Mathematics II (S1, 2025)

OYAMA Daisuke
oyama@e.u-tokyo.ac.jp

TA: Konan Shimizu

Tuesday, Friday 8:30-10:15
First session April 4
Class room 6

Syllabus/Introduction

The aim of this course is to provide students with basic tools in Analysis that are needed in advanced level micro and macro economics. The course covers the main part of the Mathematical Appendix in Mas-Colell, Whinston, and Green.

Notice

We have a class on May 16, and no class on May 23. (4/4)

Exam

Final May 30 [Examination Schedule]

Textbook

A. Mas-Colell, M.D. Whinston, and J.R. Green, Microeconomic Theory, Oxford University Press, 1995. [Amazon]

References

G. Debreu, Theory of Value, Yale University Press, 1959. [Download]
D. M. Kreps, Microeconomic Foundations I: Choice and Competitive Markets, Princeton University Press, 2012. [Amazon]
D. Oyama and T. Takenawa, On the (Non-)Differentiability of the Optimal Value Function When the Optimal Solution Is Unique, Journal of Mathematical Economics 76, 21-32 (2018).

Topics

  1. Real numbers [Slides (4/2)]
  2. Continuous functions and compact sets [Slides (4/4)]
  3. Correspondences [Slides (4/14)]
  4. Convex sets and (quasi-)concave functions [Slides (4/25)]
  5. Differentiation [Slides 1 (4/22), Slides 2 (4/22)]
  6. Negative (semi-)definite matrices [Slides (4/25)]
  7. Separating hyperplane theorems [Slides 1 (4/30), Slides 2 (4/30)]
  8. Optimization [Slides (5/9)]
  9. Envelope theorem [Slides (5/13)]
  10. Fixed point theorems [Slides (5/16)]
  11. Dynamic programming [Slides (5/20)] New

Homeworks

Homework 1 (due on April 15)
Homework 2 (due on April 22)
Homework 3 (due on April 30)
Homework 4 (due on May 9)
Homework 5 (due on May 13)
Homework 6 (due on May 20)
Homework 7 (due on May 27)

Submit your homework through UTOL

Notes

Topological Properties of Convex Sets
On the Differentiability of the Value Function

Office hours

Friday 14:00-15:30
Economics Research Building 10th floor, 1012