DRE7017 Mathematics, PhD - 2014/15

Syllabus

Syllabus

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:
Aug 18 1000-1200 : 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
Aug 19 1000-1200 : A2-030	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
Aug 20 1000-1200 : C2-065	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
Aug 22 1000-1200 : C2-045	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
Aug 25 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
Aug 27 1000-1200 : C2-065	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
Aug 29 1000-1200 : C2-045	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
Sep 01 1000-1200 : C2-095	Lecture 8 Optimal control theory: Continuous case, Pontryagin's maximum principle	[FMEA] 9 (8, 10)	Problem Set 8 Solutions Problem Set 8
Sep 02 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
Sep 03 1000-1200 : C2-065	Lecture 10 Fixed points and fixed point theorems. Correspondences.	[FMEA] 14 [S] 9, 12	Problem Set 10 Solutions Problem Set 10
Sep 17 0900-1200	Exam 17/09/2014 - Solutions Mock exam 09/2014 - Solutions