\begin{minipage}[t]{0.85\linewidth}
\textbf{Theorem 1 (Residue Theorem).}
Let $f$ be analytic in the region~$G$ except for the isolated singularities $a_1, a_2, \ldots, a_m$. 
If $\gamma$ is a closed rectifiable curve in~$G$ which does not pass through any of the points~$a_k$ 
and if $\gamma\approx 0$ in~$G$ then
\[
\frac{1}{2\pi i}\int_\gamma f = \sum_{k=1}^m n(\gamma;a_k) \mathop{\mathrm{Res}}(f;a_k).
\]

\textbf{Theorem 2 (Maximum Modulus).}
{\textit
Let $G$ be a bounded open set in~$\mathbb{C}$ and suppose that $f$ is a continuous function 
on~$G^-$ which is analytic in~$G$. Then
\[
\max \left\{|f(z)|:z\in G^-\right\}=\max \left\{|f(z)|:z\in \partial G \right\}.
\]}
\end{minipage}
