Mathematics training
Code du cours :
Intitulé : Mathematics training
Du mercredi 4/9/24 au mercredi 11/9/24, 9h-12h, salles 316 et 324.
Responsable : Amaury Lambert, Biology Department, ENS
Enseignants : Nina Vittorelli et Pierre Veron
Type d’enseignement : TD
ECTS : 0
Mots clés : maths
Prérequis pour le cours : niveau L2 biologie
Objectif et description du cours :
The aim of the course is to consolidate the mathematical foundations needed to follow the L3 in the biology department or the M1 in the IMaLiS master’s program.
Students are divided into two groups according to their needs and levels (all L3 students are affected in group 1 and M1 students will be affected according to their needs).
A compulsory questionnaire will be sent to students a week before the start of the course to assess their needs, and the sessions will be adapted accordingly.
To register, please email Amaury Lambert.
At the end of this course, students in group 1 should be able to take the L3 course “Maths I : what biologists should know” and students in group 2 should have the prerequisites for the M1 course “Maths II : what biologists might like to know”.
Contenus :
Groupe 1 (cours en français, tous les élèves de L3 vont dans le groupe 1) :
• Équations différentielles selon les besoins.
• Algèbre linéaire (calcul matriciel, applications linéaires, résolutions de systèmes linéaires, dimension et théorème du rang, diagonalisation de matrices et applications).
• Fondamentaux des probabilités (espérance, variance, lois classiques de probabilités, probabilités conditionnelles, formule de Bayes).
Group 2 (course in English) :
• Dynamical systems (linearization, equilibrium states, bifurcation diagram, cycles).
• Probability (discrete time Markov chains and applications, probability generating function).
• If needed : statistics (estimator, confidence interval, statistical tests, multiple testing).
• If needed : linear algebra (determinant, characteristic polynomial).
Course material will be available in English.
Évaluation : There is no assessment at the end of the course.
