INTRODUCTION TO MATHEMATICS 1

To ensure the stable operation of the system, users are requested not to use automated programs, browser extensions, or similar tools that generate excessive access requests or automatically retrieve data.
During course registration periods in particular, excessive requests within a short period of time may place a significant load on the system and affect the availability of services for other users.
We appreciate your cooperation in maintaining a secure and stable computing environment.
If such activity is identified, the University may take appropriate measures, including access restrictions or the disabling of the relevant functionality.

Once you log in, you can use the following functions (Keio ID required).
Affiliation information (faculty, department/major, year level, etc.) is set in the search criteria (available to new students after enrollment).
Favorite (Bookmark)
View syllabus details

Subtitle	Fundamentals of mathematics for development of economics
Lecturer(s)	ISHIKAWA, MASAHARU
Credit(s)	2
Academic Year/Semester	2026 Spring
Day/Period	Fri.2
Campus	Hiyoshi
Class Format	Face-to-face classes (conducted mainly in-person)
Registration Number	45939
Faculty/Graduate School	ECONOMICS
Department/Major	ECONOMICS Type A, B
Year Level	1
Field	FOUNDATION
Grade Type	This item will appear when you log in (Keio ID required).
Course Description	This course prepares students for the in-depth study of economics in their third and fourth years by developing the skills necessary for a deeper understanding of the discipline. Particular emphasis is placed on mathematical and deductive methods.
K-Number	FEC-EC-13173-211-12

Course Administrator	Faculty/Graduate School	FEC	ECONOMICS
Course Administrator	Department/Major	EC	ECONOMICS
Main Course Number	Level	1	First-year level coursework
	Major Classification	3	Foudation Course / Major Subjects Course - Introductory Subject
	Minor Classification	17	Foundational Course - Introduction to Mathematics
	Subject Type	3	Elective subject
Supplemental Course Information	Class Classification	2	Lecture
	Class Format	1	Face-to-face classes (conducted mainly in-person)
	Language of Instruction	1	Japanese
Academic Discipline		12	Analysis, applied mathematics, and related fields

Course Contents/Objectives/Teaching Method/Intended Learning Outcome

The lecture begins with a review of high school mathematics and the students learn the concept of limits and the basics of differentiation. The content of this lecture will be required when taking the course "Introduction to Mathematics II", which will be held in the fall semester. The content and order of the lectures may differ slightly from the description of the syllabus.

Course Taught by Faculty Member with Professional Experience

Not applicable

Active Learning MethodsDescription

Not applicable

Preparatory Study

To understand the lectures, students need to prepare and review according to their ability.

Course Plan

Lesson 1

Calculation of numbers and polynomials (1)

Lesson 2

Calculation of numbers and polynomials (2)

Lesson 3

Linear functions, quadratic functions and graphs of functions

Lesson 4

Polynomials of degree 2, polynomials of degree 3 or higher, the Factor Theorem and inequalities

Lesson 5

Fractional functions and irrational functions

Lesson 6

Composition and inverse functions

Lesson 7

Exponential functions and logarithmic functions

Lesson 8

Trigonometric functions

Lesson 9

Sequences (1)

Lesson 10

Sequences (2)

Lesson 11

Limits

Lesson 12

Differentiation and derivative (1)

Lesson 13

Differentiation and derivative (2)

Lesson 14

Monotonicity tables and graphs

Other

Maxima and minima

Method of Evaluation

Grades will be evaluated based on examinations and class participation (attendance, behavior, class assignments, etc.).

Generative AI Policy for Classes

In this course, emphasis is placed on students’ own thinking and expressive abilities. Therefore, the use of generative AI is, in principle, prohibited. Use of AI is not allowed in the following activities:
- Writing reports or assignments
- Preparing for in-class discussions or presentations
If AI use is discovered, the work may be excluded from evaluation or treated as academic misconduct and subject to disciplinary measures. If you are unsure about what is permitted, please consult the lecturer in advance.

Lab / Skill-development / On-site training	An educational approach in which students deepen their understanding of educational content through first-hand experience and trial-and-error by initiating their own activities at facilities and accommodations both on and off campus.
Fieldwork	An educational approach in which students conduct surveys and observations on their own to collect information both on and off campus.
Presentations	An educational approach in which students deepen their understanding of educational content by preparing materials and delivering presentations in class.
Discussions, Debates	An educational approach in which students deepen their understanding of educational content through sharing and discussing their opinions on designated topics.
Group work	An educational approach in which students are divided into small groups and assigned tasks on issues related to educational content.
Role-playing	An educational approach in which students deepen their understanding of educational content by being assigned specific roles to play, thus allowing them to experience different viewpoints.
Flipped classroom	An educational approach in which students study the course lecture in advance, and questions and discussions relating to that content are then held in class.
Problem-based learning	An educational approach in which students acquire knowledge and skills related to educational content by attempting to tackle specific projects or problems posed to them.

Keio University Syllabus and Timetable