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 2022/23.

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 2023. Lecture 1-14 will consist of a 3h lecture in A1-040 (Fri 12-15).
Office hours: Mon 12-14 and Fri 10-12 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 (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 07 - Aug 09	FORK 1003: Preparatory course in Mathematics, Economics and Econometrics
Fri Aug 25: 12-15, A1-040	Lecture 1: Linear systems and Gaussian elimination. Rank.	[E] 1.1 - 1.6	Problem set 1: Mon 16-18, C2-010/020/030/D1-065
Fri Sep 01: 12-15, A1-040	Lecture 2: Vectors and vector spaces. Linear Independence, bases and dimension.	[E] 2.1 - 2.4, 2.6 - 2.7	Problem set 2: Mon 16-18, C2-010/020/030/D1-065
Fri Sep 08: 12-15, A1-040	Lecture 3: Matrices, determinants and minors.	[E] 3.1 - 3.4	Problem set 3: Mon 16-18, C2-010/020/030/D1-065
Fri Sep 15: 12-15, A1-040	Lecture 4: Eigenvalues and eigenvectors. Diagonalization. Powers.	[E] 4.1 - 4.4	Problem set 4
Mon Sep 18: 16-19, A1-040	Plenary Session 1: Problems from Lecture 1-4	Key problems 2.1bdf, 2.2, 2.4, 3.3bc, 3.4bc, 4.1def, 4.2d, 4.3, 4.4b, 4.5b [E] 2.7, 2.14 Midterm 10/2022 Q7
Fri Sep 22: 12-15, A1-040	Lecture 5: Markov chains. Definiteness of quadratic forms. Orthogonal diagonalization.	[E] 2.5, 4.4 - 4.6	Problem set 5: Mon 16-18, C2-010/020/030/D1-065
Fri Sep 29: 12-15, A1-040	Lecture 6: Ortogonal diagonalization. Unconstrained Optimization. Convexity.	[E] 5.1 - 5.6	Problem set 6: Mon 16-18, C2-010/020/030/D1-065
Fri Oct 06: 12-15, A1-040	Lecture 7: Constrained Optimization. Lagrange problems.	[E] 6.1 - 6.4	Problem set 7
Mon Oct 09: 16-19, A1-040	Plenary Session 2: Problems from Lecture 5-7 + Midterm exam problems	Key problems 5.1e, 5.2de, 5.3cd, 5.4, 5.5bc, 6.1, 6.2, 6.3, 6.4, 6.5, 7.2b
Thu Oct 12: 17-18	Mock midterm exam - Solutions	All material from Lecture 1-6 is relevant for the mock midterm exam
Fri Oct 13: 12-15, A1-040	Lecture 8: Kuhn-Tucker problems. Envelope Theorems.	[E] 6.5 - 6.6	Problem set 8: Mon 16-18, C2-010/020/030/D1-065
Fri Oct 20: 12-15, A1-040	Lecture 9: Envelope Theorems. Matrix methods. Note on Minimum variance portfolios	[E] 5.6, 6.6 - 6.7	Problem set 9: Fri 16-18 D1-065, Mon 16-18, C2-010/020/D1-065
Fri Oct 27: 12-15, A1-040	Lecture 10: First order differential equations.	[E] 7.1 - 7.7	Problem set 10: Fri 16-18 D1-065
Mon Oct 30: 16-19, A1-040	Plenary Session 3: Problems from Lecture 7-9	Key problems 7.1, 7.3b, 7.4, 8.1b, 8.2, 9.2, 9.3, 9.4 Final exam 04/2022 Q3
Fri Nov 03: 12-15, A1-040	Lecture 11: Stability. Second order differential equations.	[E] 7.8 - 7.10	Problem set 11: Fri 16-18 D1-065, Mon 16-18, C2-010/020/030/D1-065
Fri Nov 10: 12-15, A1-040	Lecture 12: Systems of differential equations.	[E] 9.1 - 9.3	Problem set 12: Fri 16-18 D1-065
Mon Nov 13: 16-19, A1-040	Plenary Session 4: Problems from Lecture 10-12	Key problems 10.1c, 10.2bc, 10.3, 10.4, 11.1c, 11.2bcd, 11.3, 12.1c, 12.4 Final exam 12/2021 Q2
Fri Nov 17: 12-15, A1-040	Lecture 13: Difference equations. Systems of difference equations.	[E] 8.1 - 8.4, 9.4 - 9.5	Problem set 13 - Solutions: Fri 16-18 D1-065, Mon 16-18, C2-010/020/030/D1-065
Fri Nov 24: 12-15, A1-040	Lecture 14: Revision, Final exam 11/2022		Extra exercise session: Fri 16-18 D1-065
Mon Nov 27: 14-16	Extra exercise session (Room A2 Blue 1 / Blue 4)
Tue Nov 28: 09-14	Final exam for GRA6035 and ELE3781 - Solutions

Wed Jan 10 (not confirmed)	Final exam (retake for GRA6035)