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Paysages Mathématiques Éléments de mathématiques pour le XXIe siècle, volume 1: Fondements des mathématiques 1 (logique des propositions et des prédicats, systèmes déductifs ... de Peano, structures algébriques de base)

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Description

Ce livre est le premier volume d’une série qui doit, à terme, couvrir l’ensemble des notions du premier cycle universitaire en mathématiques, tout en débordant largement sur le deuxième cycle. De manière plus générale, cette série d’ouvrages pourra être utile à toute personne s’intéressant aux mathématiques actuelles. Elle devrait, en théorie, être accessible même sans connaissance préalable. En effet, les mathématiques sont prises à leur début et les différents concepts progressivement construits, chaque définition, théorème et démonstration ne faisant appel qu’à ce qui a été défini précédemment. Chaque ouvrage se veut à la fois didactique, avec des preuves très détaillées, des explications informelles, et de nombreux exemples et contre-exemples ; complet, voire encyclopédique, avec un exposé de nombreuses notions, des théorèmes tous démontrés, et de nombreux détails historiques ; synthétique, avec en particulier la volonté de multiplier les points de vue. Les quatre premiers volumes traitent des fondements modernes des mathématiques. Ce premier volume est essentiellement consacré à la notion de logique mathématique. Sont en particulier étudiés les sujets suivants : la logique des propositions ; le calcul booléen (algèbre de Boole) ; la logique des prédicats ; des systèmes formels utilisés dans la théorie de la démonstration (sont notamment détaillés un système déductif à la Hilbert et la déduction naturelle) ; quelques exemples d’autres logiques formelles (logique intuitionniste ...). On trouve aussi divers sujets un peu moins liés aux mathématiques formelles : des éléments de logique traditionnelle (syllogismes et diagrammes logiques) ; des exemples de paralogismes classiques. Enfin, la présentation de la logique des prédicats est aussi l’occasion d’aborder d’autres notions : une première approche de quelques structures algébriques de base (groupes, anneaux, …) ; la théorie axiomatique de l’arithmétique de Peano, qui formalise les propriétés des nombres entiers et des opérations associées (addition, multiplication).

Product Specifications

Format
paperback
Domain
Amazon UK
Release Date
29 June 2019
Listed Since
19 September 2019

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