2020 Faculty Courses School of Computing First-Year Courses
Foundations of Computing 3
- Academic unit or major
- First-Year Courses
- Instructor(s)
- Naoto Miyoshi / Hideyuki Miura / Masaaki Umehara / Mituhiro Fukuda
- Class Format
- Lecture (Zoom)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 5-6 Thu (W621,W631)
- Class
- -
- Course Code
- XCO.B103
- Number of credits
- 100
- Course offered
- 2020
- Offered quarter
- 4Q
- Syllabus updated
- Jul 10, 2025
- Language
- Japanese
Syllabus
Course overview and goals
Understand the basics of discrete structures, differential equations, mathematical optimization, discrete probabilities, etc., which are part of the curriculum of the Department of Mathematical and Computational Science. In these fields, we construct mathematical models that extract only the essence of real problems, and develop mathematical and probability theories that are conscious of algorithms that implement this model on a computer. Among them, the explanation will focus on themes that do not use much specialized background knowledge.
Course description and aims
Understand the basics of discrete structures, differential equations, mathematical optimization, discrete probabilities, etc., which are part of the curriculum of the Department of Mathematical and Computational Science.
Keywords
Discrete structures, differential equations, mathematical optimizations, discrete probability
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
Four faculty members will give lectures on each topic in omnibus format.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Linear optimization problems and polytopes | Understand the mathematical and algorithmic concepts related to the solution of linear optimization problems, which is considered the beginning of the mathematical optimization. |
| Class 2 | Discrete probability | To understand probability on discrete space and its applications. |
| Class 3 | Discrete random variables and expectations | To understand discrete-valued random variables and their applications. |
| Class 4 | Introduction to distributions 1 | To understand the definition of distributions introduced by L. Schwartz and its background. |
| Class 5 | Introduction to distributions 2 | To understand applications of distributions to differential equations and so on. |
| Class 6 | Topics on Plane Curves 1 | Fundamental properties of plane curves, length, curvature. |
| Class 7 | Topics on Plane Curves 2 | Rotation index, regular homotopy, etc |
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.
None.
Evaluation methods and criteria
Report
Related courses
- XCO.B101 ： Foundations of Computing 1
- XCO.B102 ： Foundations of Computing 2
Prerequisites
No requirements.