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 2019/20.

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.
[LN] Eriksen, Lecture Notes. My notes for the course (work in progress, finished chapters/lectures will be available from It's Learning).

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

This is a preliminary lecture plan for the autumn 2020. There may be changes due to corona/covid-19.
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.

Lecture plan	Lecturer Eivind Eriksen (Office B4-032), Office hours: Thu 12-14	Reading	Exercises
Aug 03 - Aug 05	FORK 1003: Preparatory course, Mathematics
Fri Aug 21: 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	Problem set 1: Mon 17-19, C2-020/030
Fri Aug 28: 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	Problem set 2: Mon 17-19, C2-020/030
Fri Sep 04: 0800-1045, A1-040	Lecture 3: Vectors and Linear Independence.	[ME] 10.1 - 10.3, (10.4 - 10.7), 11.1	Problem set 3: Mon 17-19, C2-020/030
Fri Sep 11: 0800-1045, A1-040	Lecture 4: Eigenvalues and eigenvectors. Diagonalization.	[ME] 23.1 - 23.4, 23.6 -23.7, (23.9)	Problem set 4
Mon Sep 14: 1700-1945, A1-040	Plenary Session 1: Problems from Lecture 1-4	Key problems TBA [WB] TBA Midterm Exam TBA
Fri Sep 18: 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)	Problem set 5: Mon 17-19, C2-020/030
Fri Sep 25: 0800-1045, A1-040	Lecture 6: Unconstrained Optimization.	[ME] 14.1 - 14.4, 14.8, 17.1 - 17.5, 30.1	Problem set 6: Mon 17-19, C2-020/030
Fri Oct 02: 0800-1045, A1-040	Lecture 7: Constrained Optimization. First Order Conditions.	[ME] 18.1 - 18.7, (12.3 - 12.5), 21.1	Problem set 7
Mon Oct 05: 1700-1945, A1-040	Plenary Session 2: Problems from Lecture 5-6 + Midterm exam 10/2018	Key problems TBA [WB] TBA Midterm Exam TBA
Fri Oct 09: 0800-1045, A1-040	Lecture 8: Constrained Optimization. Second Order Conditions.	[ME] 19.1, (19.4)	Problem set 8: Mon 17-19, C2-020/030
TBA: Not confirmed	Midterm exam	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 16: 0800-1045, A1-040	Lecture 9: Envelope Theorems.	[ME] 19.2 - 19.3, (19.4 - 19.6), (Kelly Criterion)	Problem set 9: Mon 17-19, C2-020/030
Fri Oct 23: 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)	Problem set 10
Mon Oct 26: 1700-1945, A1-040	Plenary Session 3: Problems from Lecture 7-9	Key problems TBA [WB] TBA Final Exam TBA
Fri Oct 30: 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)	Problem set 11: Mon 17-19, C2-020/030
Fri Nov 06: 0800-1045, A1-040	Lecture 12: Systems of differential equations. Difference equations.	[DE] 2.1 - 2.3 [ME] 23.2	Problem set 12: Mon 17-19, C2-020/030
Mon Nov 09: 1700-1945, A1-040	Plenary Session 4: Problems from Lecture 10-12	Key problems TBA [DE] TBA Final Exam TBA
Fri Nov 13: 0800-1045, A1-040	Lecture 13: Final exam 11/2019.
Fri Nov 20: 0800-1045, A1-040	Lecture 14: Review of important topics for the final exam.
TBA: Not confirmed	Final exam

January 2020: Not confirmed	Midterm exam (retake)
January 2020: Not confirmed	Final exam (retake)