GRA 6035 Mathematics 2018/19

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 1700-1845 (weekly). In exercise sessions, you will work with problems, and teaching assistants (and usually also the lecturer) will be available to help.

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 - Solutions
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 - Solutions
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 - Solutions
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 - Solutions
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 - Solutions
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 - Solutions
Fri Oct 05: 0800-1045, A1-040	Lecture 7: Constrained Optimization. First Order Conditions.	[ME] 18.1 - 18.7, (12.3 - 12.5), 21.1	Problems for Lecture 7 - Solutions
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 - Solutions
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.	[ME] 19.2 - 19.3, (19.4 - 19.6), (Kelly Criterion)	Problems for Lecture 9 - Solutions
Fri Oct 26: 0800-1045, A1-040	Lecture 10: First order differential equations. Separable and linear differential equations.	[DE] 1.1 - 1.6 [ME] 24.1 - 24.2, (24.4 - 24.6)	Problems for Lecture 10 - Solutions
Mon Oct 29: 1700-1945, A1-040	Plenary Session 3: Problems from Lecture 7-9 + Final exam 01/2017	Key problems 7.3b, 7.4b, 8.3, 9.1, 9.3 [WB] 7.1, 8.13 Final Exam 01/2017 3-4 12/2015 4
Fri Nov 02: 0800-1045, A1-040	Lecture 11: Exact differential equations. Stability. Second order differential equations.	[DE] 1.6 - 1.10 [ME] 24.1 - 24.3, (24.4 - 24.6)	Problems for Lecture 11 - Solutions
Fri Nov 09: 0800-1045, A1-040	Lecture 12: Systems of differential equations. Difference equations.	[DE] 2.1 - 2.3 [ME] 23.2	Problems for Lecture 12 - Solutions
Mon Nov 12: 1700-1945, A1-040	Plenary Session 4: Problems from Lecture 10-12	Key problems 10.2c, 11.2c, 11.3b [DE] 1.24, 2.3 Mock Exam 11/2017 1, 3 Final exam 01/2018 2
Fri Nov 16: 0800-1045, A1-040	Lecture 13: Final exam 11/2017.
Fri Nov 23: 0800-1045, A1-040	Lecture 14: Final exam 11/2017 4c. Review of important topics for the final exam.
Tue Nov 27: 0900-1200	Final exam 27/11/2018 - Solutions - Results

	Common mistakes at the final exam with some guidelines for the retake exam
Mon Jan 07: 0900-1000	Midterm exam 07/01/2019 - Solutions
Mon Jan 07: 1300-1600	Final exam 07/01/2019 - Solutions
	There will not be any retake exams for GRA 6035 Mathematics in May/June 2019.