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math_topics - Leo Simon Rosangela Bando Mathematical...

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Leo Simon ARE211 Rosangela Bando Fall 2007 Mathematical Methods for Agricultural and Resource Economists Syllabus SB refers to Mathematics for Economists, by Carl Simon and Larry Blume (SB). MWG refers to Mathematical Appendix to Microeconomic Theory, by Mas-Colell, Whinston and Green (MWG). The texts are only peripherally related to the course material. The chapter guides are approximate. (1) Analysis SB(12,29,A1), MWG(M.F) (a) Sequences (b) Distance/Metrics (c) Convergence of Sequences (d) Geometric series (e) Least Upper bounds and Greatest Lower Bounds (f) Cauchy Sequences (g) Topology of R n (h) Continuous Functions (i) Upper and Lower Hemi-continuous correspondences (2) Graphical Overview of Calculus & Optimization Theory (no text). (a) Necessary and Sufficient Conditions (b) Unconstrained optimization — one variable (c) Convex sets, Concave and Convex Functions (d) Separating Hyperplanes (e) Strictly Concave and Convex Functions and Strict (Locally Unique) Maxima (f) Constrained optimization — one variable
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