DRE7017 Mathematics, PhD - 2016/17

Reading

Compulsory reading: 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):

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