2021 Faculty Courses School of Environment and Society Undergraduate major in Transdisciplinary Science and Engineering
Probability theory (TSE)
- Academic unit or major
- Undergraduate major in Transdisciplinary Science and Engineering
- Instructor(s)
- Satoshi Chiba
- Class Format
- Lecture
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 1-2 Mon (S513) / 1-2 Thu (S513)
- Class
- -
- Course Code
- TSE.M301
- Number of credits
- 200
- Course offered
- 2021
- Offered quarter
- 2Q
- Syllabus updated
- Jul 10, 2025
- Language
- English
Syllabus
Course overview and goals
This lecture aims at making students to understand what is probability, why it is important, some important theorems on probability distributions and stochastic processes including Brownian motion and financial market.
Course description and aims
to understand why various quantities are observed involving probability distributions, and to understand their stochastic nature to data analysis
Student learning outcomes
実務経験と講義内容との関連 (又は実践的教育内容)
Stochastic process in quantum mechanics and experimental nuclear physics
Keywords
Probability, probability distributions, stochastic variables, Bayes' theorem, moment-generating functions, normal distributions, covariance, least-squares method, stochastic process
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
Lecture based on power point, small examinations
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Guidance and Introduction |
Shown at the end of the lecture |
| Class 2 | Intuitive introduction of sample space, events and probability |
Shown at the end of the lecture |
| Class 3 | σ-additive class, Probability distribution functions, expectation, variance, and higher moments |
Shown at the end of the lecture |
| Class 4 | Normal distribution, covariance matrix |
Shown at the end of the lecture |
| Class 5 | Conditional probability, Bayes theorem, independence of events and random variables, and conditional expectation value |
Shown at the end of the lecture |
| Class 6 | Moment generating function, characteristic function, cumulant generating function and equivalent probability measures |
Shown at the end of the lecture |
| Class 7 | A few probability distributions and their relations |
Shown at the end of the lecture |
| Class 8 | Central limit theorem and important inequalities |
Shown at the end of the lecture |
| Class 9 | Various convergences in probability theory and law of large numbers |
Shown at the end of the lecture |
| Class 10 | Stochastic process : random walk and concept of martingale |
Shown at the end of the lecture |
| Class 11 | Brownian motion |
Shown at the end of the lecture |
| Class 12 | Stieltjes integral and Ito ̂ integral |
Shown at the end of the lecture |
| Class 13 | Ito ̂ process |
Shown at the end of the lecture |
| Class 14 | Stochastic theory of financial market |
Shown at the end of the lecture |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
None
Reference books, course materials, etc.
A.H-S. Ang and W.H. Tang, Probability Concepts in Engineering, Emphasis on Applications in Civil & Environmental Engineering, Maruzen & Wiley
Evaluation methods and criteria
Based on small test shown at the end of each lecture and submitted as a report
Related courses
- ICT.M202 ： Probability and Statistics (ICT)
Prerequisites
Not specified
Other
Not specified