The course aims to provide an introduction to mathematics and then to its fundamental constructions: the numbers. The course will address the construction of natural numbers by the concept of set; sets are then carefully introduced in the first part of the course. It also develops the concept of algebraic structure by which we characterize various constructions of numerical sets such as, for example, that of the integers and that of the rational numbers. They also treat some arithmetic properties of integers then placing emphasis on the relationship with algebraic structures related to them.
Expected learning outcomes
Acquisition of the basic language of algebra. Knowledge of the main algebraic structures abstract algebra through the study of integers, polynomials in one variable and their quotients. Among the specific results that are shown over there are considerable arithmetic properties of prime numbers that are derived from algebraic properties of Gaussian integers. Finally, the essential features of the theory of modules are acquired.
Lesson period: First semester
(In case of multiple editions, please check the period, as it may vary)