| Academic Year |
2025Year |
School/Graduate School |
Liberal Arts Education Program |
| Lecture Code |
52004101 |
Subject Classification |
Area Courses |
| Subject Name |
The world of mathematics［旧パッケージ］ |
Subject Name
（Katakana） |
|
Subject Name in
English |
The world of mathematics |
| Instructor |
GU YANLEI |
Instructor
(Katakana) |
コ エンライ |
| Campus |
Higashi-Hiroshima |
Semester/Term |
1st-Year, Second Semester, 3Term |
| Days, Periods, and Classrooms |
(3T) Weds5-8：IAS K205 |
| Lesson Style |
Lecture |
Lesson Style
(More Details) |
Face-to-face, Online (on-demand) |
This is a lecture-based class, primarily held in person, with online (on-demand) sessions available only in special situations, such as severe weather, the instructor’s business trip, or other exceptional circumstances.
The first lesson will be conducted in person. |
| Credits |
2.0 |
Class Hours/Week |
4 |
Language of Instruction |
E
:
English |
| Course Level |
1
:
Undergraduate Introductory
|
| Course Area（Area） |
25
:
Science and Technology |
| Course Area（Discipline） |
01
:
Mathematics/Statistics |
| Eligible Students |
|
| Keywords |
Calculus, Probability Theory |
| Special Subject for Teacher Education |
|
Special Subject |
|
Class Status within
Liberal Arts Education | Area Courses（Courses in Natural Sciences) Category：Mathematics / Informatics |
|---|
| Expected Outcome | (1) Be able to understand fundamental mathematical concepts by developing a solid foundation in calculus, probability, and mathematical reasoning.
(2) Be able to apply mathematical principles to solve real-world problems using functions, derivatives, optimization, and probability techniques.
(3) Be able to explore the historical and practical significance of mathematics by understanding its development and applications in various research fields and everyday life. |
|---|
Class Objectives
/Class Outline |
The World of Mathematics course covers fundamental concepts in calculus, probability, and mathematical reasoning. Students will develop problem-solving skills, explore real-world applications, and gain an understanding of the historical evolution of mathematics. The course emphasizes logical thinking, quantitative reasoning, and the role of mathematics across various disciplines and in everyday life. |
| Class Schedule |
lesson1: Foundations of Calculus: Variables, Functions, and Limit
lesson2: The Evolution of Mathematical Reasoning: From Pythagoras to Modern Analysis
lesson3: The Foundations of Measurement and Mathematical Thought
lesson4: Uncovering Change: Slopes, Derivatives, and Optimization
lesson5: Mastering Derivatives: Rules and Applications for Optimization
lesson6: Understanding Change: Chain Rule and Antiderivatives
lesson7: Unifying Calculus: Antiderivatives and Integrals
lesson8: Foundations of Probability: Sets and Relations
lesson9: Probability: Probability Definitions, Independence and Density
lesson10: Counting: Sampling Techniques
lesson11: Random Variables: Distributions, Expectations, and Applications
lesson12: Conditional Probability: Conditioning, Sequential Sampling and Independence
lesson13: Expectation, Variance, and Transforms
lesson14: Important Probability Distributions: Poisson and Normal
lesson15: Review of the content from all lessons.
-Assignments and reports
-In-class tests |
Text/Reference
Books,etc. |
Reference Books
(1) Priestley, William M. Calculus: a liberal art. Springer Science & Business Media.
(2) Chung, Kai Lai. Elementary probability theory with stochastic processes. Springer Science & Business Media. |
PC or AV used in
Class,etc. |
Handouts, Microsoft Teams, Zoom, moodle |
| (More Details) |
Projector and PC |
| Learning techniques to be incorporated |
Quizzes/ Quiz format, Post-class Report |
Suggestions on
Preparation and
Review |
(1) Each lesson’s materials (e.g., slides provided by the instructor) should be reviewed both before and after class.
(2) The meaning of all English technical terms should be understood before class. |
| Requirements |
|
| Grading Method |
The grade will be based on the following two components:
(1) Continuous assessment of assignments and reports
(2) In-class tests |
| Practical Experience |
|
| Summary of Practical Experience and Class Contents based on it |
|
| Message |
The lecture content is subject to slight changes depending on the circumstances. |
| Other |
|
Please fill in the class improvement questionnaire which is carried out on all classes.
Instructors will reflect on your feedback and utilize the information for improving their teaching. |