1. Matrix algebra:
A. Linear systems: Gaussian elimination, LU decomposition,
echelon form, linear dependence rank;
B. Determinants, Cramer's rule, inverses;
C. Quadratic forms: Eigenvalues, diagonalization, linear constraints;
D. Ordinary least squares estimation.
Readings: EMEA chs. 15, 16; FMEA ch.1; Gilbert Strang,
Introduction to Linear Algebra
Also:
Matrix algebra slides, Part A
Matrix algebra slides, Part B
Matrix algebra slides, Part C
2. Real Analysis: (now taught by Pablo Beker)
Metric and normed spaces, sequences, limits, open and closed sets,
continuity, subsequences, compactness.
Readings: FMEA ch. 13, plus notes.
Carvajal 2009 notes, with minor changes
3. Unconstrained optimization: (now taught by Pablo Beker)
Concave and convex functions, Weierstrass' theorem,
first- and second-order conditions, envelope theorems.
Readings: Notes; FMEA chs. 2, 3.
Carvajal 2009 notes
4-5. Constrained Optimisation: (now taught by Pablo Beker)
(a) Linear programming and duality;
(b) Constraint qualifications, Kuhn/Tucker Theorem,
first- and second-order conditions;
(c) Comparative statics and Berge's maximum theorem;
Readings: Notes; EMEA, ch. 17; FMEA chs. 3, 13;
Rakesh Vohra, Advanced Mathematical Economics, ch. 4
Carvajal 2009 notes
6. Correspondences and fixed points: (now taught by Pablo Beker)
Correspondences as set-valued functions, closed and compact graph properties,
upper and lower hemi-continuity, Brouwer and Kakutani fixed point theorems, Cellina.
Readings: FMEA, ch. 14, plus notes.
Hammond 2009 slides on correspondences
Alternative proof of Berge's maximum theorem
Hammond 2009 slides on fixed point theorems
7. Difference and differential equations:
Readings: FMEA chs. 11, 5, 6, 7.
Hammond 2014 incomplete slides on difference equations
Hammond 2009 slides on difference equations
Hammond 2009 slides on differential equations
8. Optimal control:
Readings: FMEA, chs. 8, 9,10.
Hammond 2014 slides on calculus of variations
Hammond 2009 slides on optimal control
9. Probability:
Integral and measure, conditional probability and independence,
random variables and moments, laws of large numbers, central limit theorem.
Readings: Notes.
Hammond 2014 slides on probability
Carvajal 2009 notes
10. Stochastic dynamic programming:
Readings: FMEA ch. 12, plus notes.
Hammond 2014 slides
Hammond 2009 handwritten slides