Math_for_Econ2022

***Announcements

Final exam 2022 is up. See the bottom of this page. (2022/07/25)

Sample problem based on Final Exam 2021 is up (no due). (2022/07/16)

Rules and Regulations for the online exam is up. (2022/07/10)

Lecture Note05 is up. (2022/07/10)

Solution #3 is up. See the bottom of this page. (2022/06/15, TA: Jiahao Li)

Problem set #3 is up. See the bottom of this page. No due. (2022/05/27)

Recorded TA session #1 is up.  Please check the link: link.(2022/5/25, TA: Jiahao Li)

Solution #2 is up. See the bottom of this page. (2022/05/24, TA: Jiahao Li)

We will have the first TA session on 3rd period in Wednesday (5/25). I will record it in case you cannot attend. Please use the following zoom link: zoom link. (2022/05/22, TA: Jiahao Li)

LectureNote03 is up. (2022/05/22)

Solution #1 is up. See the bottom of this page. (2022/05/07, TA: Jiahao Li)

Problem set #2 is up. See the bottom of this page. (2022/05/02)

Problem set #1 is up. See the bottom of this page. (2022/04/25)

We'll try classroom no.2 on Apr. 11, 2022 (up Apr. 4, 2022)

*** messages/announcements (upward)

***

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: Jiahao Li

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. Dynamic optimization (Euler equation, Dynamic programming)

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.