\documentclass[11pt]{amsart}
\usepackage{amssymb,amsmath}
\newcommand{\R}{\mathbb R}
\newcommand{\C}{\mathbb C}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}[theorem]{Lemma}
\begin{document}
\begin{theorem}
The field $\C$ is a vector space over $\R$.
\end{theorem}
\begin{theorem}
A matrix of a change of the basis for a finite dimensional
linear space is nondegenerate.
\end{theorem}
\begin{proof}
Consider a linear map
$$f : M \to M$$
such that
\begin{equation} \label{map}
f(e_i) = g_i.
\end{equation}
In (\ref{map}), $\{e_i\}_{i=1}^n$ and $\{ g_i \}_{i=1}^n$ are two bases
in $M$.
The rest of the proof can be found, e.g.,
in \cite{S}\footnote{But this is not a
way to solve a homework problem}.
\end{proof}
\begin{thebibliography}{2}
\bibitem[S]{S} G. Strang, {\it Introduction to linear algebra}, third ed,
Wellesley-Cambridge press, 2003
\end{thebibliography}
\end{document}
This is an example of a bibliography. You can have references to books and
papers in the text and list them at the end.
Important: to get the references right, run latex twice.
Note the difference between the two ways to display math:
$$ $$ makes a line with your equation;
\begin{equation} \end{equation} makes a line with your equation
and gives it a number, so later you can refer to it in the text, using
\label{...} and \ref{...} operators.