]{exam}
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\begin{document}
\begin{center}
\fbox{\fbox{\parbox{5.5in}{\centering
Hyperbolic Geometry Homework 3}}}
\end{center}
\vspace{0.1in}
\makebox[\textwidth]{Name:\enspace\hrulefill}
\begin{questions}
\question[4] Show that $\SL_2(\ZZ)$ is a discrete subgroup of $\SL_2(\RR)$. That is, for each $g = \mx{a}{b}{c}{d}\in\SL_2(\ZZ)$, find an open neighborhood $U(g)$ in $\SL_2(\RR)$ such that $U(g) \cap U(g') = \emptyset$ unless $g= g'$.

\question[4] Find the hyperbolic area of the region $$R = \left\{ x + iy : 0\le x\le 1, 1\le y\le 2\right\}.$$ Can you find the area of $R$ using the Gauss-Bonnet theorem?



\end{questions}
\end{document}
