Formal and Scientific Computation

The objective of this module is to gain an understanding of how to use symbolic and numerical computation both in mathematical experimentation and to aid in solving certain problems in computer science.

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

We will introduce the various features of this type of software through examples of solving real-world problems. One of our goals will be to help students learn how to make the best use of the software and its basic building blocks to independently solve complex problems.

Among the features presented, particular emphasis will be placed on calculations within standard mathematical structures (N, Z, Q, R, C) as well as with symbolic expressions (e.g., polynomials, trigonometric expressions, sequences, series). We will also cover the use of equation solvers and graphical visualization as an experimental approach. An introduction to the underlying concepts of computational software (representations and algorithms) will also be provided to help students better understand its limitations.