\documentclass{article}
\usepackage{amssymb, amsmath, amsthm} % enables some more groovy symbols
\title{Basic \LaTeX\ Template}
\author{Mark McClure}
\date{\today} % Activate to display a given date or no date
\newtheorem*{theorem}{Theorem}
\begin{document}
\maketitle
\abstract{A sample \LaTeX\ document}
\section*{Introduction} % The * just makes the section unnumbered, which we typically want for a short document.
We'll be using \LaTeX\ a fair amount. The easiest way to start a project is just to open a working file and replace the text with your own. You can use this document for that purpose. It's about as bare bones as a document can be.
\section*{Some math}
\subsection*{Computation}
Of course, the main thing we want to do is type some math. For example, if $f(x)=e^{-x^2}$, then $f'(x)=-2xe^{-x^2}$ and
$$\int_{-\infty}^{\infty} e^{-x^2} dx = \sqrt{\pi}.$$
\subsection*{Theorem-proof}
Often, we'd like a theorem-proof setup.
\begin{theorem}
$$\sum_{n=1}^{\infty}\frac{1}{n^2} = \frac{\pi^2}{6}.$$
\end{theorem}
\begin{proof}
The proof is in the pudding!
\end{proof}
\end{document}