Formal and scientific calculation

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

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

We will introduce the different functionalities of such a software through examples of concrete problem solving. One of the objectives will be to bring the students to know how to best use the software and its basic bricks to solve complex problems in an autonomous way.

Among the features presented, some emphasis will be put 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 discuss the use of equation solving and graphical visualization as an experimental approach. An awareness of the underlying issues of calculation software (representations and algorithms) will also be proposed in order to better understand their limitations.