This course is intended to provide students with a broad range of mathematical modelling tools, through theoretical frameworks that they will be able to understand and explain. They will also be able to apply the tools seen in the course to solve original problems in applied mathematics.
Given its structure, the course will not develop in detail any particular tool or theory. Rather, its objective is to highlight a set of problem-solving techniques and tools that the student can then develop further according to his/her needs and interests in the course of his/her career (student and professional).
The course will consist of several modules dealing with modelling in particular contexts and will address the use of various tools in applied mathematics. Each module will be introduced by a situation via a concrete mathematical or engineering problem. In a participatory approach, the students, faced with the problem, will familiarise themselves with the available resolution techniques. In each module, the emphasis will be on the one hand on the mathematical modelling of the problem posed, but on the other hand on the learning of targeted theoretical concepts and notions and on the use of general tools. Examples of concepts covered (new or revised): information theory, game theory, finite element methods, Baysian inference, number theory,...
Part of the mark will be based on the student's participation in the course sessions, and in particular on the way in which he/she was able to contribute to the collective effort to solve the problems posed. Another part of the mark will be obtained in an interview (in the form of an oral examination) in which the student must be able to explain the mathematical concepts and reasoning seen in the course and to apply them in a reflective manner to new problems. All course notes and other materials will be available for consultation in preparation for this interview.