Mathematics for Economists 2020 (S1-S2)



S1-S2 terms

Monday 13:00-14:45

Classroom: online (subject to change)

Announcements (See the announcements of this page)


Akihiko Matsui

We study mathematics used in economics.



TA session

will start after grading the first problem set.

TA: Sato, Morooka


Materials covered in Math Camp.


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.


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


Homework assignments

will be posted here .

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.