# 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 |