52004101 The world of mathematics

Hiroshima University Syllabus

Japanese

Academic Year 2026Year School/Graduate School Liberal Arts Education Program

Lecture Code 52004101 Subject Classification Area Courses

Subject Name The world of mathematics

Subject Name
（Katakana）

Subject Name in
English The world of mathematics

Instructor LOU YANG

Instructor
(Katakana) ロウ　ヤン

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 course is primarily delivered through in-person lectures, with online (on-demand) sessions offered only under special circumstances such as severe weather, the instructor’s business trip, or other unavoidable situations.
The first class will be held 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; Mathematical Reasoning; Historical Evolution of Mathematics

Special Subject for Teacher Education 　 Special Subject 　

Class Status within
Liberal Arts Education Area Courses (Courses in Natural Sciences)　Category: Mathematics / Informatics
*Students who were admitted in 2018 or after can take this course as an “Area Course”. For this group of students, credits from this course will be regarded as credits for an “Area Course”.
If students who were admitted in 2017 or before take this course, it is regarded as a “Package-Based Subject”. The latter group of students cannot take this course as an “Area Course”.
Expected Outcome 1. Understand fundamental mathematical concepts by building a solid foundation in calculus, probability, and mathematical reasoning.
2. Apply mathematical principles to solve real‑world problems using functions, derivatives, optimization methods, and probability techniques.
3. Explore the historical and practical significance of mathematics by examining the development of mathematical ideas and the applications of mathematics across various research fields and everyday situations.

Class Objectives
/Class Outline The World of Mathematics course introduces fundamental ideas in calculus, probability, and mathematical reasoning. The course develops problem‑solving skills, highlights applications in real‑world contexts, and presents the historical evolution of mathematical ideas. Emphasis is placed on logical thinking, quantitative reasoning, and the contribution of mathematics to a wide range of disciplines and everyday situations.

Class Schedule lesson1 Foundations of Calculus: Variables, Functions, and Limits
lesson2 Evolution of Mathematical Reasoning
lesson3 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: 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 the content covered throughout the course

-Assignments and reports
-In‑class tests

Text/Reference
Books,etc. 1. Priestley, W. M. (2012). Calculus: A liberal art (2nd ed.). Springer Science & Business Media.
2. Chung, K. L., & AitSahlia, F. (2003). Elementary probability theory with stochastic processes and an introduction to mathematical finance (4th ed.). Springer Science & Business Media.

PC or AV used in
Class,etc. Handouts, Microsoft Teams, 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 None.

Grading Method The grade will be based on the following two components:
1. continuous assessment of assignments and reports, and
2. in‑class tests.

Practical Experience

Summary of Practical Experience and Class Contents based on it

Message The lecture content may be adjusted slightly 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.

Academic Year	2026Year	School/Graduate School	Liberal Arts Education Program
Lecture Code	52004101	Subject Classification	Area Courses
Subject Name	The world of mathematics
Subject Name （Katakana）
Subject Name in English	The world of mathematics
Instructor	LOU YANG
Instructor (Katakana)	ロウ　ヤン
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 course is primarily delivered through in-person lectures, with online (on-demand) sessions offered only under special circumstances such as severe weather, the instructor’s business trip, or other unavoidable situations. The first class will be held 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; Mathematical Reasoning; Historical Evolution of Mathematics
Special Subject for Teacher Education		Special Subject
Class Status within Liberal Arts Education	Area Courses (Courses in Natural Sciences)　Category: Mathematics / Informatics *Students who were admitted in 2018 or after can take this course as an “Area Course”. For this group of students, credits from this course will be regarded as credits for an “Area Course”. If students who were admitted in 2017 or before take this course, it is regarded as a “Package-Based Subject”. The latter group of students cannot take this course as an “Area Course”.
Expected Outcome	1. Understand fundamental mathematical concepts by building a solid foundation in calculus, probability, and mathematical reasoning. 2. Apply mathematical principles to solve real‑world problems using functions, derivatives, optimization methods, and probability techniques. 3. Explore the historical and practical significance of mathematics by examining the development of mathematical ideas and the applications of mathematics across various research fields and everyday situations.
Class Objectives /Class Outline	The World of Mathematics course introduces fundamental ideas in calculus, probability, and mathematical reasoning. The course develops problem‑solving skills, highlights applications in real‑world contexts, and presents the historical evolution of mathematical ideas. Emphasis is placed on logical thinking, quantitative reasoning, and the contribution of mathematics to a wide range of disciplines and everyday situations.
Class Schedule	lesson1 Foundations of Calculus: Variables, Functions, and Limits lesson2 Evolution of Mathematical Reasoning lesson3 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: 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 the content covered throughout the course -Assignments and reports -In‑class tests
Text/Reference Books,etc.	1. Priestley, W. M. (2012). Calculus: A liberal art (2nd ed.). Springer Science & Business Media. 2. Chung, K. L., & AitSahlia, F. (2003). Elementary probability theory with stochastic processes and an introduction to mathematical finance (4th ed.). Springer Science & Business Media.
PC or AV used in Class,etc.	Handouts, Microsoft Teams, 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	None.
Grading Method	The grade will be based on the following two components: 1. continuous assessment of assignments and reports, and 2. in‑class tests.
Practical Experience
Summary of Practical Experience and Class Contents based on it
Message	The lecture content may be adjusted slightly 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.

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