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 2020/21.

Reading material

[E] Eriksen, Graduate Mathematics for Business, Economics and Finance, Cappelen Damm 2021 - List of corrections
[EP] Eriksen, Problems and Solutions - Graduate Mathematics for Business, Economics and Finance, Cappelen Damm (in print) - List of corrections
[WB] Eriksen, Digital Workbook for GRA 6035 Mathematics - workbook with problems/solutions. Solutions to advanced problems in Lecture 4.

Exams

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

Lecture plan

This is the lecture plan for the autumn semester 2021. Lecture 1-13 will consist of a 2h lecture in A1-040 (Fri 08-10) + 1h video lecture (Fri 11-12).
Office hours: Thu 1400-1600 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 1700-1945 (four sessions). In plenary sessions, I will solve selected problems. See the lecture plan below for details.
Exercise sessions: Mon 1700-1845 (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 09 - Aug 11	FORK 1003: Preparatory course in Mathematics, Economics and Econometrics
Fri Aug 27: 0800-0945, A1-040	Lecture 1: Linear systems and Gaussian elimination. Rank.	[E] 1.1 - 1.6	Problem set 1: Mon 17-19, C2-010/020/030/D1-065
Fri Sep 03: 0800-0945, A1-040	Lecture 2: Vectors and Linear Independence. Vector spaces.	[E] 2.1 - 2.4, 2.6 - 2.7	Problem set 2: Mon 17-19, C2-010/020/030/D1-065
Fri Sep 10: 0800-0945, A1-040	Lecture 3: Matrices, determinants and minors.	[E] 3.1 - 3.4	Problem set 3: Mon 17-19, C2-010/020/030/D1-065
Fri Sep 17: 0800-0945, A1-040	Lecture 4: Eigenvalues and eigenvectors. Diagonalization. Markov chains.	[E] 4.1 - 4.4	Problem set 4
Mon Sep 20: 1700-1945, A1-040	Plenary Session 1: Problems from Lecture 1-4	Key problems 1.1c, 1.3, 2.1, 2.3, 2.4, 3.3, 3.4bc, 4.1ef, 4.3, 4.4c [E] 3.11, 3.12b, 3.13, 3.14, 4.6 Midterm 10/2019 Q8, 01/2020 Q8
Fri Sep 24: 0800-0945, A1-040	Lecture 5: Definiteness of quadratic forms. Markov chains.	[E] 2.5, 4.4 - 4.6	Problem set 5: Mon 17-19, C2-010/020/030/D1-065
Fri Oct 01: 0800-0945, A1-040	Lecture 6: Unconstrained Optimization.	[E] 5.1 - 5.5, 5.7	Problem set 6: Mon 17-19, C2-010/020/030/D1-065
Thu Oct 07: 1800-2045, A1-040	Plenary Session 2: Problems from Lecture 4-6 + Midterm exam problems	Key problems 5.1, 6.1, 6.3, 6.4, 6.5 Midterm 01/2020 Q4,5,7 10/2019 Q7-8 01/2019 Q5,7 05/2018 Q2,5 10/2018 Q8 01/2017 Q8
Fri Oct 08: 0800-0945, A1-040	Lecture 7: Constrained Optimization. Lagrange problems.	[E] 6.1 - 6.4, 6.6	Problem set 7: Mon 17-19, C2-010/020/030/D1-065
Fri Oct 08: 1500-1600	Midterm exam - Solutions	All material from Lecture 1 - Lecture 6 is relevant for the midterm exam.
Fri Oct 15: 0800-0945, A1-040	Lecture 8: Kuhn-Tucker problems. Envelope Theorems.	[E] 6.5 - 6.6	Problem set 8: Mon 17-19, C2-010/020/030/D1-065
Fri Oct 22: 0800-0945, A1-040	Lecture 9: Matrix methods and optimization	[E] 5.6, 6.7	Problem set 9: Mon 17-19, C2-010/020/030/D1-065
Fri Oct 29: 0800-0945, A1-040	Lecture 10: First order differential equations. Separable and linear differential equations.	[E] 7.1 - 7.6	Problem set 10
Mon Nov 01: 1700-1945, A1-040	Plenary Session 3: Problems from Lecture 7-9	Key problems TBA [E] TBA Final Exam TBA
Fri Nov 05: 0800-0945, A1-040	Lecture 11: Exact differential equations. Stability. Second order differential equations.	[E] 7.7 - 7.10	Problem set 11: Mon 17-19, C2-010/020/030/D1-065
Fri Nov 12: 0800-0945, A1-040	Lecture 12: Difference equations.	[E] 8.1 - 8.3	Problem set 12: Mon 17-19, C2-010/020/030/D1-065
Fri Nov 19: 0800-0945, A1-040	Lecture 13: Systems of differential and difference equations.	[E] 9.1 - 9.5	Problem Set 13
Mon Nov 22: 1700-1945, C1-010	Plenary Session 4: Problems from Lecture 10-13	Key problems TBA [E] TBA Final Exam TBA
Fri Nov 26: 1500-1745, A1-040	Lecture 14: Revision, exam problems
Thu Dec 02: 0900-1200	Final exam

January 2022: Not confirmed	Midterm exam (retake)
January 2022: Not confirmed	Final exam (retake)