\babel@toc {french}{}\relax 
\contentsline {chapter}{AVANT$-$PROPROS}{iii}{chapter*.1}%
\contentsline {chapter}{AUTRES OUVRAGES}{iv}{chapter*.2}%
\contentsline {chapter}{SITES INTERNET}{v}{chapter*.3}%
\contentsline {chapter}{\numberline {1}Nombres complexes}{1}{chapter.1}%
\contentsline {section}{\numberline {I}Introduction historique}{2}{section.1.1}%
\contentsline {section}{\numberline {II}Construction algébrique des nombres complexes}{3}{section.1.2}%
\contentsline {subsection}{\numberline {1}Base des nombres complexes}{3}{subsection.1.2.1}%
\contentsline {subsection}{\numberline {2}Opérations algébriques}{4}{subsection.1.2.2}%
\contentsline {subsection}{\numberline {3}Propriétés sur les conjugués}{5}{subsection.1.2.3}%
\contentsline {subsection}{\numberline {4}Formule du binôme de Newton}{6}{subsection.1.2.4}%
\contentsline {subsection}{\numberline {5}\'Equations}{10}{subsection.1.2.5}%
\contentsline {subsubsection}{\numberline {a}\'Equations du premier degré}{10}{subsubsection.1.2.5.1}%
\contentsline {subsubsection}{\numberline {b}\'Equation du second degré}{10}{subsubsection.1.2.5.2}%
\contentsline {section}{\numberline {III}Du point de vue géométrique}{11}{section.1.3}%
\contentsline {subsection}{\numberline {1}Image d'un nombre complexe}{11}{subsection.1.3.1}%
\contentsline {subsection}{\numberline {2}Module d'un nombre complexe}{12}{subsection.1.3.2}%
\contentsline {subsection}{\numberline {3}Arguments d'un nombre complexe}{15}{subsection.1.3.3}%
\contentsline {section}{\numberline {IV}Forme exponentielle d'un nombre complexe}{17}{section.1.4}%
\contentsline {subsection}{\numberline {1}Définition}{17}{subsection.1.4.1}%
\contentsline {subsection}{\numberline {2}Formules d'Euler}{17}{subsection.1.4.2}%
\contentsline {subsection}{\numberline {3}Formules d'addition et de duplication}{18}{subsection.1.4.3}%
\contentsline {subsection}{\numberline {4}Formules de Moivre}{19}{subsection.1.4.4}%
\contentsline {section}{\numberline {V}\'Equations polynomiales complexes}{20}{section.1.5}%
\contentsline {subsection}{\numberline {1}Factorisation de $\text {z}^\text {n}-\text {a}^\text {n}$}{20}{subsection.1.5.1}%
\contentsline {subsection}{\numberline {2}Factorisation polynomiale}{21}{subsection.1.5.2}%
\contentsline {section}{\numberline {VI}Utilisation des nombres complexes en géométrie}{22}{section.1.6}%
\contentsline {subsection}{\numberline {1}Distance et angles}{22}{subsection.1.6.1}%
\contentsline {subsection}{\numberline {2}Quotient de deux complexes}{23}{subsection.1.6.2}%
\contentsline {subsection}{\numberline {3}Racines n-ième de l'unité}{24}{subsection.1.6.3}%
\contentsline {section}{\numberline {VII}Python et les nombres complexes}{26}{section.1.7}%
\contentsline {section}{Enoncés}{27}{section*.5}%
\contentsline {section}{Corrigés des exercices}{41}{section*.12}%
\contentsline {chapter}{\numberline {2}Arithmétique}{75}{chapter.2}%
\contentsline {section}{\numberline {I}Divisibilité}{76}{section.2.1}%
\contentsline {section}{\numberline {II}Division euclidienne}{77}{section.2.2}%
\contentsline {section}{\numberline {III}Congruences}{77}{section.2.3}%
\contentsline {section}{\numberline {IV}PGCD de deux entiers}{78}{section.2.4}%
\contentsline {subsection}{\numberline {1}Notion de PGCD}{78}{subsection.2.4.1}%
\contentsline {subsection}{\numberline {2}Algorithme d'Euclide}{79}{subsection.2.4.2}%
\contentsline {section}{\numberline {V}Théorème de Bézout et théorème de Gauss}{80}{section.2.5}%
\contentsline {section}{\numberline {VI}Nombres premiers}{81}{section.2.6}%
\contentsline {section}{Enoncés}{83}{section*.66}%
\contentsline {section}{Corrigés des exercices}{99}{section*.67}%
\contentsline {chapter}{\numberline {3}Matrices}{140}{chapter.3}%
\contentsline {section}{\numberline {I}Introduction}{141}{section.3.1}%
\contentsline {subsection}{\numberline {1}Définition}{141}{subsection.3.1.1}%
\contentsline {subsection}{\numberline {2}Notation et vocabulaire}{141}{subsection.3.1.2}%
\contentsline {section}{\numberline {II}Opérations sur les matrices}{142}{section.3.2}%
\contentsline {subsection}{\numberline {1}Somme et différence}{142}{subsection.3.2.1}%
\contentsline {subsection}{\numberline {2}Produit d'une matrice par un réel}{142}{subsection.3.2.2}%
\contentsline {section}{\numberline {III}Produit de matrices}{143}{section.3.3}%
\contentsline {subsection}{\numberline {1}Définition}{143}{subsection.3.3.1}%
\contentsline {subsection}{\numberline {2}Matrices identité et matrices diagonales}{144}{subsection.3.3.2}%
\contentsline {subsection}{\numberline {3}Puissances d'une matrice carrée}{145}{subsection.3.3.3}%
\contentsline {subsection}{\numberline {4}Matrice inverse d'une matrice carrée}{145}{subsection.3.3.4}%
\contentsline {section}{\numberline {IV}Applications}{147}{section.3.4}%
\contentsline {subsection}{\numberline {1}Résolution de systèmes linéaires}{147}{subsection.3.4.1}%
\contentsline {subsection}{\numberline {2}Suites numériques imbriquées}{148}{subsection.3.4.2}%
\contentsline {section}{\numberline {V}Python et les matrices}{150}{section.3.5}%
\contentsline {subsection}{\numberline {1}Définir une matrice}{150}{subsection.3.5.1}%
\contentsline {subsection}{\numberline {2}Somme, différence et produit de deux matrices}{150}{subsection.3.5.2}%
\contentsline {subsection}{\numberline {3}Inverse d'une matrice}{151}{subsection.3.5.3}%
\contentsline {subsection}{\numberline {4}Puissance d'une matrice}{151}{subsection.3.5.4}%
\contentsline {section}{Enoncés}{152}{section*.152}%
\contentsline {section}{Corrigés des exercices}{159}{section*.154}%
\contentsline {chapter}{\numberline {4}Graphes}{173}{chapter.4}%
\contentsline {section}{\numberline {I}Introduction}{174}{section.4.1}%
\contentsline {subsection}{\numberline {1}Approche intuitive}{174}{subsection.4.1.1}%
\contentsline {subsection}{\numberline {2}Définitions}{174}{subsection.4.1.2}%
\contentsline {section}{\numberline {II}Vocabulaire}{175}{section.4.2}%
\contentsline {subsection}{\numberline {1}Sommets adjacents}{175}{subsection.4.2.1}%
\contentsline {subsection}{\numberline {2}Graphe complet}{175}{subsection.4.2.2}%
\contentsline {subsection}{\numberline {3}Ordre d'un graphe}{176}{subsection.4.2.3}%
\contentsline {subsection}{\numberline {4}Chaîne d'un graphe}{176}{subsection.4.2.4}%
\contentsline {subsection}{\numberline {5}Graphe connexe}{176}{subsection.4.2.5}%
\contentsline {section}{\numberline {III}Différents types de graphes}{176}{section.4.3}%
\contentsline {subsection}{\numberline {1}Graphes non orientés et orientés}{176}{subsection.4.3.1}%
\contentsline {subsection}{\numberline {2}Graphe pondéré}{177}{subsection.4.3.2}%
\contentsline {subsection}{\numberline {3}Graphe probabiliste}{178}{subsection.4.3.3}%
\contentsline {section}{\numberline {IV}Graphes et matrices}{178}{section.4.4}%
\contentsline {subsection}{\numberline {1}Matrice d'adjacence d'un graphe}{178}{subsection.4.4.1}%
\contentsline {subsection}{\numberline {2}Matrice d'un graphe pondéré ou probabiliste}{180}{subsection.4.4.2}%
\contentsline {section}{Enoncés}{182}{section*.175}%
\contentsline {section}{Corrigés des exercices}{195}{section*.176}%
\contentsfinish