RANDOM: AN INTRODUCTION TO PROBABILITY (PART 2)
4 to 6 hours / week
Students’ level in mathematics should match that of a Grande École preparatory class or year two of a bachelor’s degree, with a principal focus on analysis (differential and integral calculation, sequences and series etc.). Course on demand.
The second part of the Introduction to Probability course offers the same content as the class taught by Sylvie Méléard in the first year of École Polytechnique’s core curriculum. You can access the first part of the course here: Random: An Introduction to Probability (Part 1).
ABOUT THE COURSE
Probabilistic modeling is present in a large number of fields such as physics, computer science, telecommunications networks, finance, insurance, biology and medicine.
The course gives a thorough and gradual introduction to the notion of random variables, working towards understanding the law of large numbers and central limit theorem. The necessary mathematical concepts are introduced throughout the course and a number of marked exercises are proposed.
This course also provides an overview of random variable simulation methods, such as the Monte Carlo method. Interactive digital experiments are also offered, to give you a visual representation of the taught concepts.
Random vectors (Weeks 1-2)
Convergence and the law of large numbers (Weeks 3-4)
Characteristic functions, convergence in law and central limit theorem (Weeks 5-6)
FORMAT OF COURSE
The course is divided into weekly classes, comprising videos of classroom sessions, videos of exercise correction sessions and multiple-choice quizzes. A number of weeks also include classes that present the basics of random variable simulation and interactive digital experiments that are usable immediately.
Multiple-choice quizzes help you verify that you have understood the class content and allow you to obtain a certificate of attendance at the end of the course.
This class is based on the book “Random: Introduction to Probability Theory and Calculus” (Aléatoire, introduction à la théorie et au calcul des probabilités) by Sylvie Méléard, published by Les Éditions de l’École Polytechnique. It has kindly been provided free of charge for students of the course, in PDF format.
What kind of certificate will be awarded for this course?
A certificate of attendance. To receive this, students must achieve the average in the weekly multiple-choice quizzes.