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% ================================ Debut du document ===========================

\begin{document}

\begin{titlepage}

\begin{center}

\begin{minipage}[t]{0.6\textwidth}
  \begin{flushleft}
  Universit\'e Paris 5 Descartes\\
UFR Math\'ematiques et Informatique\\
 Licence 1, 2\ieme\ semestre 2014–2015
  \end{flushleft}
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    \includegraphics [width=60mm]{Logo-Paris-Descartes_large.jpg}
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    \emph{Auteurs :}\\
    \firstauthor\\ \secauthor
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    \emph{Encadrant:} \\
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{\large Soutenu le \datesout}

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\end{titlepage}



\newpage

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\tableofcontents 

\cleardoublepage % pour laisser une page blanche au verso de la page de garde



\section{Introduction}

\subsection{Formules math\'ematiques}
Soit la fonction $f$, d\'efinie par $f(x)=2x$.

Soit la fonction $f$, d\'efinie par \[ \forall x\in I, f(x)=2x^2. \]
Soit la fonction \[ f_n : x\mapsto\alpha^2\sqrt{\pi}+ \frac{1}{2}\, \sum_{i=1}^{n}{\ln x}. \]
La fonction $\zeta$ de Riemann satisfait \[\zeta(s)= \sum_{n=1}^{+\infty}\frac1{n^s} =\prod_{p\in\mathcal P} \frac1{1-p^{-s}}.\]

Soit la matrice \[A= \begin{pmatrix}
0 & 1\\ 2& \pi
\end{pmatrix}.\]
\subsection{Equations}
Une \'equation.
\begin{equation}
\label{eq:defa}
a= \sum_{n=1}^{+\infty} \frac{1}{n^{\alpha}}
\end{equation}
Une autre sans num\'ero.
\begin{equation*}
b= \int_{0}^{1} x^{2} d x
\end{equation*}

Plusieurs \'equations align\'ees
\begin{align}
a&= 1+2+3\\
b&= 2+3+4
\end{align}
Sans num\'eros
\begin{align*}
a&= 1+2+3\\
b&= 2+3+4
\end{align*}


\subsection{Environnements}

\begin{dft}
Soit $\alpha= \lim_{n\to\infty} \left(1- \frac{1}{n}\right)^{n}$\end{dft}

\begin{thm}[Th\'eor\`eme de Pythagore]
\label{th:gamma}
Le triangle $ABC$ est rectangle en $A$ si et seulement si $AB^{2}+ AC^{2}= BC^{2}$.
\end{thm}

\begin{rem}
Pour tout $x>0$, \[ \Gamma(x)\text{ est bien d\'efinie.} \]
\end{rem}

\subsection{Faire r\'ef\'erence}
L'\'equation \eqref{eq:defa}, le Th\'eor\`eme \ref{th:gamma}.
\section{Divers}
\subsection{Enumerations}

\begin{itemize}
\item premierement ; \item deuxiemement.
\end{itemize}

\begin{enumerate}
 \item Primo.
 \item Secundo.
\end{enumerate}

\subsection{Tableaux}

\begin{tabular}{|rl|c|}
\hline
right & left & center \\ Xavier & Martine & Fran\c cois\\ \hline
Resistance & Inductance & Capacite\\
 \hline
\end{tabular}

\subsection{Polices}

$A$, $\mathcal{A}$, $\mathbf{A}$, $\mathfrak{A}$, $\mathbb{A}$

\section{deuxieme section}

\subsection{sous-section}

\subsubsection{Sous-partie}

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\subsubsection{Sous-partie}

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\subsection{sous-section}

\subsubsection{Sous-partie}

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\subsubsection{Sous-partie}

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\end{document}