% sample latex2e file
% useful for summary of papers and other simple stuff
% genuine finger-typed files by Christina C. Christara

\documentclass[12pt]{article}
%\documentclass[12pt]{mypaper}

%\linespread{1.1} % for more than single spacing

% take more advantage of the size of paper
\addtolength{\topmargin}{-2cm}
\addtolength{\textheight}{4cm}
\addtolength{\evensidemargin}{-2cm}
\addtolength{\oddsidemargin}{-2cm}
\addtolength{\textwidth}{4cm}

% some standard packages
\usepackage{times}

% convenient abbreviations
\newcommand{\EQ}{\begin{equation}}
\newcommand{\EN}{\end{equation}}

\begin{document}
\begin{center}
\large{\bf{This is the title of the paper\\
summarized}}
\end{center}
\begin{center}
{\large{Author1 Name1, Author2 Name2} \small{and} \large{Author3 Name3}\\
\small{Journal Name, Volume, Year, Pages or Other Publication information\\
}}
\end{center}
\begin{center}
Summary by Name
\end{center}

A pr\'{e}cis of a scientific paper usually starts with
a few sentences on the problem the paper tries to solve,
and the motivation for the work, including the usefulness
of the method and results, as well as the difficulties
to obtain them.

Then the description of the problem comes in more details.
It is often necessary to give a few equations,
and indicate the quantities that are given and those that
are unknown and being computed through the method.
For example, the Black-Scholes equation
\EQ
\frac{\partial V}{\partial t}
+ \frac{\sigma^2 S^2}{2} \frac{\partial^2 V}{\partial S^2}
+ r S \frac{\partial V}{\partial S} - rV = 0 \label{eq:BS}
\EN
is a Partial Differential Equation (PDE) describing
how the option value $V(S, t)$ depends on the stock price $S$ and time $t$.
In equation (\ref{eq:BS}), $\sigma$ is the volatility of the underlying asset,
and $r$ is the interest rate. Both $\sigma$ and $r$ are considered given,
while $V$ is the quantity being computed (or approximated).

The same PDE can be written in a more condensed format as
\[
V_t + \frac{\sigma^2 S^2}{2} V_{SS} + r S V_S - rV = 0.
\]

A PDE is associated with some initial and/or boundary conditions,
to give rise to a complete PDE problem.
For equation (\ref{eq:BS}) to have a unique solution, we must pose
two conditions in $S$ and one in $t$.
The two conditions in $S$ are often referred to as {\em boundary conditions}.
For example, we may specify that
\[
V(S, t) = V_a(t) \;\mbox{on}\; S = a, \;\mbox{and}\;
V(S, t) = V_b(t) \;\mbox{on}\; S = b,
\]
for some given functions $V_a(t)$ and $V_b(t)$ and
some appropriate $a$ and $b$.
The condition in $t$ is often referred to as {\em initial condition}.
If we proceed forward in time, we impose the initial condition on $t=0$,
e.g.
\[
V(S, t) = V_0(S) \;\; \mbox{on}\;\; t=0
\]
for some given function $V_0(S)$.
However, there are cases in which we integrate a PDE backwards.
In such cases 
the condition in $t$ is imposed at the {\em final} point of time $t = T$,
e.g.
\[
V(S, t) = V_T(S) \;\; \mbox{on}\;\; t=T
\]
for some given function $V_T(S)$.

Next, the method(s) for solving or approximating the solution to the problem
is (are) described. A method for solving a PDE problem may consist
of a discretization technique (such as finite difference or finite element)
which converts the PDE into an algebraic system of equations,
and solution techniques for the system of equations.
If the PDE is time-dependent, the numerical method usually involves
solving a system at each time step.
If the paper is presenting a new method,
the advantages of the new method over past methods
for the same problem must be emphasized.

Other papers may be presenting a review of different methods
for solving the same problem, in which case the comparison
between the methods is important.
The comparison may be in terms of accuracy, efficiency, applicability
to a wide range or similar problems, or other characteristics.

A paper may include some mathematical analysis of a method or methods,
often expressed as theorems or other mathematical results,
as well as numerical experiments to verify the effectiveness
of the method(s).

A summary usually ends with some criticism (positive or negative)
about particularly strong or weak points in the method(s),
and questions about potential new problems or ideas arising.

To run this latex file, type on any Unix (Solaris or linux) machine
\begin{verbatim}
% latex simple.tex
% latex simple.tex
% dvips simple.dvi
\end{verbatim}

\noindent
This will create a postscript file, {\tt simple.ps}.
You can view it with
\begin{verbatim}
% gv simple.ps
\end{verbatim}
or print it with
\begin{verbatim}
% lpr simple.ps
\end{verbatim}

\noindent
If you prefer to get a pdf file, you type
\begin{verbatim}
% latex simple.tex
% latex simple.tex
% dvipdf simple.dvi
\end{verbatim}
and proceed accordingly.

It is worth noting that the command {\tt latex simple.tex}
must be run {\em twice}, if there are labels of equations
in the latex file. In this example, there is only one label,
the label for the Black-Scholes equation (\ref{eq:BS}).

%This is just a short example of a latex file.
Notice that lines that start with \% are considered comments
in latex, except if they are in the verbatim environment.
If you want to write a percent mark at any point of the document,
preceed it by a backslash, such as \%.

\medskip
\noindent
This is just a short example of a latex file.
You can copy it to your directory and run latex on it,
to see how the output looks like.
\end{document}