A Math Sample File (example3.tex)

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\begin{document}

\begin{itemize}

\item Note $a_{5^2} \tan(\vec{u} \cdot \vec{v}) = 0$ when $\vec{u}
\perp \vec{v}$.

\item The sequence $x_1, x_2, \ldots, x_n, \ldots$ is said to {\em
converge} to $x_\infty$ provided that $\forall \epsilon > 0$,
$\exists N$ such that $n \geq N \Rightarrow |x_n - x_\infty| <
\epsilon$.

\item Recall $\lim_{n \rightarrow \infty} \left ( 1 +
\frac{1}{n}\right)^n = e$.

\end{itemize}

Frequently, an equation will look much better displayed:
\[
\lim_{n \rightarrow \infty} \left ( 1 +
\frac{1}{n}\right)^n = e
\]
To get an equation number, you have to use the {\em equation}
environment:
\begin{equation}
\Gamma(x+1) = \int_0^\infty e^{-x} t^{x+1} dt
\end{equation}
You can combine arrays and delimiters to get 
\[
\left[\begin{array}{ccc}
1 & 2 & 3 \\
1 & 4 & 9 \\
1 & 8 & 27
\end{array}\right]
\]
Another useful trick with arrays and delimeters gives multiline
definitions:
\[
f(x) \stackrel{\rm def}{=}
\left \{ \begin{array}{ll}
x^2 & \mbox{if $ x > 0$} \\
-x^2 & \mbox{if $ x \leq 0$}
\end{array} \right.
\]
\end{document}