Introduction to the Mathematical Modelling Courses

Scientific Areas and Career Guidance

Mathematical modelling allows us to solve issues arising in different areas (physics, biology, economics…) through the analysis and the numerical simulation of suggested mathematical models.

This course enables high-level students of applied mathematics to pursue a career in higher education and research. Our graduates also go on to join programmes in the high-tech industry, or within the R&D and decision-making divisions of large companies. The course also trains mathematicians with an engineering profile in all aspects of computation and scientific computing: skills which are highly sought-after by industrial research departments or service companies specialising in scientific computation.

Learning Objectives of the Masters Degree

Students can expect to acquire the following knowledge and skills at the end of the Masters course:

  1. Theory of partial derivative equations, numerical discretisation, error analysis;
  2. Continuous and discrete optimisation, calculus of variations, game theory;
  3. Finite or infinite dimensional control theory, optimal control theory, inverse problems;
  4. Analysis, simulation and modelling tools that are used in life sciences;
  5. Scientific computing, scientific computation, parallel computation, computer-aided design.

Students will also acquire knowledge in various applied fields: computer science, biology, physics, mechanics, economics...

Although it is typical for a Masters degree to lead on to a PhD, this is not compulsory and a Masters offers many other opportunities.

For students who wish to pursue a PhD, the academic staff can provide individual support to help applicants write their thesis proposal.

Teaching Calendar

The year is divided into four periods of time as indicated below:

Semester 1 Semester 2
Period September/October Mid-October/December January/March March/September
Title Basic Courses Fundamental Courses Specialised Courses Internship or Dissertation
Duration 6 weeks 8 weeks 10 weeks 3 to 6 months
ECTS 12 18 12 18

During the first period, students must take at least four courses among the five that are offered. Every course consists of a three-hour lecture, and either a three-hour tutorial per week for the two numerical courses or a two-hour tutorial for the three more theoretical courses. The methods of assessment consist of several exams that account for 12 ECTS.

Fundamental and Specialised Courses are worth 6 ECTS each.

Therefore, it is compulsory to attend at least 3 Fundamental Courses and 2 Specialised Courses..

Results can only compensate each other within a single semester.

Any student who has obtained less than 10 can sit the second session of the examination.


To assist students and guide them towards the subjects and careers of their choice, we have organised the study programme into broad themes, called Majors. They are concerned as much with areas of application as with the methods used. The list of Majors is:

Students will choose a Major at the end of the Basic Courses.

Each Major offers a coherent syllabus of Fundamental and Specialised Courses, paving the way for many career opportunities. The choice of modules within each Major is up to the students. Any change of courses across Majors must be determined in conjunction with the coordinator of the chosen Major, whose role is to check the consistency between a student's choice of courses and his/her intended career path.

External courses (from other Masters degrees) can also be validated once the coordinator of the Major has approved them. The objective is to make sure the student succeeds in his/her project.

Internship or introductory research dissertation

The introductory research work corresponds to the fourth period that begins in early April. This can potentially begin earlier, at the same time as the Specialised Courses, once the internship supervisor has agreed.

Passing the Basic and Fundamental Courses is compulsory before starting the internship. Depending on the student’s intended career path, the internship can be in one of the following areas:

It can take place in a public research laboratory or in a company. Every year, industrial research centres offer many research internships. You can consult the local list of internship offers.

Note that we are posting them here as we are receiving them: they are included here only to provide students with general guidance. We remind students that it is up to them to find their own internship. Students have to start looking for their placement early in the year, from October onwards. This job search is part of the students’ career plan. A meeting describing internships and theses will take place during the month of december.

The internship tutor is responsible for assessing a student’s work. He/She can choose to set up an oral exam, or to assess the the (compulsary) written report of the completed project.

Institutes which jointly manage this course

Our training course is jointly provided by Sorbonne Université (main school), the École Polytechnique and the École Nationale des Ponts et Chaussées.