==== Elective course unit ====
** General information **
  * Course name in French: Electifs
  * ECTS credits: 4 (see below what must be done to get these ECTS)
  * ** <color red> Period: Fall-Winter Semester (from early September until end of January/early February) </color>**
  * Level : Undergraduate (Bachelor 4th Year) or Graduate (Master 1st Year)
  * Teaching hours: 90 hours divided into 3 courses (30 hours each)
  * Language of instruction: usually French

Warning! The elective course unit consists of 3 courses. Students must choose ** one and ONLY ONE ** course in each list.

Three courses in Mathematics can be attended as they are offered in two separate lists:
  - Numerical mathematics and simulation (List 1),
  - Introduction to stochastic processes (List 2),
  - Advanced analysis (List 3).

Due to timetable constraints, you cannot attend more than one course in a list.

==== Numerical mathematics and simulation (available in course list 1) ====
** General information **
  * Course name in French: Mathématiques numériques et simulation
  * ECTS credits: see explanation above
  * ** <color red> Period: Fall-Winter Semester (from early September until end of January/early February) </color>**
  * Level : Undergraduate (Bachelor 4th Year) or Graduate (Master 1st Year)
  * Teaching hours: 30 hours (Lectures = tba hours, Tutorials = tba hours, Self-study = tba hours) 
  * Language of instruction: French
  * Coordinator: Marie Billaud-Friess
  * Instructor(s): Marie Billaud-Friess, Mitra Fouladirad, Guillaume Chiavassa, Christophe Pouet
  * Last update 14/03/2025 by C. Pouet

** Brief description **

This course is an advanced course in Mathematics dealing with simulation, stochastic algorithms and Itô integration. 

** Learning outcomes **

  * tba

** Prerequisites **
Tba

** Assessment **
Tba

** Course content **
  - Simulation of random variables
    * tba
  - Monte-Carlo methods
    * tba
  - Stochastic algorithms
     * tba
  - Introduction to Itô integration
** Bibliography **


==== Introduction to stochastic processes (available in course list 2) ====
** General information **
  * Course name in French: Introduction aux processus stochastiques
  * ECTS credits: see explanation above
  * ** <color red> Period: Fall-Winter Semester (from early September until end of January/early February) </color>**
  * Level : Undergraduate (Bachelor 4th Year) or Graduate (Master 1st Year)
  * Teaching hours: 30 hours (Lectures = tba hours, Tutorials = tba hours, Self-study = tba hours) 
  * Language of instruction: French
  * Coordinator: Mitra Fouladirad
  * Instructor(s): Mitra Fouladirad, Thibaut Le Gouic
  * Last update 14/03/2025 by C. Pouet

** Brief description **

This course is an advanced course in Mathematics dealing with random processes. 

** Learning outcomes **

  * tba

** Prerequisites **
Tba

** Assessment **
Tba

** Course content **
  - Conditional expectation
    * tba
  - Markov chains
    * tba
  - Poisson process
     * tba
** Bibliography **

==== Advanced analysis (available in course list 1) ====
** General information **
  * Course name in French: Analyse mathématique
  * ECTS credits: see explanation above
  * ** <color red> Period: Fall-Winter Semester (from early September until end of January/early February) </color> **
  * Level : Undergraduate (Bachelor 4th Year) or Graduate (Master 1st Year)
  * Teaching hours: 30 hours (Lectures = tba hours, Tutorials = tba hours, Self-study = tba hours) 
  * Language of instruction: French
  * Coordinator: Magali Tournus
  * Instructor(s): Magali Tournus
  * Last update 01/04/2022 by C. Pouet

** Brief description **

This course is an advanced course in Mathematics dealing with functional analysis. 

** Learning outcomes **

  * tba

** Prerequisites **
Tba

** Assessment **
Tba

** Course content **
  - Tba
    * tba
** Bibliography **