| 回 | 項目 | 内容 |
| 第1回 | Guidance | Lecture plan and evaluation policy are introduced. |
| 第2回 | Set Theory and Topological Space 1 | Aim & Scope: Basic set theory and concept of topological space are introduced.
Goal: Understanding why set theory and topological space must be introduced in economics. |
| 第3回 | Set Theory and Topological Space 2 | Aim & Scope: Several important characteristics and results in topological space are introduced.
Goal: Understanding basic behavior of topological space. |
| 第4回 | Measure and Preference Relation | Aim & Scope: We learn how to measure distance between two things to extend our thinking to preference field.
Goal: Understanding how to generate indifference curve. |
| 第5回 | Measure and Stochastic Events | Aim & Scope: We learn how to measure probability of an event.
Goal: Understanding what is measure-zero and what is stochastic event. |
| 第6回 | Convex Analysis and Optimization Problems 1 | Aim & Scope: We learn what are convex set and separating hyper-plane to extend our thinking to constrained optimization problems.
Goal: Rethinking utility/production maximization and expenditure/cost minimization problems in a more general way. |
| 第7回 | Convex Analysis and Optimization Problems 2 | Aim & Scope: Applications and limitations of the method of Lagrange multiplier are introduced.
Goal: Understanding the use of the method, KKT condition, Farkas's lemma, and cusp. |
| 第8回 | Envelope Theorem and Its Applications | Aim & Scope: Envelope theorem and its applications to economics are introduced.
Goal: Understanding how to use envelope theorem in economics. |
| 第9回 | Fixed Point Theorems and Market Equilibria | Aim & Scope: Brower's, Kakutani's, and contraction mapping are introduced to apply them in economics.
Goal: Understanding why equilibria in economics are fixed points. |
| 第10回 | Introduction to Game Theory | Aim & Scope: Basic frameworks of normal form and strategic form games are introduced.
Goal: Understanding games in more general form. |
| 第11回 | Existence of Nash Equilibria and Fixed Point Theorems | Aim & Scope: Existence of Nash equilibria is discussed.
Goal: Understanding existence and non-existence of pure and mixed strategy Nash equilibria. |
| 第12回 | Introductions to Dynamic Programming and Dynamic Games | Aim & Scope: We learn basic philosophy of dynamic programming and how to apply to an economic analysis.
Goal: Understanding Bellman equation and its handling. |
| 第13回 | Search and Matching Models | Aim & Scope: We learn search & matching models with applications to monetary and labor economics.
Goal: Understanding applications of dynamic programming. |
| 第14回 | Review of lectures | We review all topics taught in this course. |
| 第15回 | Summary | We conclude the course. |
