Formal and scientific calculation

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

In particular, students must 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 various features of this software through examples of solving concrete problems. One of the objectives will be to teach students how to make the best use of the software and its basic building blocks to solve complex problems independently.

Among the features presented, particular emphasis will be placed on calculations in standard mathematical structures (N, Z, Q, R, C) as well as 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 offered in order to better understand their limitations.