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 2024/25.

Reading material

[E] Eriksen, Graduate Mathematics for Business, Economics and Finance, Cappelen Damm 2021 - List of corrections
[EP] Eriksen, Graduate Mathematics for Business, Economics and Finance - Problems and solutions, Cappelen Damm 2021 - List of corrections

Exams

A 5h written final exam (counts for 100%). There is a re-take exam in the spring semester.
Previous exam problems with solutions.

Lecture plan

This is the lecture plan for the autumn semester 2025. Lecture 1-14 will consist of a 3h lecture in A1-040 on Fri at 09-12 (with some exceptions, see below).
Office hours: Fri 13-15 at my office B3y-085. I have an open door policy, which means that you may come to my office at other times (no appointment needed).
Plenary sessions: Mon 16-19 (four sessions). In plenary sessions, I will solve selected problems. See the lecture plan below for details.
Exercise sessions: Mon 16-18 and Fri 14-16 (weekly). In exercise sessions, you will work with problems, and teaching assistants will be available to help. See the lecture plan below for details.

Date:	Topic:	Reading:	Exercises:
Aug 04 - Aug 06	FORK 1003: Preparatory course in Mathematics, Economics and Econometrics
Fri Aug 22: 09-12, A1-040	Lecture 1: Linear systems and Gaussian elimination. Rank.	[E] 1.1 - 1.6	Problem set 1: Fri 14-16 / Mon 16-18 D3-020
Fri Aug 29: 12-15, A1-040	Lecture 2: Vectors spaces. Span and linear Independence. Orthogonal projection.	[E] 2.1 - 2.7	Problem set 2: Fri 16-18 / Mon 16-18 D3-020
Fri Sep 05: 09-12, A1-040	Lecture 3: Matrices, determinants and minors.	[E] 3.1 - 3.4	Problem set 3: Fri 14-16 / Mon 16-18 D3-020
Fri Sep 12: 09-12, A1-040	Lecture 4: Eigenvalues and eigenvectors. Diagonalization. Powers.	[E] 4.1 - 4.4	Problem set 4: Fri 14-16 D3-020
Mon Sep 15: 16-19, A1-040	Plenary Session 1: Problems from Lecture 1-4
Fri Sep 19: 09-12, A1-040	Lecture 5: Markov chains. Quadratic forms. Orthogonal diagonalization.	[E] 2.5, 4.4 - 4.6	Problem set 5: Fri 14-16 / Mon 16-18 D3-020
Fri Sep 26: 09-12, A1-040	Lecture 6: Unconstrained Optimization. Convexity.	[E] 5.1 - 5.6	Problem set 6: Fri 14-16 / Mon 16-18 D3-020
Fri Oct 03: 09-12, A1-040	Lecture 7: Constrained Optimization. Lagrange problems.	[E] 6.1 - 6.4	Problem set 7: Fri 14-16 D3-020
Mon Oct 06: 16-19, A1-040	Plenary Session 2: Problems from Lecture 5-7
Fri Oct 10: 10-13, A1-040	Lecture 8: Kuhn-Tucker problems.	[E] 6.5	Problem set 8: Fri 14-16 / Mon 16-18 D3-020
Fri Oct 17: 09-12, A1-040	Lecture 9: Envelope theorems. Minimum variance portfolio.	[E] 5.7, 6.6 - 6.7	Problem set 9: Fri 14-16 / Mon 16-18 D3-020
Fri Oct 24: 10-13, A1-040	Lecture 10: First order differential equations.	[E] 7.1 - 7.7	Problem set 10: Fri 14-16 D3-020
Thu Oct 30: 16-19, A1-040	Plenary Session 3: Problems from Lecture 8-10
Fri Oct 31: 10-13, A1-040	Lecture 11: Stability. Second order differential equations.	[E] 7.8 - 7.10	Problem set 11: Fri 14-16 / Mon 16-18 D3-020
Fri Nov 07: 09-12, A1-040	Lecture 12: Systems of differential equations.	[E] 9.1 - 9.3	Problem set 12: Fri 16-18 Fri D3-020
Mon Nov 10: 16-19, A1-040	Plenary Session 4: Problems from Lecture 11-12 + Exam problems
Fri Nov 14: 09-12, A1-040	Lecture 13: Difference equations. Systems of difference equations.	[E] 8.1 - 8.4, 9.4 - 9.5	Problem set 13: Fri 14-16 / Mon 16-18 D3-020
Fri Nov 21: 10-13, A1-040	Lecture 14: Revision, Exam problems: Final exam 11/2023		Extra exercise session: Fri 14-16 D3-020
Nov/Dec 2025	Final exam for GRA6035 and ELE3781

Jan 2026	Final exam (retake for GRA6035)