### 2020　Foundations of Computing 3

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School of Computing
Instructor(s)
Miyoshi Naoto  Miura Hideyuki  Umehara Masaaki  Fukuda Mituhiro
Course component(s)
Lecture
Mode of instruction
ZOOM
Day/Period(Room No.)
Thr5-6(W621,W631)
Group
-
Course number
XCO.B103
Credits
1
2020
Offered quarter
4Q
Syllabus updated
2020/11/30
Lecture notes updated
-
Language used
Japanese
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### 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. 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.

### Student learning outcomes

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 that will be developed

 ✔ 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/Required learning

Course schedule Required learning
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

### Out-of-Class Study Time (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.

None.

None.

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### Related courses

• XCO.B101 ： Foundations of Computing 1
• XCO.B102 ： Foundations of Computing 2

No requirements.