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) Instructor Akihiko Matsui We study mathematics used in economics. Language English TA session will start after grading the first problem set. TA: Sato, Morooka Prerequisites Materials covered in Math Camp. Textbooks 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. Contents　 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) Metric spaces (definition, complete metric spaces, totally bounded sets, sequentially compact sets, continuity, Weierstrass theorem (existence of maximum), parametric continuity.) Fixed point theorems (Brouwer's fixed point theorem, Kakutani's fixed point theorem, etc.) Dynamic optimization (Euler equation, Dynamic programming) Grade 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.