Added stick section

Advanced/Knots/parts/3 sticks.tex

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+\section{Knots and Sticks}
+
+\definition{}
+The \textit{stick number} of a knot is the smallest number of \say{sticks} you must glue together to make the knot. An example of this is below.
+
+\begin{center}
+	\includegraphics[width=30mm]{images/sticks.png}
+\end{center}
+
+\problem{}
+Make the trefoil knot with sticks. \par
+How many do you need?
+
+\begin{solution}
+	\begin{center}
+		\includegraphics[width=20mm]{images/stick trefoil.png}
+	\end{center}
+\end{solution}
+
+\vfill
+
+\problem{}
+How many sticks will you need to make a figure-eight knot?
+
+\begin{solution}
+	The figure-eight knot has stick number 7. \par
+	In fact, this is the \textit{only} knot with stick number 7.
+\end{solution}
+
+\vfill
+\pagebreak
+
+\problem{}
+Make the knot $5_1$ (refer to the knot table) with eight sticks.
+
+\vfill
+
+\problem{}
+Show that the only nontrivial knot you can make with six sticks is the trefoil.
+
+\vfill
+
+\problem{}
+Let $S(k)$ be the stick number of a knot $k$. \par
+Show that $S(j \boxplus k) \leq s(j) + s(k) - 1$
+
+
+\vfill
+
+\problem{}
+What is the stick number of $(\text{trefoil} \boxplus \text{trefoil})$?
+
+\begin{solution}
+	You can make $(\text{trefoil} \boxplus \text{trefoil})$ with 8 sticks.
+
+	\begin{center}
+		\includegraphics[angle=90, width=40mm]{images/stick trefoil composition.png}
+	\end{center}
+\end{solution}
+
+\vfill
+\pagebreak