Syntax and semantics in algebra

Jean-François Nicaud (1) , Denis Bouhineau (1) , Jean-Michel Gélis (2)

1 IRIN
2 IUFM Versailles - Institut universitaire de formation des maîtres - Académie de Versailles

This paper is the first chapter of a cognitive, didactic and computational theory of algebra that presents, in a formal way, well known elements of mathematics (numbers, functions and polynomials) as semantic objects, and expressions as syntactic constructions. The link between syntax and semantics is realised by morphisms. The paper highlights preferred semantics for algebra and defines formally algebraic problems.

Domaines: Environnements Informatiques pour l'Apprentissage Humain; Education

Jean-François Nicaud, Denis Bouhineau, Jean-Michel Gélis. Syntax and semantics in algebra. Proceedings of the 12th ICMI Study Conference. The University of Melbourne, 2001, Australia. 12 p. ⟨hal-00962023⟩