Mathematics II (S1, 2015)

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

TA: Mengli Sha

Monday, Thursday 13:00-14:45
First session April 6
Class room 3

Syllabus (PDF file)

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.

Exams

Final June 1 Examination Schedule New

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]
N.L. Stokey and R.E. Lucas, Recursive Methods in Economic Dynamics, Harvard University Press, 1989. [Amazon]
M.L. Puterman, Markov Decision Processes: Discrete Stochastic Dynamic Programming, Wiley-Interscience, 2005.

Topics

  1. Real numbers
  2. Continuous functions and compact sets
  3. Correspondences
  4. Differentiation in one variable
  5. Differentiation in several variables
  6. Convex sets and (quasi)concave functions
  7. Negative (semi)definite matrices
  8. Unconstrained maximization
  9. Constrained maximization
  10. Envelope theorem
  11. Separating hyperplane theorems
  12. Fixed point theorems
  13. Dynamic Programming

Notes

On the (Non-)Differentiability of the Optimal Value Function When the Optimal Solution Is Unique
On the Differentiability of the Support Function
On the Differentiability of the Value Function

Office hours

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