Mathématique: cours-Résumés-TD-Exercices et examens corrigés


Le début des études de mathématiques est :

– très difficile, du fait de l’abstraction (définition, proposition, démonstration) et de l’utilisation d’un langage particulier, le langage mathématique,

– facile, car une grande partie des sujets a déjà été traitée au lycée.

Les mathématiques à l’université sont caractérisées par la certitude absolue de leurs résultats. Il ne suffit plus – comme souvent au lycée – d’expliquer un phénomène par beaucoup d’exemples ou d’apprendre une technique de calcul ; à l’université il s’agit de le démontrer, c’est-à-dire d’écrire une démonstration (aussi appelée une preuve) qui, par une chaîne d’arguments faciles à suivre et compréhensibles pour tous, ne laisse aucun doute sur la vérité d’une assertion.

Pour pouvoir dire qu’une assertion est vraie avec une certitude absolue, il faut que tous les mots qui sont utilisés aient une signification très précise qui est la même pour tous.

Le langage mathématique diffère du langage du quotidien par :

– sa précision, tout terme à une définition précise ;

– son formalisme, souvent, on utilise des symboles et des formules.

Ci-dessous la liste des cours:

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