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 2021/22.

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 1h midterm exam (counts for 20%), and a 3h written final exam (counts for 80%). There are re-take exams in the spring semester. Both midterm and final exam must be passed.
Previous exam problems with solutions.

Lecture plan

This is the lecture plan for the autumn semester 2022. Lecture 1-14 will consist of a 3h lecture in A1-040 (Fri 14-17).
Office hours: Mon 12-14 and Fri 10-12 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).
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 08 - Aug 10	FORK 1003: Preparatory course in Mathematics, Economics and Econometrics
Fri Aug 26: 14-17, 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 02: 14-17, A1-040	Lecture 2: Vectors and Linear Independence. Vector spaces.	[E] 2.1 - 2.4, 2.6 - 2.7	Problem set 2: Mon 16-18, C2-010/020/030/D1-065
Fri Sep 09: 14-17, 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 16: 14-17, A1-040	Lecture 4: Eigenvalues and eigenvectors. Diagonalization. Markov chains.	[E] 4.1 - 4.4	Problem set 4
Mon Sep 19: 16-19, A1-040	Plenary Session 1: Problems from Lecture 1-4	Key problems 2.2, 2.3a, 2.4ef, 3.1, 3.3, 3.4, 4.3, 4.4, 4.5 [E] 4.8b Midterm 01/2022 Q4-5
Fri Sep 23: 14-17, A1-040	Lecture 5: Definiteness of quadratic forms. Markov chains.	[E] 2.5, 4.4 - 4.6	Problem set 5: Mon 16-18, C2-010/020/030/D1-065
Fri Sep 30: 14-17, A1-040	Lecture 6: Unconstrained Optimization.	[E] 5.1 - 5.5, 5.7	Problem set 6: Mon 16-18, C2-010/020/030/D1-065
Fri Oct 07: 14-17, A1-040	Lecture 7: Constrained Optimization. Lagrange problems.	[E] 6.1 - 6.4, 6.6	Problem set 7
Mon Oct 10: 16-19, A1-040	Plenary Session 2: Problems from Lecture 4-6 + Midterm exam problems	Key problems 6.1, 6.2a, 6.3c, 6.5b Midterm Mock midterm 10/2022 Q2,4-11,14,17,19,21-22 Midterm 01/2020 Q7
Fri Oct 14: 09-10	Midterm exam for GRA6035 - Solutions - Results	All material from Lecture 1 - Lecture 6 is relevant for the midterm exam.
Fri Oct 14: 14-17, 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 21: 14-17, A1-040	Lecture 9: Matrix methods and optimization	[E] 5.6, 6.7	Problem set 9: Mon 16-18, C2-010/020/030/D1-065
Fri Oct 28: 14-17, A1-040	Lecture 10: First order differential equations.	[E] 7.1 - 7.7	Problem set 10
Mon Oct 31: 16-19, A1-040	Plenary Session 3: Problems from Lecture 7-9	Key problems 7.3, 7.4, 8.1, 8.2, 9.1 - 9.4 [E] 6.3 - 6.5 Final exams 11/2017 3-4, 11/2018 3-4, 01/2019 5, 11/2019 4, 01/2022 3, 04/2022 1,3
Fri Nov 04: 14-17, A1-040	Lecture 11: Stability. Second order differential equations.	[E] 7.8 - 7.10	Problem set 11: Mon 16-18, C2-010/020/030/D1-065
Fri Nov 11: 14-17, A1-040	Lecture 12: Systems of differential equations.	[E] 9.1 - 9.3	Problem set 12
Mon Nov 14: 16-19, A1-040	Plenary Session 4: Problems from Lecture 10-12	Key problems 10.2c, 10.3b, 10.4c, 11.2d, 11.3, 12.1a, 12.3 Final exams 04/2022 2ad, 01/2022 1,2c 01/2020 3a, 12/2015 2c
Fri Nov 18: 14-17, A1-040	Lecture 13: Difference equations. Systems of difference equations.	[E] 8.1 - 8.4, 9.4 - 9.5	Problem set 13: Mon 16-18, C2-010/020/030/D1-065
Fri Nov 25: 14-17, A1-040	Lecture 14: Revision, exam problems from final exam 12/2021		Extra exercise session: Mon 16-18, D1-065
Wed Nov 30: 14-17	Final exam for GRA6035 and ELE3781 - Solutions

Jan 09 2023: 17-18	Midterm exam (retake for GRA6035)
Jan 09 2023: 09-12	Final exam (retake for GRA6035)