Mathematics II (S1, 2024)

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

Wednesday, Friday 8:30-10:15
First session April 5
Class room 513

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.

Exam

Final May 29 [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
  2. Continuous functions and compact sets
  3. Correspondences
  4. Convex sets and (quasi-)concave functions
  5. Differentiation
  6. Negative (semi-)definite matrices
  7. Separating hyperplane theorems
  8. Optimization
  9. Envelope theorem
  10. Fixed point theorems
  11. Dynamic programming

Notes

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