DRE7017 Mathematics, PhD - 2016/17

Lecture plans for DRE 7017 Mathematics PhD for the adacemic years 2012-2016

Reading

Compulsory reading:

Sydsæter, Hammond, Seierstad, Strøm: Further Mathematics for Economic Analysis, 2nd Edition, Prentice Hall 2008 [FMEA]
Simon, Blume: Mathematics for Economists, International Student Edition, Norton 1994 [ME]

There is a certain overlap between [FMEA] and [ME]. Some advanced topics (in particular optimal control theory) are only covered in [FMEA], while [ME] is better and more complete for many of the more basic themes, and with many more examples and exercises. The following books are also useful (the book by Sundaram is especially recommended; the others are more difficult to read):

Sundaram: A first course in optimization theory [S]
de la Fuente: Mathematical methods and models for economists
Rudin: Principles of mathematical analysis

Lecture Plan

Date:	Topic:	Reading:	Problem Sets:
Mon Aug 22 1400-1600 : C2-095	Lecture 1 Matrices. Eigenvalues and eigenvectors. Quadratic forms and definiteness.	[LSGE] Notes on Gaussian elimination [FMEA] 1.1 - 1.7 [ME] 6 - 9, 23 [S] 1.3, 1.5	Problem Set 1 Solutions Problem Set 1
Wed Aug 24 1400-1600 : C2-095	Lecture 2 Euclidean spaces. Sequences. Topology.	[ES] Notes on Euclidean Spaces [FMEA] A.1 - A.3, 13.1 -13.2 [ME] A1, 10, 12, 29 [S] A, C, 1.1 - 1.2	Problem Set 2 Solutions Problem Set 2
Fri Aug 26 1000-1200 : C2-095	Lecture 3 Functions. Continuity. Derivatives.	[FMEA] 2.9, 13.3 [ME] 13.4, 14 [S] 1.4, 3	Problem Set 3 Solutions Problem Set 3
Mon Aug 29 1400-1600 : C2-095	Lecture 4 Convex sets. Separation theorems. (Quasi)Convex/concave functions.	[FMEA] 2.2 - 2.3, 2.5, 13.5 - 13.6 [ME] 21.1 - 21.2 [S] 1.2, 1.6, 7.1 - 7.2, 8.1 - 8.3	Problem Set 4 Solutions Problem Set 4
Fri Sep 02 1000-1200 : C2-095	Lecture 5 Optimization problems. Unconstrained optimization	[FMEA] 3.1 - 3.2 [ME] 17 [S] 2, 4, 7.3 - 7.6, 8.4 - 8.7	Problem Set 5 Solutions Problem Set 5
Mon Sep 05 1400-1600 : C2-095	Lecture 6 Constrained optimization. Lagrange and Kuhn-Tucker problems.	[FMEA] 3.3 - 3.6 [ME] 18 - 19 [S] 5 - 6, 7.7, 8.8	Problem Set 6 Solutions Problem Set 6
Fri Sep 09 1000-1200 : C2-095	Lecture 7 Differential equations. Systems of differential equations. Linearization.	[FMEA] 5 - 7 [ME] 24 - 25 Helpman, Innovation, imitation and IPR, Econometrica '93	Problem Set 7 Solutions Problem Set 7
Mon Sep 12 1400-1600 : C2-095	Lecture 8 Optimal control theory: Continuous case, Pontryagin's maximum principle	[FMEA] 9 (8, 10)	Problem Set 8 Solutions Problem Set 8
Fri Sep 16 1000-1200 : C2-095	Lecture 9 Optimal control theory: Discret case, Bellman's equation	[FMEA] 12 [S] 11- 12	Problem Set 9 Solutions Problem Set 9
Mon Sep 19 1400-1600 : C2-095	Lecture 10 Fixed points and fixed point theorems. Correspondences.	[FMEA] 14 [S] 9, 12	Problem Set 10 Solutions Problem Set 10
Fri Oct 14	Exam 14/10/2016 - Solutions