Tentative Topics Outline:
The lecture are divided into four parts.
Part I. Review of modern economics and mathematics as well as partial equilibrium theory: Nature and role of modern economics, the standard Analytical framework of modern economics, key assumptions commonly adopted in microeconomics, partial equilibrium theory, theory of markets, perfect competition, monopoly, monopolistic competition, oligopoly, monopsony, roles of mathematics, language and methods of mathematic, continuity and concavity of functions, separating hyperplane theorem, unconstrained and constrained optimization, correspondences (point to set mappings), fixed point theorems, KKM lemma, maximum theorem.
Readings: Mathematical Appendix of Mas‑Colell, Whinston, and Green, and Chapters 1 and 6 of my lecture notes.