Math modelling major
Master 1 courses
1st Semester
Shared courses
Organisation: Lectures (12h)
Lecturers: Bianca Habermann, Laurent Tichit
Evaluation: project and continuous monitoring
Scientific seminars constitute a good way to broaden your scientific horizon. In this regard, MSc students will frequently attend CENTURI seminars. At the end of the semester, students will be asked to write a summary of two seminars they have attended.
The students will learn to work in an interdisciplinary group, to deepen a subject and to communicate on it.
Organisation: Lectures (10h), TD (8h), TP (12h)
Lecturers: Claudio Rivera Baeza
Evaluation: final exam, projects and oral presentation
This lecture is composed of studies on different articles, tutorial sessions to assimilate the concepts and practical work to implement the concepts on concrete cases.
The aim of this course is to present the analysis of interaction networks in biology. The courses/TD focus on the construction and interpretation of static networks "at large
scale", e.g. protein-protein interaction networks. And on dynamic networks, modelled by different mathematical formalisms, which make it possible to simulate, for example, genetic regulation.
Organisation: Lectures (6h), TD (6h), TD (6h)
Evaluation: project and continuous monitoring
Students are asked to pick 2 of the 3 following optional courses:
- Developmental Biology
- Immunology
- Neurobiology
Organisation: Project during the semester
Evaluation: project
Internship in a research laboratory practicing interdisciplinary studies.
Organisation: Lectures (6h), TD (6h), TP (6h)
Lecturers: Pierre Pudlo
Evaluation: continuous exam and projects
This course focus on inferential statistics.
The lectures will propose a summary of the basic concepts, which will be applied in exercises (TD), practical work on computers (TP) and personal assignments (R programming project). Introduction to inferential statistics.
Mathematics courses
Organisation: Lectures (6h), TD (6h), TP (6h)
Lecturers: Florence Hubert
Evaluation: final exam and projects
The course focus on Optimization with or without constraint and examples of regression problems .
The lectures will propose a summary of the basic concepts, which will be applied in exercises (TD), practical work on computers (TP) and personal assignments (python programming project).
Scientific Calculus
Organisation: Lectures (8h), TP (15h)
Lecturers: Julien Olivier
Evaluation: final exam and projects
Part of this course will be specifically dedicated to learning more advanced Python tools: advanced use of Numpy, hollow matrix manipulation and object-oriented design. From a mathematical point of view, this course will focus on the study of equations in 1 dimensional space: returns/complements on the transport equation (Von Neumann stability, decentration, CFL condition), stationary or unstationary advection-diffusion equation. This course will be an opportunity to discover or to deepen certain properties of numerical schemes (stability, convergence, etc.) which will not have been treated in the other courses. The schemas will be essentially finite volume type schemas. A large part of the time will be devoted to the elaboration of the scientific computation approach: academic test cases for validation, error curves, before tests in more general cases.
Advanced Scientific Calculus
Organisation: Lectures (8h), TP (15h)
Lecturers: Julien Olivier
Evaluation: final exam and projects
This course focuses on finite volume numerical schemes for 2-dimensional space equations: transport and stationary or unstationary advection-diffusion. A large part of the course is devoted to the manipulation of finite volume meshes and to the assembly of the matrices of the schemes by the edge structure. Some properties of these numerical schemes will be studied (L2 or L-infinite stability, convergence, preservation of positivity, ...). In this course we will also develop the scientific calculation approach (test cases, error curves, ...).
Probabilistic numerical methods
Organisation: Lectures (12h), TP (12h)
Lecturers: Erwan Hillion
Evaluation: continuous exam
This course will present different algorithms based on probabilistic tools, and allowing to solve various problems: simulation of random variables, approximate calculation of integrals, simulation of invariant measures, stochastic optimization,... This teaching will be composed of four chapters: Simulation of random variables, Monte-Carlo Method, MCMC, Metropolis-Hastings algorithm, Simulated annealing.
Parametric estimation methods
Organisation: Lectures (12h), TP (9h)
Lecturers: Oleg Lepski
Evaluation: final exam and continuous exam
This teaching will focus on the in-depth study of Bayesian and maximum likelihood methods, exponential inequalities (finite sample) and the optimality of these methods according to the minimax approach via local asymptotic normality. Hands-on computer work will be used to numerically illustrate these methods and their limitations. Estimators will be computed in more complicated models requiring the use of numerical methods (EM algorithm, MCMC).