WMEA1300 Mathematics for Economic Analysis

Hiroshima University Syllabus

Japanese

Academic Year 2024Year School/Graduate School Graduate School of Humanities and Social Sciences (Master's Course) Division of Humanities and Social Sciences Economics Program

Lecture Code WMEA1300 Subject Classification Specialized Education

Subject Name 経済数学

Subject Name
（Katakana）ケイザイスウガク

Subject Name in
English Mathematics for Economic Analysis

Instructor HORIE MAYUMI

Instructor
(Katakana) ホリエ　マユミ

Campus Higashi-Senda Semester/Term 1st-Year, Second Semester, Second Semester

Days, Periods, and Classrooms (2nd) Mon11-12：Higashi-Senda Seminar Rm 3

Lesson Style Lecture Lesson Style
(More Details) 　

Credits 2.0 Class Hours/Week 　 Language of Instruction J : Japanese

Course Level 5 : Graduate Basic

Course Area（Area） 24 : Social Sciences

Course Area（Discipline） 03 : Economics

Eligible Students 1st year students

Keywords calculus, linear algebra, constrained optimization, Lagrange multiplier method, convex analysis

Special Subject for Teacher Education 　 Special Subject 　

Class Status
within Educational
Program
(Applicable only to targeted subjects for undergraduate students)
Criterion referenced
Evaluation
(Applicable only to targeted subjects for undergraduate students)

Class Objectives
/Class Outline This course provides a thorough explanation of the basic concepts of mathematics that students need to acquire in order to study the mathematical methods used in economics and finance at the graduate level. To this end, the course will cover derivatives, linear algebra, and optimization theory primarily, and then proceed up to convex analysis.
While it is necessary to develop mastery of formulas, problem solving methods, and calculation methods, the course also aims to provide students with a solid understanding of definitions, theorems, and proofs, as well as the mathematical logic and thinking behind them. To this end, the course will follow the descriptions in the text, while adding explanations as to why the definitions are given the way they are and why such theorems are important. If necessary, exercises will be given as homework.
The course content will be modified according to the students' goals and level of understanding.

Class Schedule lesson1 Differentiation (1): Real numbers; Limit of a sequence
lesson2 Differentiation (2): Series; Functions
lesson3 Differentiation (3): One-variable calculus
lesson4 Differentiation (4): Calculus of two variables
lesson5 Linear algebra (1): Vectors and matrices
lesson6 Linear algebra (2): Vector space
lesson7 Linear algebra (3): Linear mapping and the rank of a matrix
lesson8 Linear algebra (4): Determinants; Systems of linear equations
lesson9 Linear algebra (5): Eigenvalues and eigenvectors; Quadratic forms
lesson10 Optimization Theory (1): Unconstrained optimization problems; Taylor's Theorem
lesson11 Optimization Theory (2): Local optimization; Equality constraints
lesson12 Optimization theory (3): Implicit function theorem; Lagrange multiplier method
lesson13 Optimization Theory (4): Envelope theorem
lesson14 Convex Analysis (1): Convex sets and convex functions; Optimization of convex functions
lesson15 Convex Analysis (2): Separation theorem

Students are required to solve and submit assignments (homework).
A final exam will be scheduled at the end of this course.

Text/Reference
Books,etc. TBA

PC or AV used in
Class,etc. 　

(More Details)

Learning techniques to be incorporated 　

Suggestions on
Preparation and
Review Students are required to prepare for the course by reading the relevant parts of the textbook. Students will be assigned exercises, so please be sure to solve the problems before the next lecture. Explanations of problems may be provided in the form of explanatory videos, so please be sure to watch and review them. (On average, about 2 hours of study time for preparation, review, and problem solving will be expected.)

Requirements Preparation such as an introduction to mathematics for economics and a review of high school math textbooks (especially calculus) will help you better understand the contents of this course.

Grading Method Grades will be evaluated based on the final examination with 70 points and assignments with 30 points, for a total of 100 points.

Practical Experience

Summary of Practical Experience and Class Contents based on it

Message

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	2024Year	School/Graduate School	Graduate School of Humanities and Social Sciences (Master's Course) Division of Humanities and Social Sciences Economics Program
Lecture Code	WMEA1300	Subject Classification	Specialized Education
Subject Name	経済数学
Subject Name （Katakana）	ケイザイスウガク
Subject Name in English	Mathematics for Economic Analysis
Instructor	HORIE MAYUMI
Instructor (Katakana)	ホリエ　マユミ
Campus	Higashi-Senda	Semester/Term	1st-Year, Second Semester, Second Semester
Days, Periods, and Classrooms	(2nd) Mon11-12：Higashi-Senda Seminar Rm 3
Lesson Style	Lecture	Lesson Style (More Details)

Credits	2.0	Class Hours/Week		Language of Instruction	J : Japanese
Course Level	5 : Graduate Basic
Course Area（Area）	24 : Social Sciences
Course Area（Discipline）	03 : Economics
Eligible Students	1st year students
Keywords	calculus, linear algebra, constrained optimization, Lagrange multiplier method, convex analysis
Special Subject for Teacher Education		Special Subject
Class Status within Educational Program (Applicable only to targeted subjects for undergraduate students)
Criterion referenced Evaluation (Applicable only to targeted subjects for undergraduate students)
Class Objectives /Class Outline	This course provides a thorough explanation of the basic concepts of mathematics that students need to acquire in order to study the mathematical methods used in economics and finance at the graduate level. To this end, the course will cover derivatives, linear algebra, and optimization theory primarily, and then proceed up to convex analysis. While it is necessary to develop mastery of formulas, problem solving methods, and calculation methods, the course also aims to provide students with a solid understanding of definitions, theorems, and proofs, as well as the mathematical logic and thinking behind them. To this end, the course will follow the descriptions in the text, while adding explanations as to why the definitions are given the way they are and why such theorems are important. If necessary, exercises will be given as homework. The course content will be modified according to the students' goals and level of understanding.
Class Schedule	lesson1 Differentiation (1): Real numbers; Limit of a sequence lesson2 Differentiation (2): Series; Functions lesson3 Differentiation (3): One-variable calculus lesson4 Differentiation (4): Calculus of two variables lesson5 Linear algebra (1): Vectors and matrices lesson6 Linear algebra (2): Vector space lesson7 Linear algebra (3): Linear mapping and the rank of a matrix lesson8 Linear algebra (4): Determinants; Systems of linear equations lesson9 Linear algebra (5): Eigenvalues and eigenvectors; Quadratic forms lesson10 Optimization Theory (1): Unconstrained optimization problems; Taylor's Theorem lesson11 Optimization Theory (2): Local optimization; Equality constraints lesson12 Optimization theory (3): Implicit function theorem; Lagrange multiplier method lesson13 Optimization Theory (4): Envelope theorem lesson14 Convex Analysis (1): Convex sets and convex functions; Optimization of convex functions lesson15 Convex Analysis (2): Separation theorem Students are required to solve and submit assignments (homework). A final exam will be scheduled at the end of this course.
Text/Reference Books,etc.	TBA
PC or AV used in Class,etc.
(More Details)
Learning techniques to be incorporated
Suggestions on Preparation and Review	Students are required to prepare for the course by reading the relevant parts of the textbook. Students will be assigned exercises, so please be sure to solve the problems before the next lecture. Explanations of problems may be provided in the form of explanatory videos, so please be sure to watch and review them. (On average, about 2 hours of study time for preparation, review, and problem solving will be expected.)
Requirements	Preparation such as an introduction to mathematics for economics and a review of high school math textbooks (especially calculus) will help you better understand the contents of this course.
Grading Method	Grades will be evaluated based on the final examination with 70 points and assignments with 30 points, for a total of 100 points.
Practical Experience
Summary of Practical Experience and Class Contents based on it
Message
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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