RANDOM: AN INTRODUCTION TO PROBABILITY (PART 1)

PRESENTATION:
The first 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 second part of the course here: Random: An Introduction to Probability (Part 2).

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.

COURSE SYLLABUS

Probability spaces (Weeks 1-3)
Random variables on a finite or countable set (Weeks 4-5)
Real-valued random variables (Weeks 6-8)
REQUIREMENTS

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.).

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.

RECOMMENDED READING

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.