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Mathematics and programming training

Year : M1/M2
Semester : S1
ECTS : 0
Coordinator : Morgane Thomas-Chollier, Biology Department, ENS (MC ENS)
Hours : 30h

During the first week of the new term, this training aims at providing the students the opportunity to

  • get familiar with our computing and numeric environement (mandatory)
  • update their knowledge in maths and informatics (programming in Python and R)

The first day includes an introduction to the computer working environment of the ENS, necessary for all newly-arrived students in M1 or M2.

For newly-arrived students, this training (both maths and informatics) is a pre-requisite for the Data analysis course.

This week will start on Monday 30th August 2021. The teaching will be remotely in 2021, with the possibility to access the teaching rooms at ENS and meet fellow students.

PDF - 90 ko
Planning 2021

Themes :

1. WORKING ENVIRONMENT (mandatory for all newly-arrived students)
The computer room is equipped with machines running under the Linux environment (Ubuntu). The students will learn how to login on the machines, become familiar with the graphical environment and also use the command line.

The students will also learn how to use the remote access to machines (VPN, X2Go), usage of the cloud to share documents, email access, informatics security, and our Moodle platform.

We chose to make the students work with python, a simple and powerful programming language. For the start of new term, the aim would be to have understood the various types of data (especially lists and dictionaries), to be able to write a function (notion of local and global variables), be able to use modules, and understand how to read and to write in a file (module sys and os). The last session is devoted to the langage R.
This introductory course aims to provide students with basic mathematical tools necessary for most subsequent courses. The first half of the course will be an introduction to the study of dynamical systems, and will start with a review of linear algebra ; we will then study the resolution of systems of linear differential equations, before generalising some results to non-linear equations (e.g., study of the fixed points in the Lotka–Volterra equations). The second half of the couse will provide students with basic knowledge in probability and statistics—which is crucial to any biologist nowadays—and will cover the main theorems that give rise to common hypothesis tests broadly used the scientific community.
The course will be mostly self-contained ; however, few pre-requisites include basic concepts in linear algebra (matrices, eigenvectors, eigenvalues, diagonalisation), analysis (derivatives, differential equations), and probability (basic combinatorics, probability density function, central limit theorem).

Lecture1 is considered as pre-requisite for the maths training. You are expected to study the document ("Lecture 1") and prepare the associated exercices before the training week.

PDF - 366.2 ko
Lecture 1 (pre-requisite)
PDF - 157.1 ko

Organization :

The teaching unit is organised over the first week of the semester. The organisation is online with the possibility to use the ENS rooms. It is possible to follow only one training (maths or informatics).

Further reading

Linux command-line :
- Interactive MOOC (English) :
- Other courses are listed on this page :

- Python documentation :
- A good Python course, by a professor at Paris 7 :
- For those wishing to go further : a free book in French :
- Another book, in English :

- Various documentation in many languages on CRAN :
- A resource in French

Teaching team :

Pierre Vincens (MCU, ENS, Paris)
Antonin AFFHOLDER (teaching assistant, ENS, Paris)
Adil MIDOUN (teaching assistant, ENS, Paris)
Othman LAHRACH (teaching assistant, ENS, Paris)
Joseph JOSEPHIDES (teaching assistant, ENS, Paris)
Antoine SICARD (teaching assistant, ENS, Paris)
Corentin CLERC (teaching assistant, ENS, Paris)