cours_maths_mpi_notes.tex

% Set up the document's format to A4 and the font's size to 12pt.
\documentclass[a4paper,12pt]{report}

% Set up the document's title, author and date.
\title{Maths -- MPI}
\author{Romain Bricout}
\date{\today}

% Set up the input's encoding to UTF-8, the document's font and language to T1 (adapted to french) and french (the grammar linter uses this parameter).
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage[frenchb]{babel}

\usepackage[dvipsnames]{xcolor}

% Set up the document's margins.
\usepackage{geometry}
\geometry{hmargin=1.5cm,vmargin=1.5cm}

% The three main maths packages. They are used for a lot of things.
\usepackage{amssymb,amsmath}
\usepackage{mathtools}

% Useful to create nice and easy signs or variations tables.
\usepackage{tkz-tab}

% Useful to create any kind of visual representation (graph functions, illustrate geometry problems, etc)
\usepackage{tikz}
\usetikzlibrary{patterns,angles,quotes,arrows,arrows.meta,bending,matrix,calc}

% Allows to edit the itemize environment's default item document-wide.
\usepackage{enumitem}

% Allows to define \notfoo or \nfoo (not recommended) in order for \not\foo to work as wished.
\usepackage{newtxmath}

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\DeclareMathSymbol{\Phi}{\mathord}{CMletters}{8}
\DeclareMathSymbol{\Omega}{\mathord}{CMletters}{10}
\DeclareMathSymbol{\lambda}{\mathord}{CMletters}{21}

% Makes the table of contents clickable and gives useful commands for links in general.
\usepackage[hypertexnames=false]{hyperref}
\hypersetup{colorlinks=false,linktoc=all}

% Gives the llbracket and rrbracket commands for integer intervals.
\usepackage{stmaryrd}

% Useful to insert nice-looking quotes.
\usepackage{epigraph}

% Allows to insert chapter-specific table of contents.
\usepackage{minitoc}
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% Useful when units are needed.
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locale=FR,
detect-all,
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list-final-separator={et},
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\usepackage{needspace}

% Useful for better-looking oneline fractions
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% Trick to make semicolons considered like relation operators (such as =) and therefore being equidistantly spaced from the two numbers around it.
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% Commands for size-adaptative parentheses, brackets, curly brackets, absolute value and magnitude.
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% Shortcut for forcing displaystyle in inline mode.
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% More explicitly named commands for the creation of tkz-tab tables.
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% Shortcut for the curve and the domain of the given function.
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\begin{document}
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\maketitle

\begin{abstract}
Ce document réunit l'ensemble de mes cours de Mathématiques de MPI, ainsi que les exercices les accompagnant. Le professeur était M. Walbron. J'ai adapté certaines formulations me paraissant floues ou ne me plaisant pas mais le contenu pur des cours est strictement équivalent.

Les éléments des tables des matières initiale et présentes au début de chaque chapitre sont cliquables (amenant directement à la partie cliquée). C'est également le cas des références à des éléments antérieurs de la forme, par exemple, \guillemets{Démonstration 5.22}.

Cette version contient, en plus des cours imprimés distribués durant l'année, toutes les démonstrations qui vont avec. Voir l'autre version pour n'avoir que les cours bruts.
\end{abstract}

\dominitoc\tableofcontents

\part{Cours}

\include{cours/chap1_evn/chap1_evn_notes.tex}

\include{cours/chap2_series_numeriques_vectorielles/chap2_series_numeriques_vectorielles_notes.tex}

\include{cours/chap3_familles_sommables/chap3_familles_sommables_notes.tex}

\include{cours/chap4_algebre_lineaire/chap4_algebre_lineaire_notes.tex}

\include{cours/chap5_reduction_endomorphismes/chap5_reduction_endomorphismes_notes}

\include{cours/chap6_integrales_generalisees/chap6_integrales_generalisees_notes}

\include{cours/chap7_integrales_parametre/chap7_integrales_parametre_notes}

\include{cours/chap8_espaces_prehilbertiens_reels/chap8_espaces_prehilbertiens_reels_notes}

\include{cours/chap9_endomorphismes_espace_euclidien/chap9_endomorphismes_espace_euclidien_notes}

\include{cours/chap10_fonctions_vectorielles/chap10_fonctions_vectorielles_notes}

\include{cours/chap11_suites_series_fonctions/chap11_suites_series_fonctions_notes}

\include{cours/chap12_series_entieres/chap12_series_entieres_notes}

\include{cours/chap13_probabilites/chap13_probabilites_notes}

\include{cours/chap14_variables_aleatoires_discretes/chap14_variables_aleatoires_discretes_notes}

\include{cours/chap15_equations_differentielles_lineaires/chap15_equations_differentielles_lineaires_notes}

\include{cours/chap16_calcul_differentiel/chap16_calcul_differentiel_notes}

\include{cours/chap17_structures_algebriques/chap17_structures_algebriques_notes}

\part{Exercices}

\setcounter{chapter}{0}

\include{exercices/chap1_evn/chap1_evn_notes.tex}

\include{exercices/chap2_series_vectorielles/chap2_series_vectorielles_notes.tex}

\include{exercices/chap3_familles_sommables/chap3_familles_sommables_notes.tex}

\include{exercices/chap4_algebre_lineaire/chap4_algebre_lineaire_notes.tex}

\include{exercices/chap5_reduction_endomorphismes/chap5_reduction_endomorphismes_notes}

\include{exercices/chap6_integrales_generalisees/chap6_integrales_generalisees_notes}

\include{exercices/chap7_integrales_parametre/chap7_integrales_parametre_notes}

\include{exercices/chap8_espaces_prehilbertiens_reels/chap8_espaces_prehilbertiens_reels_notes}

\include{exercices/chap9_endomorphismes_espace_euclidien/chap9_endomorphismes_espace_euclidien_notes}

\include{exercices/chap10_fonctions_vectorielles/chap10_fonctions_vectorielles_notes}

\include{exercices/chap11_suites_series_fonctions/chap11_suites_series_fonctions_notes}

\include{exercices/chap12_series_entieres/chap12_series_entieres_notes}

\include{exercices/chap13_probabilites/chap13_probabilites_notes}

\include{exercices/chap14_variables_aleatoires_discretes/chap14_variables_aleatoires_discretes_notes}

\include{exercices/chap15_equations_differentielles_lineaires/chap15_equations_differentielles_lineaires_notes}

\include{exercices/chap16_calcul_differentiel/chap16_calcul_differentiel_notes}

\include{exercices/chap17_structures_algebriques/chap17_structures_algebriques_notes}
\end{document}