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% This file is part of PSNFSS 9.2
\listfiles
\documentclass{article}
\usepackage{geometry}
%\pagestyle{empty}
\usepackage[sc,osf,slantedGreek]{mathpazo}
\linespread{1.08} % Palatino needs more leading
\usepackage[scaled]{helvet}
\usepackage{courier}
\parindent=0pt
\pagestyle{empty}
\normalfont
\usepackage[T1]{fontenc}
\begin{document}
\begin{center}
\scshape\Large Sebastian's math test
\end{center}
The default math mode font is $Math\ Italic$. This should not be
confused with ordinary \emph{Text Italic} -- notice the different spacing\,!
\verb|\mathbf| produces bold roman letters: $ \mathbf{abcABC} $.
If you wish to embolden complete formulas,
use the \verb|\boldmath| command \emph{before} going into math mode.
This changes the default math fonts to bold.
\begin{tabular}{ll}
\texttt{normal} & $ x = 2\pi \Rightarrow x \simeq 6.28 $\\
\texttt{mathbf} & $\mathbf{x} = 2\pi \Rightarrow \mathbf{x} \simeq 6.28 $\\
\texttt{boldmath} & {\boldmath $x = \mathbf{2}\pi \Rightarrow x
\simeq{\mathbf{6.28}} $}\\
\end{tabular}
\smallskip
Greek is available in upper and lower case:
$\alpha,\beta \dots \Omega$, and there are special
symbols such as $ \hbar$.
The following letters should be upright: $\upGamma, \upDelta\dots \upOmega$.
Digits in formulas $1, 2, 3\dots$ may differ from those in text: 4, 5, 6\dots
There is a calligraphic alphabet \verb|\mathcal| for upper case letters
$ \mathcal{ABCDE}\dots $, and there are letters for number sets: $\mathbb{A\dots Z} $,
which are produced using \verb|\mathbb|.
\begin{equation}
\sigma(t)=\frac{1}{\sqrt{2\pi}}
\int^t_0 e^{-x^2/2} dx
\end{equation}
\begin{equation}
\prod_{j\geq 0}
\left(\sum_{k\geq 0}a_{jk} z^k\right)
= \sum_{k\geq 0} z^n
\left( \sum_{{k_0,k_1,\ldots\geq 0}
\atop{k_0+k_1+\ldots=n} }
a{_0k_0}a_{1k_1}\ldots \right)
\end{equation}
\begin{equation}
\pi(n) = \sum_{m=2}^{n}
\left\lfloor \left(\sum_{k=1}^{m-1}
\lfloor(m/k)/\lceil m/k\rceil
\rfloor \right)^{-1}
\right\rfloor
\end{equation}
\begin{equation}
\{\underbrace{%
\overbrace{\mathstrut a,\ldots,a}^{k\ a's},
\overbrace{\mathstrut b,\ldots,b}^{l\ b's}}
_{k+l\ \mathrm{elements}} \}
\end{equation}
\[
\mbox{W}^+\
\begin{array}{l}
\nearrow\raise5pt\hbox{$\mu^+ + \nu_{\mu}$}\\
\rightarrow \pi^+ +\pi^0 \\[5pt]
\rightarrow \kappa^+ +\pi^0 \\
\searrow\lower5pt\hbox{$\mathrm{e}^+
+\nu_{\scriptstyle\mathrm{e}}$}
\end{array}
\]
\[
\frac{\pm
\left|\begin{array}{ccc}
x_1-x_2 & y_1-y_2 & z_1-z_2 \\
l_1 & m_1 & n_1 \\
l_2 & m_2 & n_2
\end{array}\right|}{
\sqrt{\left|\begin{array}{cc}l_1&m_1\\
l_2&m_2\end{array}\right|^2
+ \left|\begin{array}{cc}m_1&n_1\\
n_1&l_1\end{array}\right|^2
+ \left|\begin{array}{cc}m_2&n_2\\
n_2&l_2\end{array}\right|^2}}
\]
Mathematical accents:
\[
\mbox{ acute=}\acute{a}
\mbox{ grave=}\grave{a}
\mbox{ ddot=}\ddot {a}
\mbox{ tilde=}\tilde{a}
\mbox{ bar=}\bar {a}
\mbox{ breve=}\breve{a}
\mbox{ check=}\check{a}
\mbox{ hat=}\hat {a}
\mbox{ vec=}\vec {a}
\mbox{ dot=}\dot {a}
\]
\end{document}
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