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\begin{document}
\title[MAT2000]{Some examples on how to use Latex}

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\subjclass[2010]{}
\date{\today}
\keywords{}

\author{Superman}

\maketitle

\begin{abstract} We give some examples on how to use LaTex.\end{abstract}

\section{Introduction}

This is a test.

\begin{theorem}\label{main}
Let $f\in\mathcal C([0,1])$ and assume that $f(0)<0$ and $f(1)>0$.
Then there exists a $c\in (0,1)$ such that $f(c)=0$.
\end{theorem}

According to Theorem \ref{main} f has a zero.



\begin{prop}
\end{prop}

\section{Background/preliminaries}
\begin{definition} Let $\N$ be the set of non-negative natural numbers and $\R$ the set of real numbers.\end{definition}
%
\begin{remark}We give this definition just in case there are some ignorant readers.\end{remark}

\subsection{Greek letters}
Just spell them out, like $\alpha$, $\beta$, $\gamma$, $\delta$ etc. In the Short
Math Guide For Latex (\cite{Ams Latex Guide}), which you can find on the course
homepage, there is a complete list of the Greek letters, as well as lists of various
mathematical symbols like $\angle$, $\emptyset$,$\cdots$,$\cap$ and many others.
There is also a lot of information on how to display mathematical formulas.

\subsection{Centered formulas}
You do not have to understand this formula/definition, but you can learn
 some LaTex by comparing the LaTex-code and the result.

$$x = \lim_{n \rightarrow \infty}x_n \Leftrightarrow \forall \epsilon > 0
 \exists n \in \N \forall m \geq n(|x - x_n| < \epsilon)$$

Subindexes are written like this: $x_\omega$, $\Omega_{n_1 + n_2}$.
\newline
Note the use of curly brackets when the subindex contains more than one symbol.
If we need some vertical space, write \vspace{2mm}, or something like that. The space will appear at the first new line, so if we want control, we write \vspace{3mm}\newline
Superindexes are written like this:
$$x^{n^2 + 3} - x^{n-1} = 5x^n$$
\newline
And both are written like this
$$ x_{i,j}^k $$

\section{Proof of the main theorem}

In this section we are going to prove Theorem \ref{main}:

\begin{theorem}
Let $f\in\mathcal C([0,1])$ and assume that $f(0)<0$ and $f(1)>0$.
Then there exists a $c\in (0,1)$ such that $f(c)=0$.
\end{theorem}

\begin{proof}
As in \cite{Wold1}

$\D$

\end{proof}
\section{Norsk tekst}
Det er mulig {\aa} skrive p{\aa} norsk ogs{\aa}.
\newline
\begin{nremark}
Du kan selvf\o lgelig ogs{\aa} bruke norske betegnelser som Teorem, Lemma, Korollar, Bemerkning, Oppgave, mm. 
\end{nremark}


\section{General advice}

\begin{problem}\label{main}
When I want to do something fancy using LaTex, what should I do?
\end{problem}
\begin{solution}\hspace*{2mm}
\begin{itemize}
\item Ask a friend
\item Ask someone else
\item Look up in a manual
\item Search for some package that does what you want.
\end{itemize}
\end{solution}
If you want the options in an order of priority, use enumeration:
\begin{enumerate}
\item Ask a friend
\item Look up in a manual
\item Search the web for how to do it
\item Ask an expert.
\end{enumerate}

\section{Error messages}
When you work with LaTex, the standard procedure is:
\begin{itemize}
\item[a)] You write a source file in a text editor
\item[b)] You typeset the file
\item[c)] You get error messages
\end{itemize}
It is worth to notice
\begin{itemize}
\item The error message will refer to a \emph{line} in the source file.
\item
A line is the space between two uses of carriage return.
\item One carriage return will not produce a line-shift in the typeset manuscript, only in the source file.
\item Two consecutive carriage returns produce a line-shift  and a new paragraph, see below:
\end{itemize}
What happens if we use one carriage return?
Nothing.
\newline
What happens if we use two carriage returns?

A new paragraph.



\bibliographystyle{amsplain}
\begin{thebibliography}{10}

\bibitem{Wold1}
Wold, E. F.; Proper holomorphic embeddings.  \text{Internat. J. Math} 16 (2007) pp. 65--79.
\bibitem{Ams Latex Guide}
Downes, Michael : Short Math Guide for Latex. http://www.ams.org/tex/short-math-guide.html

www.ams.org

math sci net








\end{thebibliography}
\end{document}
