Formal and scientific calculation

The aim of this module is to understand the use of formal and numerical calculus both in mathematical experimentation and in helping to solve certain problems in computer science.

In particular, students should be able to understand how calculation software works (interpreter, calculation libraries, interactive use), as well as the basic syntax of the language used.

We will introduce the different functionalities of such software through examples of concrete problem solving. One of the objectives will be to enable students to make the best possible use of the software and its basic building blocks to solve complex problems independently.

Among the functionalities presented, a certain emphasis will be placed on calculation in the usual mathematical structures (N,Z,Q,R,C) but also with symbolic expressions (e.g. polynomials, trigonometric expressions, sequences, series). We will also cover the use of equation solving and graphical visualization as an experimental approach. We'll also look at the underlying issues of calculation software (representations and algorithms), to better understand their limitations.