Special Mathematics Lecture (Introduction to probability)

Goals of the Course

【Standardized across all programs】 In a global and interconnected society, mathematics play a central role. They are at the root of all communications tools, and serve as a universal language for natural and social sciences. All current technological developments are based on them. Mathematics can also be learned, enjoyed, and shared by everybody. Studying mathematics is also learning humility, tolerance, and diversity.

The aim of these Special Mathematics Lectures is to provide a solid knowledge on various mathematical topics. Concomitantly, students will develop a rigorous argumentation and a critical thinking. Each semester, a new subject is proposed, and these lectures are accessible to all students of Nagoya University, independently of their major and of their academic age. These special lectures also offer a unique opportunity to study in an international, transdisciplinary, and friendly environment.

Objectives 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. Thus, we shall study the basic abstract theory of probability, and discuss some applications according to the interest and to the motivation of the students. The presentation will be accessible to all students, independently of their major.

Course Contents or Plan

1. Events and probabilities
2. Discrete valued random variables
3. Random variables: general case
4. Limit theorems
5. Random processes
6. Markov chains

Course Prerequisites and Related Courses

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 need an approval from 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. Achievement of the objectives stated in the [Objectives of the Course] section will be considered the criterion for passing the course. Students need to notify the course withdrawal to the instructor when they have no intention of finishing the course 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.

Notice for students

It is expected that the students show a certain maturity in studying independently and in choosing some exercises and problems to solve. Study sessions might be organized on a weekly basis.

Textbook

Lecture Notes

Lecture videos

The lecture videos are available on YouTube:

Special Mathematics Lecture (Introduction to probability)

Additional information

Reference Website

This lecture is provided under Creative Commons Attribution-Non Commercial-ShareAlike 4.0 International.

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