2025 (Current Year) Faculty Courses School of Engineering Undergraduate major in Systems and Control Engineering
Fundamentals of Data Science
- Academic unit or major
- Undergraduate major in Systems and Control Engineering
- Instructor(s)
- Masayuki Tanaka
- Class Format
- Lecture
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - Class
- -
- Course Code
- SCE.I205
- Number of credits
- 200
- Course offered
- 2025
- Offered quarter
- 4Q
- Syllabus updated
- Apr 1, 2025
- Language
- Japanese
Syllabus
Course overview and goals
The real-world signal can be considered as a random signal. The random signal processing is a technique to estimate parameters from the random signal. For that purpose, typical probability distributions will introduced. Then, statistical estimators will be discussed. The course will demonstrate how to use the statistical estimators for real-world problems.
This course will provide a comprehensive overview of the probability distributions and the statistical estimators. The derivations of Gaussian and Poisson distributions will be presented. Law of large numbers and central limit theorem will be proven. Maximum likelihood and maximum a priori will be introduced. The course will conclude by discussing how to apply those estimators to the real-world problem.
Course description and aims
By the end of this course, students will be able to:
1. Explain and derive Gaussian and Poisson distributions
2. Prove and use the law of large numbers and the central limit theorem
3. Explain and apply the maximum likelihood and the maximum a posteriori estimators
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)
A faculty who has a private company experience give a lecture.
Keywords
Gaussian distribution, Poisson distribution, the law of large numbers, the central limit theorem, the maximum likelihood estimator, and a posteriori estimator
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
Assignment is checked and reviewed. Then, main points are discussed in detailed. Student are asked to provide the solution of quick expiries during class.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Introduction of the course | Understand importance |
| Class 2 | Various types of distributions | Understand various types of distributions |
| Class 3 | Moment generating function | Understand moment generating function |
| Class 4 | The law of large numbers | Understand the law of large numbers |
| Class 5 | The central limit theorem | Understand moment the central limit theorem |
| Class 6 | Least square | Understand Least square |
| Class 7 | Maximum likelihood | Understand Maximum likelihood |
| Class 8 | Conditional probability, posterior distribution, and Bayes’ theorem | Understand conditional probability, posterior distribution, and Bayes’ theorem |
| Class 9 | Maximum a posteriori estimator | Understand maximum a posteriori estimator |
| Class 10 | Stochastic process, filter | Understand stochastic process, filter |
| Class 11 | Optimization of quadratic form | Understand optimization of quadratic form |
| Class 12 | Optimization of function | Understand optimization of function |
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)
Slides
Reference books, course materials, etc.
Books in Japanese
Evaluation methods and criteria
Assignments, excersises, final exams.
Related courses
- SCE.I201 ： Introduction to Measurement Engineering
Prerequisites
Basics of statistics
Other
Students who already have the credits for Probability Theory and Statistics (CSC.T242) can not take this class.