Advanced CPES Sc subject S1

Teaching takes the form of projects, undertaken by pairs of students, supplemented on an ongoing basis by digital sessions allowing students to practice physics and chemistry concepts on a computer.

Depending on requirements, a few more traditional classes are planned to supplement the students' training.

Indicative program:

1. Preliminaries: visualization of scalar and vector fields: gradient, divergence, rotational, Laplacian, contour lines, surface and volume integrals, numerical solutions to point mechanics problems

2. Supervised projects offered to students: these involve the acquisition, processing, and interpretation of data. The general theme we have chosen is to train students to understand the ideas of "statistical field theory," i.e., the concept of probability applied to functions. This theme is omnipresent in modern science: image processing and analysis, AI, statistical physics, dynamic systems and stochastic processes, sequencing, epidemiology, economics, observational cosmology, etc. and the combination of numerical methods, mathematical ideas, and modeling seems to emerge naturally (examples of projects, purely indicative list: sand grain statistics, Poisson and Gaussian distributions, link with Beer-Lambert's law via the concept of effective cross section; observational data in cosmology: matter/radiation distribution on the scale of the universe; statistics and epidemiological dynamics; microscopy and analysis of Brownian motion; etc.).

3. Chemistry supplements: Slater's effective theory for atoms (effective screen potential), molecular orbitals, fragment approach

Continuous assessment through oral defenses and presentations of project results.

Written exams for course supplements.