In this paper, we present a didactic production intended for first-year graduate students in mathematics, who have some basic knowledge in linear algebra. The aim of this production is to introduce the concepts of module and draw a parallel between vector spaces and modules. For this purpose, we first remind the readers of algebraic structures as groups, rings and fields. Next, we introduce a new structure, the module, along with some fundamentals results. Finally, we bring forward the notion of basis within the framework of modules. Existence and characterization theorems enable us to emphasize the difference between vector spaces and modules. In order to make the students' understanding easier, we suggest examples and solved exercises. Through some didactic comments, we also formulate personal thoughts and choices that led to the way the subject is presented in this work.
Des espaces vectoriels aux modules: une perspective didactique
HENROTTE, M. (Author). 2009
Student thesis: Master types › Master in Mathematics