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 2018/19.

Reading material

[ME] Simon, Blume, Mathematics for Economists, International Student Edition, Norton 1994 - main textbook.
[WB] Eriksen, Digital Workbook for GRA 6035 Mathematics - workbook with problems/solutions. Solutions to advanced problems in Lecture 4.
[LN] Eriksen, Lecture Notes. My notes covering Lecture 1 (available from It's Learning). Lecture notes for the remaining lecture may be posted in It's Learning later in the semester, depending on when they are written.
[DE] Eriksen, Differential Equations - notes on differential equations - Solutions to problems in [DE].

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 students in Oslo. For students in Bergen, the lecture plan will be published separately.
Office hours: Thu 1200-1400 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).
Lectures: Fri 0800-1045 (weekly), 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 (and usually also the lecturer) will be available to help.

Lectures in Oslo	Lecturer Eivind Eriksen (Office B4-032), Office hours: Thu 12-14	Reading	Exercises
Jul 31- Aug 02	FORK 1003: Preparatory course, Mathematics
Fri Aug 23: 0800-1045, A1-040	Lecture 1: Linear systems and Gaussian elimination. Rank.	[ME] 6.1, (6.2), 7.1 - 7.4, (7.5), (28.1), [LN] Ch. 1	Problem set 1 - Solutions
Fri Aug 30: 0800-1045, A1-040	Lecture 2: Matrices and matrix algebra. Determinants, minors and rank.	[ME] 8.1 - 8.4, (8.5 - 8.6), 9.1 - 9.2, (9.3), 26.1 - 26.3, (26.4), 26.5	Problem set 2 - Solutions
Fri Sep 06: 0800-1045, A1-040	Lecture 3: Vectors and Linear Independence. Linear subspaces and rank.	[ME] 10.1 - 10.3, (10.4), 10.5, (10.6 - 10.7), 11.1 - 11.4, (27.1 - 27.5)	Problem set 3 - Solutions
Fri Sep 13: 0800-1045, A1-040	Lecture 4: Eigenvalues and eigenvectors. Diagonalization.	[ME] 23.1 - 23.4, 23.6-23.7, (23.9)	Problem set 4 - Solutions
Mon Sep 16: 1700-1945, A1-040	Plenary Session 1: Problems from Lecture 1-4	Key problems 2.3c, 4.1ef, 4.3 [WB] 1.15, 2.18b, 2.21, 3.1, 3.5, 3.12, 3.14, 4.3b, 4.5, 4.6, 4.9, 4.10 Midterm Exam 10/2017 1-5
Fri Sep 20: 0800-1045, A1-040	Lecture 5: Markov chains. Quadratic Forms and Definiteness.	[ME] 13.1 - 13.5, 16.1 - 16.4, 23.8, (Google's Pagerank algorithm)	Problem set 5 - Solutions
Fri Sep 27: 1400-1645, A1-040	Lecture 6: Unconstrained Optimization. Convex and concave functions.	[ME] 14.1 - 14.4, 14.8, 17.1 - 17.5, 30.1	Problem set 6 - Solutions
Fri Oct 04: 0800-1045, A1-040	Lecture 7: Constrained Optimization. First Order Conditions.	[ME] 18.1 - 18.7, (12.3 - 12.5), 21.1	Problem set 7 - Solutions
Mon Oct 07: 1700-1945, A1-040	Plenary Session 2: Problems from Lecture 5-6 + Midterm exam 10/2018	Key problems 5.1c, 5.2e, 5.3d, 6.1d, 6.3bd, 6.4d, 7.2c [WB] 5.15, 6.1c, 6.2a Midterm Exam 10/2018 1-8, 10/2016 5, 05/2017 8
Fri Oct 11: 0800-1045, A1-040	Lecture 8: Constrained Optimization. Second Order Conditions. NDCQ.	[ME] 19.1, (19.4)	Problem set 8 - Solutions
Fri Oct 11: 1500-1600	Midterm exam - Solutions - Results	All material from Lecture 1-6, including Problems for Lecture 1-6 and Review of Lecture 6, is relevant for the midterm exam
Fri Oct 18: 0800-1045, A1-040	Lecture 9: Envelope Theorems. Kelly Criterion.	[ME] 19.2 - 19.3, (19.4 - 19.6), (Kelly Criterion)	Problem set 9 - Solutions
Fri Oct 25: 0800-1045, A1-040	Lecture 10: First order differential equations.	[DE] 1.1 - 1.6 [ME] 24.1 - 24.2, (24.4 - 24.6)	Problem set 10 - Solutions
Mon Oct 28: 1700-1945, A1-040	Plenary Session 3: Problems from Lecture 7-9	Key problems 7.1d, 7.4b, 8.2d, 8.3b, 9.1, 9.3 [WB] 7.1f, 8.13 Final Exam 01/2017 3-4, 11/2017 3-4
Fri Nov 01: 0800-1045, A1-040	Lecture 11: Exact differential equations. Stability. Second order differential equations.	[DE] 1.6 - 1.10 [ME] 24.1 - 24.3, (24.4 - 24.6)	Problem set 11 - Solutions
Fri Nov 08: 1400-1645, A1-040	Lecture 12: Systems of differential equations. Difference equations.	[DE] 2.1 - 2.3 [ME] 23.2	Problem set 12 - Solutions
Mon Nov 11: 1700-1945, A1-040	Plenary Session 4: Problems from Lecture 10-12	Key problems 10.2c, 11.1bc, 11.3c, 12.2, 12.3 [WB] 10.15, 12.7 [DE] 1.20, 2.4 Exam Final exam 12/2012 3, 06/2018 2bc
Fri Nov 15: 0800-1045, A1-040	Lecture 13: Revision of Lecture 1-12.		Problem set 13
Fri Nov 22: 0800-1045, A1-040	Lecture 14: Final exam 11/2018.
Wed Nov 27: 0900-1200	Final exam 27/11/2019 - Solutions

January 2020: Not confirmed	Midterm exam (retake)
January 2020: Not confirmed	Final exam (retake)
	There will not be any retake exams for GRA 6035 Mathematics in May/June 2020.