Special Math Lecture (Introduction to probability)

A dinosaur
LecturerSerge RICHARD, Professor
DepartmentG30, 2021 Spring
Recommended for:Hu(J)・La(S)・Ec(S)・Sc(P・C・B)・En(P・C・Au)・Ag(B) (2.0・1.5 hours / session One session / week 15 weeks / semester)

Goals of the Course

Probability is playing an essential role in many research fields, and in particular for describing complex systems. Our goal is to provide the necessary background information for understanding the use and the power of probability. The presentation will be accessible to all students, independently of their major.

Objectives of the Course

Study the basic abstract theory of probability, and discuss some applications according to the interest and to the motivation of the students.

Course Content

  1. Events and probabilities
  2. Discrete valued random variables
  3. Multivariate discrete distributions
  4. Probability generating function
  5. Distribution function and density function, Examples of density functions
  6. Multivariate distributions and independence
  7. Moments and moment generating functions
  8. The main limit theorems
  9. Branching processes
  10. Random walk (1D)
  11. Random process in continuous time

Lecture Notes

The cumulative notes

Basic knowledge on calculus and linear algebra, as provided in Calculus I & II and in Linear algebra I & II. Motivated 1st year students can also attend without these prerequisites but after a discussion with the instructor.

Course Evaluation Method and Criteria

The final grade will be based on the active participation during the lectures and on some written reports. Students will be encouraged to work on applications related to their major during the semester.

Study Load (Self-directed Learning Outside Course Hours)

Students are expected to read their notes, and to be familiar with the content of the previous lectures before each new lecture.

Last updated

January 20, 2022