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 Autumn 2025

Lectures: Fri 09-12 (with some exceptions, see the lecture plan below). A 3h lecture in A1-040 covering the theory in the course.
Office hours: Fri 12-14 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 A1-040. 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: 08-11, A1-040	Lecture 1: Linear systems and Gaussian elimination. Rank.	[E] 1.1 - 1.6	Problem set 1: Fri 14-16 / Mon 16-18 B5y-160
Fri Aug 29: 12-15, A1-040	Lecture 2: Span and linear Independence. Orthogonal projection.	[E] 2.1 - 2.7	Problem set 2: Fri 16-18 / Mon 16-18 B5y-160
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 D3-020/30
Fri Sep 12: 09-12, A1-040	Lecture 4: Eigenvalues and eigenvectors. Diagonalization.	[E] 4.1 - 4.4	Problem set 4: Fri 14-16 D3-020/030
Mon Sep 15: 16-19, A1-040	Plenary Session 1: Key Problems 2.2, 2.4, 3.4c, 3.5, 4.1d, 4.2, 4.3, 4.4, 4.5 Midterms 01/'20 Q4, 10/'21 Q3, 01/'23 Q2-3 [E] 1.14, 2.14
Fri Sep 19: 09-12, A1-040	Lecture 5: Markov chains. Orthogonal diagonalization. Quadratic forms.	[E] 4.4 - 4.6	Problem set 5: Fri 14-16 / Mon 16-18 D3-020/030
Fri Sep 26: 09-12, A1-040	Lecture 6: Principal minors. Unconstrained Optimization. Convexity.	[E] 5.1 - 5.6	Problem set 6: Fri 14-16 / Mon 16-18 D3-020/030
Fri Oct 03: 09-12, A1-040	Lecture 7: Constrained Optimization. Lagrange problems.	[E] 6.1 - 6.4	Problem set 7: Fri 14-16 D3-020/030
Mon Oct 06: 16-19, A1-040	Plenary Session 2: Key Problems 5.2d, 5.4bc, 5.5af, 6.2bcd, 6.3bd, 6.4be, 6.5ab, 7.1c, 7.2b, 7.3b, 7.4cd Final exams 11/2023 Q3
Fri Oct 10: 09-12, A1-040	Lecture 8: Kuhn-Tucker problems. Minimum variance portfolios.	[E] 6.5	Problem set 8: Fri 14-16 / Mon 16-18 D3-020/030
Fri Oct 17: 09-12, A1-040	Lecture 9: Envelope theorems. Examples.	[E] 5.7, 6.6 - 6.7	Problem set 9: Fri 14-16 / Mon 16-18 D3-020/030
Fri Oct 24: 10-13, A1-040	Lecture 10: First order differential equations. Stability.	[E] 7.1 - 7.8	Problem set 10: Fri 14-16 D3-020/030
Thu Oct 30: 16-19, A1-040	Plenary Session 3: Key Problems 6.4be, 7.4cd, 8.3b, 8.4, 9.3, 9.4 Final exams 01/2024 Q4, 12/2021 Q3
Fri Oct 31: 10-13, A1-040	Lecture 11: Second order differential equations. Systems of differential equations.	[E] 7.9 - 7.10, 9.1 - 9.3	Problem set 11: Fri 14-16 / Mon 16-18 D3-020/030
Fri Nov 07: 09-12, A1-040	Lecture 12: Difference equations. Systems of difference equations.	[E] 8.1 - 8.4, 9.4 - 9.5	Problem set 12: Fri 16-18 Fri D3-020/030
Mon Nov 10: 16-19, A1-040	Plenary Session 4: Key Problems 10.2c, 10.3b, 10.4b, 11.4b, 12.1f Final exams 11/2022 Q1, 01/2017 Q1, 12/2016 Q1-4
Fri Nov 14: 09-12, A1-040	Lecture 13: Exam problems: Final exam 11/2024		Problem set 13: Fri 14-16 / Mon 16-18 D3-020/030
Fri Nov 21: 10-13, A1-040	Lecture 14: Revision. More exam problems from Final 11/2023		Problem set 14: Fri 14-16 D3-020/030
Mon Nov 24: 09-14	Final exam for GRA6035 and ELE3781 - Solutions - Results

Fri Jan 09 2026: 09-14	Final exam (retake for GRA6035) - Solutions