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 2023/24.

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 2024. 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 and Fri 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 05 - Aug 07	FORK 1003: Preparatory course in Mathematics, Economics and Econometrics
Fri Aug 23: 12-15, A1-040	Lecture 1: Linear systems and Gaussian elimination. Rank.	[E] 1.1 - 1.6	Problem set 1: Fri 16-18 D1-065 + Mon 16-18, C2-010/D1-065
Fri Aug 30: 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 D1-065 + Mon 16-18, C2-010/D1-065
Fri Sep 06: 12-15, A1-040	Lecture 3: Matrices, determinants and minors.	[E] 3.1 - 3.4	Problem set 3: Fri 16-18 D1-065 + Mon 16-18, C2-010/D1-065
Fri Sep 13: 12-15, A1-040	Lecture 4: Eigenvalues and eigenvectors. Diagonalization. Powers.	[E] 4.1 - 4.4	Problem set 4: Fri 16-18 D1-065
Mon Sep 16: 16-19, A1-040	Plenary Session 1: Problems from Lecture 1-4 Key problems 1.4, 2.1bdf, 2.3, 2.4cd, 2.5bc, 3.2bc, 3.3b, 3.4b, 4.1def, 4.2, 4.3, 4.4, 4.5 Midterm 01/'20 Q4,Q8, 10/'22 Q6,Q8
Fri Sep 20: 12-15, A1-040	Lecture 5: Markov chains. Definiteness of quadratic forms. Orthogonal diagonalization.	[E] 2.5, 4.4 - 4.6	Problem set 5: Fri 16-18 D1-065 + Mon 16-18, C2-010/D1-065
Fri Sep 27: 12-15, A1-040	Lecture 6: Orthogonal diagonalization. Unconstrained Optimization. Convexity.	[E] 5.1 - 5.6	Problem set 6: Fri 16-18 D1-065 + Mon 16-18, C2-010/D1-065
Fri Oct 04: 10-11	Mock Midterm Exam - Solutions
Fri Oct 04: 12-15, A1-040	Lecture 7: Constrained Optimization. Lagrange problems.	[E] 6.1 - 6.4	Problem set 7: Fri 16-18 D1-065
Mon Oct 07: 16-19, A1-040	Plenary Session 2: Problems from Lecture 5-7 Key problems 5.1cde, 5.2d, 5.3, 5.4bc, 5.5bf, 6.2b, 6.3cd, 6.4bce, 6.5ab, 7.1d, 7.2b, 7.3b, 7.4d
Fri Oct 11: 12-15, A1-040	Lecture 8: Kuhn-Tucker problems.	[E] 6.5	Problem set 8: Fri 16-18 D1-065 + Mon 16-18, C2-010/D1-065
Fri Oct 18: 12-15, A1-040	Lecture 9: Envelope theorems. Minimum variance portfolio.	[E] 5.7, 6.6 - 6.7	Problem set 9: Fri 16-18 D1-065 + Mon 16-18, C2-010/D1-065
Fri Oct 25: 12-15, A1-040	Lecture 10: First order differential equations.	[E] 7.1 - 7.7	Problem set 10: Fri C2-020/16-18 D1-065
Thu Oct 31: 16-19, A1-040	Plenary Session 3: Problems from Lecture 8-10 Key problems 8.1b, 8.2, 9.1c, 9.2bc, 10.2c, 10.3c, 10.4bc Exam problems 01/'24 Q4e, 01/'22 Q3
Fri Nov 01: 12-15, A1-040	Lecture 11: Stability. Second order differential equations.	[E] 7.8 - 7.10	Problem set 11: Fri 16-18 Fri C2-020/D1-065 + Mon 16-18, C2-010/D1-065
Fri Nov 08: 12-15, A1-040	Lecture 12: Systems of differential equations.	[E] 9.1 - 9.3	Problem set 12: Fri 16-18 Fri C2-020/D1-065
Mon Nov 11: 16-19, A1-040	Plenary Session 4: Problems from Lecture 11-12 + Exam problems Key problems 11.3c, 12.2ab, 12.3, 12.4bc, 12.5be Exam problems 01/'24 Q1d, Q3d, 11/'19 Q4bc 11/'18 Q2c,Q5
Fri Nov 15: 12-15, A1-040	Lecture 13: Difference equations. Systems of difference equations.	[E] 8.1 - 8.4, 9.4 - 9.5	Problem set 13: Fri 16-18 Fri C2-020/D1-065 + Mon 16-18, C2-010/D1-065
Fri Nov 22: 12-15, A1-040	Lecture 14: Revision, Exam problems: Final exam 11/2023		Extra exercise session: Fri C2-020/16-18 D1-065
Mon Nov 25: 09-14	Final exam for GRA6035 and ELE3781 - Solutions - Results

Fri Jan 10 2025: 09-14	Final exam (retake for GRA6035)