DRE 7017 Mathematics PhD

Course description for DRE 7017 Mathematics PhD, a course in mathematics for PhD students in Economics/Finance.
For material from 2018/19(the last time the course ran), see DRE 7017 Mathematics PhD 2018/19.

Reading

[FMEA] Sydsæter, Hammond, Seierstad, Strøm: Further Mathematics for Economic Analysis, 2nd Edition, Prentice Hall 2008 - main textbook.
[ME] Simon, Blume, Mathematics for Economists, International Student Edition, Norton 1994 - alternative main textbook (does not cover optimal control theory).
[GE] Eriksen, Linear systems and Gaussian elimination - notes on Gaussian elimination.
[ES] Eriksen, Notes on Euclidean spaces.
[DE] Eriksen, Differential equations with solutions to problems.

[S] Sundaram: A first course in optimization theory - additional text on optimization (not required for the course, but recommended).
de la Fuente: Mathematical methods and models for economists - additional text (difficult to read, not necessary for the course).
Rudin: Principles of mathematical analysis - additional text (difficult to read, not necessary for the course).

Exams

Written final exam (counts for 100%). Passing grades: A-E.
Previous exam problems:

Final exam:	Mock exam:
Final exam 13/10/2020 - Solutions
Final exam 02/10/2018 - Solutions
Final exam 01/06/2017 - Solutions
Final exam 14/10/2016 - Solutions
Final exam 17/09/2014 - Solutions	Mock exam 09/2014 - Solutions

Lecture plan

Lecture plan	Lecturer Karoline Moe	Reading	Exercises
Mon Aug 17: 1500-1645, C2-095	Lecture 1: Matrices. Eigenvalues and eigenvectors. Quadratic forms and definiteness.	[GE] 1-3 [FMEA] 1.1 - 1.7 [ME] 6 - 9, 23 [S] 1.3, 1.5	Problem Set 1 - Solutions
Thu Aug 20: 0900-1045, C2-095	Lecture 2: Euclidean spaces. Sequences. Topology.	[ES] 1-2 [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
Mon Aug 24: 1500-1645, C2-095	Lecture 3: Functions. Continuity. Derivatives.	[FMEA] 2.9, 13.3 [ME] 13.4, 14 [S] 1.4, 3	Problem Set 3 - Solutions
Thu Aug 27: 0900-1045, 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
Mon Aug 31: 1500-1645, 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
Thu Sep 03: 0900-1045, 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
Mon Sep 07: 1500-1645, C2-095	Lecture 7: Differential equations. Systems of differential equations. Linearization.	[FMEA] 5 - 7 [ME] 24 - 25 [DE] 1 - 2 Helpman, Innovation, imitation and IPR, Econometrica '93	Problem Set 7 - Solutions
Mon Sep 14: 1500-1645, C2-095	Lecture 8: Optimal control theory: Continuous case, Pontryagin's maximum principle.	[FMEA] 9 (8, 10)	Problem Set 8 - Solutions
Mon Sep 21: 1500-1645, C2-095	Lecture 9: Optimal control theory: Discret case, Bellman's equation.	[FMEA] 12 [S] 11- 12	Problem Set 9 - Solutions
Mon Sep 28: 1500-1645, C2-095	Lecture 10: Fixed points and fixed point theorems. Correspondences.	[FMEA] 14 [S] 9, 12	Problem Set 10 - Solutions
Tue Oct 13: 0900-1200	Final exam - Solutions