Mathematics I

This course aims to provide the tools necessary to handle the basics of mathematical formalism and method.

At the end of the course, students will be able to handle elementary set theory and elementary functions. They will know the notions of group, ring and field, and they will be able to apply them to various fundamental examples (natural, integer, rational, real and complex numbers, permutation group, remainder classes). They will be able to solve systems of linear congruences in an algorithmic and non-algorithmical way. They will know the fundamental properties of vector spaces and their bases, linear applications and their matrix representation, which will provide theoretical and algorithmic methods for solving systems of linear equations.