Mathematics and Economic Modelling 2014 (Summer)

Summer semester Thursday 14:50-16:30 Problem sets Problem set 1 Problem set 2 Problem set 3   Mathematics and Economic Modeling: Corrections (2014/7/17) Mathematics and Economic Modeling: Problem set 4 is up here. (2014/7/17)   Seminar room no. 2 in Kojima Hall <= changed! 　We study mathematics used in economics.   Instructor Akihiko Matsui   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. Friedman, "Foundations of modern analysis," Dover.   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.) (if time allows) basics of measure theory 　 Grade Grade is based on midterm and final exams. 　 Homework assignments There will be 4-6 homework assignments (no need to hand in)