Knowledge Base/Tools/LaTeX
A minimalistic LaTeX article
The following article can be used as a template for your own articles:
\documentclass[12pt]{article}
\usepackage{amsmath}
\title{Welcome to \LaTeX}
\author{Paul Bilokon}
\date{17 June, 2009}
\begin{document}
\maketitle
\begin{abstract}
A sample article.
\end{abstract}
This is a \textbf{very} \textit{simple} Hello \LaTeX document!
\section{Option Pricing}
\subsection{Black-Scholes}
Here are some formul{\ae} from \cite{Black1973}:
\begin{align*}
d_1 &= \frac{\ln(S/K) + (r + \sigma^2/2)(T - t)}{\sigma \sqrt{T - t}}, \\
d_2 &= d_1 - \sigma \sqrt{T - t}.
\end{align*}
\begin{thebibliography}{99}
\bibitem{Black1973} \textsc{Black, F. and Scholes, M.} The Pricing of
Options and Corporate Liabilities. \emph{Journal of Political
Economics}, 81 (1973), 637--659.
\end{thebibliography}
\end{document}
Including bibliography entries stored in a file
If your bibliography file is called foobar.bib and is located in the same directory as your *.tex file, you can add the following
\bibliographystyle{plain}
\bibliography{foobar}
just before
\end{document}
Including bibliography entries even if they are not cited
Add
\nocite{*}
just before your bibliography inclusion, i.e. something like this:
\nocite{*}
\bibliographystyle{plain}
\bibliography{foobar}
% These lines come just before...
\end{document}
The command \nocite{*} causes LaTeX to include every entry in your .bib file.
Putting a copyright (registered, trademark) sign in Failed to parse (unknown function\LaTeX): \LaTeX
The registered ®, copyright ©, and trademark ™ signs can be inserted as follows:
Widget\textsuperscript{\textcopyright}
Widget\textsuperscript{\textregistered}
Widget\textsuperscript{\texttrademark}
Note that these are inserted in text mode, not maths, so there are no $s. \textsuperscript ensures that the signs appear in superscript, as it is usually required. However, for copyright ©, you may often need something like this:
Copyright \textcopyright Paul Bilokon, 2007.
"Not a subset" looks strange
If your 
looks strange, try replacing
\not{\subseteq}
with
\not\subseteq
Two equations on one line
Sometimes you may wish to put two equations on one line separating them by appropriate horizontal spacing. You can achieve this as follows:
\begin{equation}
\frac{dN}{dt} = a(t) N(t), \quad N(0) = N_0 \text{(constant)},
\label{eq:population-growth-model}
\end{equation}
Here \quad is responsible for the spacing.
What do I need to do in order to use \mathbb
For example, \mathbb{R} looks like 
(reals); \mathbb{N} looks like 
(natural numbers).
In order to use it,
\usepackage{amsfonts}
How to cite a particular chapter, section, etc.
Like so:
\cite[Section~1.3]{bierens-2004}
How to include URLs in the bibliography
Use the url package by Donald Arseneau.
In the preamble:
\usepackage{url}
In a BibTeX entry:
@misc{
c.elmohamed,
author = "Saleh Elmohamed",
title = "Examples in {H}igh {P}erformance {F}ortran",
howpublished = "Website",
year = {1996},
note = {\url{http://www.npac.syr.edu/projects/
cpsedu/summer98summary/ examples/hpf/hpf.html}}
}
For more information, see this tip by Leo Breebaart.
Defining and using "variables"
To define:
\def \LectureTitle {Discrete Dynamical Systems}
\def \LectureNumber {2}
To use:
\title{\LectureTitle}
\subtitle{Lecture \LectureNumber}
Diagonal argument
Here is one way to express the diagonal argument (something like this) in Failed to parse (unknown function\LaTeX): \LaTeX
\begin{tabular}{cccccccccccc}
$I_1^1$ & $\rightarrow$ & $I_2^1$ & & $I_3^1$ & $\rightarrow$ & $I_4^1$ & & $I_5^1$ & $\rightarrow$ & $I_6^1$ & $\cdots$ \\
& $\swarrow$ & & $\nearrow$ & & $\swarrow$ & & $\nearrow$ & & $\swarrow$ & & \\
$I_1^2$ & & $I_2^2$ & & $I_3^2$ & & $I_4^2$ & & $I_5^2$ & & $I_6^2$ & $\cdots$ \\
$\downarrow$ & $\nearrow$ & & $\swarrow$ & & $\nearrow$ & & $\swarrow$ & & $\nearrow$ & & \\
$I_1^3$ & & $I_2^3$ & & $I_3^3$ & & $I_4^3$ & & $I_5^3$ & & $I_6^3$ & $\cdots$ \\
& $\swarrow$ & & $\nearrow$ & & $\swarrow$ & & $\nearrow$ & & $\swarrow$ & & \\
$I_1^4$ & & $I_2^4$ & & $I_3^4$ & & $I_4^4$ & & $I_5^4$ & & $I_6^4$ & $\cdots$ \\
$\downarrow$ & $\nearrow$ & & $\swarrow$ & & $\nearrow$ & & $\swarrow$ & & $\nearrow$ & & \\
$I_1^5$ & & $I_2^5$ & & $I_3^5$ & & $I_4^5$ & & $I_5^5$ & & $I_6^5$ & $\cdots$ \\
$\vdots$ & & $\vdots$ & & $\vdots$ & & $\vdots$ & & $\vdots$ & & $\vdots$ & \\
\end{tabular}
