math-ulm-2023/math-ulm-2023.tex at main · lairez/math-ulm-2023 · GitHub

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\documentclass[a4paper,parskip=half-,headings=small]{scrartcl}

\usepackage{libertine}
\usepackage[T1]{fontenc}
\usepackage[libertine,vvarbb]{newtxmath}
\usepackage{microtype}
\usepackage[hypertexnames=false]{hyperref}
\usepackage[french]{babel}
\usepackage[scale=.85]{plex-sans}

\usepackage{mathtools}
\usepackage[shortlabels]{enumitem}

\usepackage[style=apa, backend=biber]{biblatex}
\addbibresource[glob]{*.bib}

\addtokomafont{author}{\sffamily}
\addtokomafont{date}{\sffamily}

\renewcommand{\leq}{\leqslant}
\renewcommand{\geq}{\geqslant}
\renewcommand{\epsilon}{\varepsilon}
\renewcommand{\phi}{\varphi}

\newcommand{\st}{\ \middle|\ }

\usepackage{fontawesome}
\usepackage{graphicx}

\title{Épreuve orale “Mathématiques Ulm”}
\subtitle{Concours MP --- Session 2023}
\author{Pierre Lairez \and Romain Tessera}
\date{}

\begin{document}

\maketitle
\begin{center}
  \begin{minipage}{.7\linewidth}
    \footnotesize\sffamily
    Ce document rassemble les exercices posés aux candidats au concours d'entrée de l'ENS Ulm, en filière MP, lors de l'épreuve orale “Mathématiques Ulm”.
    \bigskip

    \faGithub{} \url{https://github.com/lairez/math-ulm-2023}

    \bigskip
    \raisebox{-.4ex}{\includegraphics[height=2ex]{cc-zero.pdf}}
    Document publié sous licence \href{https://creativecommons.org/publicdomain/zero/1.0/deed.fr}{``CC0 1.0 Universel''}.
  \end{minipage}
\end{center}

\input{sec/00_tchebychev_wronskien.tex}
\input{sec/01_divis_card_GLnFp.tex}
\input{sec/02_monomisation_locale.tex}
\input{sec/03_espace_translatee.tex}
\input{sec/04_somme_alternee.tex}
\input{sec/05_union_de_fermes.tex}
\input{sec/06_isoperimetrique_discrete.tex}
\input{sec/07_antisymetrique.tex}
\input{sec/08_isometries_affines.tex}
\input{sec/10_resultant.tex}
\input{sec/11_composantes_connexes.tex}
\input{sec/12_translation_impossible.tex}
\input{sec/13_valuation_padique_produit.tex}
\input{sec/14_generateur_groupe_matriciel.tex}
\input{sec/15_angle_pavage.tex}
\input{sec/16_cosinus_rationnel.tex}
\input{sec/17_wronskien_peano.tex}
\input{sec/18_distance_mat_sym.tex}
\input{sec/19_norme_inverse.tex}
\input{sec/20_disques_carres.tex}
\input{sec/21_certification_racine.tex}
\input{sec/21_mediane_moyenne.tex}
\input{sec/22_sous_espace_stable.tex}
\input{sec/23_hermite_kakeya.tex}
\input{sec/24_groupe_de_polynomes.tex}
\input{sec/25_somme_deux_carres.tex}
\input{sec/26_hermite_sylvester.tex}

\printbibliography

\end{document}