\documentclass{amsart}
\usepackage{amsmath, amssymb, amsthm}
\theoremstyle{definition}
\newtheorem{problem}{Problem}
\theoremstyle{remark}
\newtheorem*{solution}{Solution}
% The above code produces ``Theorem environments" that help organize
% the information in your p-set by nicely labeling and numbering it.
% For usage, see the body of this template.
\setcounter{problem}{9}
% Resets the problem number to 9. Since LaTeX increments the counter
% when a new problem environment is established, the first problem will
% be listed as Problem 10. If you want the problems to start at 1, either
% comment out this line (with a %) or change 9 to 0.
\title{Problem Set \#$\aleph_0$, 18.100C}
\author{G.~Cantor}
\date{February 4, 2011}
% These lines produce reasonably formatted title information
% for your p-set once \maketitle is invoked in the body of the document.
\begin{document}
\maketitle
\begin{problem}
Produce some \LaTeX~code that exhibits some useful features.
\end{problem}
\begin{solution}
The following unnumbered formula presents the expression
$\sum_{n=1}^{\infty} \frac{1}{n^2} < \infty$ in math mode:
\[
\sum_{n=1}^{\infty} \frac{1}{n^2} < \infty.
\]
It is possible to reference the numbered equation
\begin{equation}
\label{defIntegral}
\int_{0}^{1} x\, dx = \frac{1}{2}
\end{equation}
since it is supplied with a ``label." This sentence refers to
equation (\ref{defIntegral}).
By using two line breaks, we have produced a new paragraph;
in it we include a bibliographic reference to Rudin \cite{Rudin}.
The last theorem you will read about in that text is
\cite[Theorem 8.20]{Rudin}.
\end{solution}
\begin{problem}
Prove that \LaTeX~numbers theorem environments appropriately.
\end{problem}
\begin{solution}
This follows by inspection upon compiling the .tex file. Note
that you must compile the document twice in order for label
and bibliographic references to appear. If installed on your
system, the command \texttt{dvipdf} \emph{fileName.dvi} will convert
\LaTeX's .dvi output to .pdf.
\end{solution}
\begin{thebibliography}{9}
\bibitem{Rudin}
Walter Rudin,
\emph{Principles of mathematical analysis}.
McGraw-Hill Book Co.,
3rd Edition,
1976.
\end{thebibliography}
\end{document}