Mathematics for Economist 2023

A revision of Solution to PS02 is up. (2023/07/23)

Solution to PS03 is up. (2023/07/23)

Solution to PS02 is up. (2023/07/17)

Problem set 03 is up (no due). (2023/07/16)

Lecture note 05 is up. (2023/07/10)

Problem set 02 is up. (2023/07/06)

Lecture note 04 is up. (2023/06/19)

Lecture note 03 is up. (2023/05/22)

Solution to PS01 is up. (2023/05/18)

TA session will be held 16:50-18:35 on May  24 at Classroom 6. (2023/05/17)

You do not have to solve Problem 3(2)(2) of Problem  set 01 because it is out of course materials. (2023/05/03) 

Problem set 01 is up. (2023/04/25)

Lecture note 02 is up. (2003/04/24)

Lecture note 01 is up (see the bottom of this page). (2023/04/07)

***Syllabus***

S term

Mon. 8:30-10:15

Instructor

Akihiko Matsui

We study mathematics used in economics. Lecture notes will be (have been) posted on this page (see below).

Language

English

TA session

will start after grading the first problem set.

TA:  Shinji Koiso

Prerequisites

Materials covered in Math Camp.

Textbooks

No specific textbook is used. However, the following books may be referred to. You need to have at least one book on real analysis.

Sundaram, "A first course in optimization theory" Cambridge.

Bartle, "The elements of real analysis," Wiley.

Kolmogorov & Fomin, "Introductory real analysis," Dover.

Kamien & Schwartz, "Dynamic optimization" North-Holland.

Contents

• 1. Topology in the Euclidean space (Sets: openness, closedness, boundedness, and compactness, neighborhoods, etc. Functions & correspondences: continuity, upper-hemi continuity, lower-hemi continuity. Sequences: subsequences, convergence, Cauchy. Nested cells theorem, cluster points, Bolzano-Weierstrass theorem, Heine-Borel theorem, etc)

  2. Metric spaces (definition, complete metric spaces, totally bounded sets, sequentially compact sets, continuity, Weierstrass theorem (existence of maximum), parametric continuity.)

  3. Fixed point theorems (Brouwer's fixed point theorem, Kakutani's fixed point theorem, etc.)

  4. To be determined

Grade

Grade is based on homework assignments (about 10%) and final exam (about 90%).

Homework assignments

will be posted on this page (see below).

You may form a group of at most three (individual work is fine, too).

Submit one file per group with all the members' names written.

All the information is subject to change.