### 2022　Mathematics for Industrial Engineering and Economics

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Undergraduate major in Industrial Engineering and Economics
Instructor(s)
Shioura Akiyoshi
Class Format
Lecture    (Livestream)
Media-enhanced courses
Day/Period(Room No.)
Tue7-8(西9号館311号室)  Fri7-8(西9号館311号室)
Group
-
Course number
IEE.A202
Credits
2
2022
Offered quarter
2Q
Syllabus updated
2022/4/19
Lecture notes updated
-
Language used
Japanese
Access Index

### Course description and aims

This course studies basic mathematics for management sciences and economics. The contents include Euclidean space, metric space, topological space, convergence of sequences, continuous functions, convex sets, and convex functions.

Knowledge and ability through this course will help students to solve real problems in management sciences and economics.

### Student learning outcomes

By the end of this course, students will be able to:
1. Understand fundamental properties of Euclidean space and can solve application problems.
2. Understand fundamental properties of metric space and topological space, and can solve application problems.
3. Understand fundamental properties of convergence of sequences and continuous functions, and can solve application problems.
4. Understand fundamental properties of convex sets and convex functions, and can solve application problems.

### Keywords

Euclidean space, metric space, topological space, convergence of sequences, continuous functions, convex sets, convex functions

### Competencies that will be developed

 ✔ Specialist skills Intercultural skills Communication skills Critical thinking skills ✔ Practical and/or problem-solving skills

### Class flow

In each lecture, lecture materials will be uploaded to T2SCHOLA so that students can read and understand the content.

Lectures will be given online via Zoom, and video recordings of the lectures will be made available for a limited time.
A hybrid format will be available if requested.

Before the end of the class, exercises related to the contents of the day's class will be presented, and students are expected to solve them before the next class as a report.
Submission is optional.

A mid-term exam and a final exam will be given to check the level of understanding.

### Course schedule/Required learning

Course schedule Required learning
Class 1 Euclidean space Announced in classes.
Class 2 open and closed sets Announced in classes.
Class 3 metric space Announced in classes.
Class 4 topological space Announced in classes.
Class 5 convergence of sequences Announced in classes.
Class 6 convergence of sequences Announced in classes.
Class 7 mid-term exam check the level of understanding of the classes 1-6.
Class 8 continuous functions Announced in classes.
Class 9 Cauchy sequence and sub-sequence Announced in classes.
Class 10 minimization of continuous functions Announced in classes.
Class 11 convex sets Announced in classes.
Class 12 convex functions Announced in classes.
Class 13 convex functions Announced in classes.
Class 14 final exam check the level of understanding of the classes 8-13.

### 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.

### Textbook(s)

KEIEIKOGAKU NO SURI I, Miyakawa, Mizuno, and Yajima, Asakura-Syoten, 2004.

None required

### Assessment criteria and methods

Students will be assessed on their understanding of Euclidean space, metric space, topological space, convergence of sequences, continuous functions, convex sets, and convex functions.
Students' course scores are based on midterm and final exams (70%) and reports (30%).

### Related courses

• IEE.A201 ： Basic Mathematics for Industrial Engineering and Economics
• IEE.A203 ： Mathematical Engineering

### Prerequisites (i.e., required knowledge, skills, courses, etc.)

If the number of students enrolling in the course becomes very large, there may be a possibility of limiting the number of students who belong to departments other than the Department of Industrial Engineering and Economics.