GRA 6035 Mathematics

Course description for GRA 6035 Mathematics, a core course in mathematics for MSc Business/Finance. It covers linear algebra and matrix methods, optimisation in several real variables, and differential and difference equations.
For material from last year's course, see GRA 6035 Mathematics 2017/18.

Reading material

[ME] Simon, Blume, Mathematics for Economists, International Student Edition, Norton 1994 - main textbook.
[WB] Eriksen, Digital Workbook for GRA 6035 Mathematics - workbook with problems/solutions. Solutions to advanced problems in Lecture 4.
[DE] Eriksen, Differential Equations - notes on differential equations. Solutions to problems in [DE].
[GE] Eriksen, Linear Systems and Gaussian Elimination - notes on Gaussian elimination. Problems/solutions included in [WB] Lecture 1.

Exams

Multiple choice midterm exam (counts for 20%), and written final exam (counts for 80%). There are re-take exams in the spring semester. Both exams must be passed.
Previous exam problems with solutions.

Lecture plan

Office hours: Thu 1200-1400 at my office B4-032. I have an open door policy, which means that you may come to my office at other times (no appointment needed).
Lectures: Fri 0800-1045 (weekly), Plenary sessions: Mon 1700-1945 (four sessions). In plenary sessions, I will solve selected problems. See the lecture plan below for details.
Exercise sessions: Mon/Tue 1700-1845 (weekly). In exercise sessions, you will work with problems, and teaching assistants (and usually also the lecturer) will be available to help. See the plan for exercise sessions for details.

Date:	Topic:	Reading:	Exercises:
Jul 30 - Aug 10	FORK 1003: Preparatory course, Mathematics
Fri Aug 24: 0800-1045, A1-040	Lecture 1: Linear systems and Gaussian elimination. Rank.	[ME] 6.1, (6.2), 7.1 - 7.4, (7.5) [GE] 1-3	Problems for Lecture 1
Fri Aug 31: 0800-1045, A1-040	Lecture 2: Matrices and matrix algebra. Determinants and minors.	[ME] 8.1 - 8.4, (8.5 - 8.6), 9.1 - 9.2, (9.3), 26.1 - 26.3, (26.4), 26.5	Problems for Lecture 2
Fri Sep 07: 1400-1645, A1-040	Lecture 3: Vectors and Linear Independence.	[ME] 10.1 - 10.3, (10.4 - 10.7), 11.1	Problems for Lecture 3
Fri Sep 14: 0800-1045, A1-040	Lecture 4: Eigenvalues and eigenvectors. Diagonalization.	[ME] 23.1 - 23.4, 23.6 -23.7, (23.9)	Problems for Lecture 4
Mon Sep 17: 1700-1945, A1-040	Plenary Session 1: Problems from Lecture 1-4	Key problems 3.3, 4.1de, 4.3 [WB] 1.15, 2.18b, 3.12, 3.14, 4.3b, 4.5, 4.6, 4.9, 4.10 Midterm Exam 10/2017 Question 1-5
Fri Sep 21: 0800-1045, A1-040	Lecture 5: Markov chains. Quadratic Forms and Definiteness.	[ME] 13.1 - 13.5, 16.1 - 16.4, 23.8 (Google's Pagerank algorithm)	Problems for Lecture 5
Fri Sep 28: 0800-1045, A1-040	Lecture 6: Unconstrained Optimization.	[ME] 14.1 - 14.4, 14.8, 17.1 - 17.5, 30.1	Problems for Lecture 6
Fri Oct 05: 0800-1045, A1-040	Lecture 7: Constrained Optimization. First Order Conditions.	[ME] 14.1 - 14.4, 14.8, 17.1 - 17.5, 30.1	Problems for Lecture 7
Mon Oct 08: 1700-1945, A1-040	Plenary Session 2: Problems from Lecture 5-6 + Midterm exam 10/2017	Key problems 5.1cd, 5.3e, 6.1d, 6.2, 6.4de, 7.2 [WB] 5.8, 5.9, 5.15, 6.1c, 6.2a, 6.22 Midterm Exam 10/2017 6-8, 10/2015 1-8
Fri Oct 12: 0800-1045, A1-040	Lecture 8: Constrained Optimization. Second Order Conditions.	[ME] 19.1, (19.4)	Problems for Lecture 8
Fri Oct 12: 1500-1600	Midterm exam 12/10/2018 - Solutions - Results	All material from Lecture 1-6, including Problems for Lecture 1-6 and Review of Lecture 6, is relevant for the midterm exam
Fri Oct 19: 0800-1045, A1-040	Lecture 9: Envelope Theorems. Bordered Hessians.	[ME] 19.2 - 19.3, (19.4 - 19.6)	[WB] Lecture 9
Fri Oct 26: 0800-1045, A1-040	Lecture 10: First order differential equations.	[ME] 24.1 - 24.2, (24.4 - 24.6) [DE] 1.1 - 1.7	[WB] Lecture 10
Mon Oct 29: 1700-1945, A1-040	Plenary Session 3: Problems from Lecture 7-9
Fri Nov 02: 0800-1045, A1-040	Lecture 11: Stability. Second order differential equations. Systems of differential equations.	[ME] 24.1 - 24.3, (24.4 - 24.6) [DE] 1.8 - 1-10, 2.1 - 2.2	[WB] Lecture 11
Fri Nov 09: 0800-1045, A1-040	Lecture 12: Systems of differential equations. Difference Equations.	[ME] 23.2 [DE] 2.1 - 2.3	[WB] Lecture 12
Mon Nov 12: 1700-1945, A1-040	Plenary Session 4: Problems from Lecture 10-12
Fri Nov 16: 0800-1045, A1-040	Lecture 13: TBA
Fri Nov 23: 0800-1045, A1-040	Lecture 14: Review Lecture. Final exam 11/2017.
Tue Nov 27: 0900-1200	Final exam.

Mon Jan 07: 0900-1000	Retake midterm exam.
Mon Jan 07: 1300-1600	Retake final exam.
	There will not be any retake exams for GRA 6035 Mathematics in May/June 2019.