＜概要/Course Content Summary＞
Virtually all fields of inquiry benefit from analytical and problem-solving skills based on mathematics, and a variety of mathematical techniques have been applied to the social sciences. This course aims to serve as an introduction to fundamental ideas and techniques in precalculus and calculus that are important for mathematically addressing various issues in the social sciences. We examine essential mathematical concepts theoretically and discuss how to use them to establish mathematically sound frameworks for solving practical problems in the social sciences. A wide range of real-world examples (drawn from academic and government sources, industrial, commercial, and business sectors, and current events) will be provided in class.
＜到達目標/Goals,Aims＞
Our learning objectives are to:
• Understand fundamental concepts in precalculus and calculus.
• Understand the methods of mathematical investigation and the nature of mathematical knowledge.
• Develop basic skills in mathematical reasoning.
• Use mathematical concepts and frameworks to analyze real-world problems in the social sciences.
• Mathematically evaluate some of the advances in our understanding of various issues in the social sciences.
＜授業計画/Schedule＞
（実施回/
Week）
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（内容/
Contents）
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（授業時間外の学習/
Assignments）
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（実施回/ Week）
Week 1
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（内容/ Contents）
Introduction (why mathematics?)
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（授業時間外の学習/ Assignments）
Assignment: Read Chapters 1-2.
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（実施回/ Week）
Week 2
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（内容/ Contents）
Numbers, polynomials, operations on polynomials, polynomial equations
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（授業時間外の学習/ Assignments）
Assignment: Read Chapter 3 of Nakama and solve homework problems.
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（実施回/ Week）
Week 3
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（内容/ Contents）
Mental mathematics, functions
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（授業時間外の学習/ Assignments）
Assignment: Read Chapters 4-5 of Nakama and solve homework problems.
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（実施回/ Week）
Week 4
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（内容/ Contents）
Functions, graphs, polynomial functions
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（授業時間外の学習/ Assignments）
Assignment: Read Chapter 5 of Nakama and solve homework problems.
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（実施回/ Week）
Week 5
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（内容/ Contents）
Linear models in the social sciences
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（授業時間外の学習/ Assignments）
Assignment: Read Chapter 6 of Nakama and solve homework problems.
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（実施回/ Week）
Week 6
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（内容/ Contents）
Quadratic models in the social sciences
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（授業時間外の学習/ Assignments）
Assignment: Read Chapter 6 of Nakama and solve homework problems.
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（実施回/ Week）
Week 7
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（内容/ Contents）
Functions in economics
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（授業時間外の学習/ Assignments）
Assignment: Read Chapter 7 of Nakama and solve homework problems.
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（実施回/ Week）
Week 8
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（内容/ Contents）
Regression, differentiation
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（授業時間外の学習/ Assignments）
Assignment: Read Chapters 8-10 of Nakama and solve homework problems.
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（実施回/ Week）
Week 9
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（内容/ Contents）
Midterm evaluation
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（授業時間外の学習/ Assignments）
Assignment: Read Chapter 10 of Nakama and solve homework problems.
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（実施回/ Week）
Week 10
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（内容/ Contents）
Differentiation
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（授業時間外の学習/ Assignments）
Assignment: Read Chapter 10 of Nakama and solve homework problems.
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（実施回/ Week）
Week 11
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（内容/ Contents）
Rules of differentiation
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（授業時間外の学習/ Assignments）
Assignment: Read Chapter 10 of Nakama and solve homework problems.
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（実施回/ Week）
Week 12
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（内容/ Contents）
Extrema and derivatives, optimization
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（授業時間外の学習/ Assignments）
Assignment: Read Chapter 11 of Nakama and solve homework problems
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（実施回/ Week）
Week 13
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（内容/ Contents）
Trigonometric functions, exponential functions
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（授業時間外の学習/ Assignments）
Assignment: Read Chapter 12 of Nakama and solve homework problems.
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（実施回/ Week）
Week 14
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（内容/ Contents）
Integration (definite and indefinite integration), fundamental theorems of calculus
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（授業時間外の学習/ Assignments）
Assignment: Read Chapter 13 of Nakama and solve homework problems.
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（実施回/ Week）
Week 15
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（内容/ Contents）
Final evaluation
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（授業時間外の学習/ Assignments）
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Course Requirements and Assignments
a) Attendance, readings, and participation
You are required to attend the lectures and have an attendance record of at least 80%. You are also required to read lecture notes and solve homework problems each week. You are expected to actively contribute to class discussions.
b) Midterm examination
You are required to take an exam in Week 9. This is not an open-book exam.
c) Final examination
At the end of the course, you are required to take an exam. This is not an open-book exam.
Note: The schedule, requirements, and assignments will be subject to changes or revisions.
＜成績評価基準/Evaluation Criteria＞
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Contributions to class discussions, attendance
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10%
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Assignment
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30%
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Examination
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60%
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Additional Information: Plagiarism and cheating
Doshisha University does not tolerate plagiarism, cheating, or helping others to cheat. These actions will result in an automatic “F” in the course. Plagiarism is defined as misrepresenting the work of others (whether published or not) as your own. It may be inadvertent or intentional. Any facts, statistics, quotations, or paraphrasing of any information that is not common knowledge must be cited. For more information on paper writing, including how to avoid plagiarism and how to use citations, you can find many helpful resources in the library.
＜テキスト/Textbook＞
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Nakama, T.
, Mathematical Methods for the Social Sciences
:
Precalculus and Calculus
.
(2019)
.
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＜備考/Remarks＞
INSTRUCTOR: Takehiko Nakama
EMAIL: nakama@jhu.edu
Note: This syllabus will be subject to changes or revisions.
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