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 2019/20.

Reading material

[ME] Simon, Blume, Mathematics for Economists, International Student Edition, Norton 1994 - main textbook.
[E] Eriksen, Mathematics. New textbook for the course (work in progress, finished chapters/lectures will be available from It's Learning).
[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 a preliminary lecture plan for the autumn 2020. There may be changes due to corona/covid-19.
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 0800-0945 (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 will be available to help.

Lecture plan	Lecturer Eivind Eriksen (Office B4-032), Office hours: Thu 12-14	Reading	Exercises
All lectures	Live stream A1-040 - Recorded videos: See It's Learning
Aug 03 - Aug 05	FORK 1003: Preparatory course, Mathematics
Fri Aug 21: 0800-0945, A1-040	Lecture 1: Linear systems and Gaussian elimination. Rank.	[ME] 6.1, (6.2), 7.1 - 7.4, (7.5) Alternative: [E] Ch. 1	Problem set 1 - Solutions
Fri Aug 28: 0800-0945, A1-040	Lecture 2: Vectors and Linear Independence. Vector spaces.	[ME] 10.1 - 10.3, (10.4 - 10.7), 11.1 Alternative: [E] Ch. 2	Problem set 2 - Solutions
Fri Sep 04: 0800-0945, A1-040	Lecture 3: Matrices, determinants and minors.	[ME] 8.1 - 8.4, 9.1 - 9.2, 26.1 - 26.3, 26.5 Alternative: [E] Ch. 3	Problem set 3 - Solutions
Fri Sep 11: 0800-0945, A1-040	Lecture 4: Eigenvalues and eigenvectors. Diagonalization. Markov chains.	[ME] 23.1 - 23.4, 23.6 -23.7, (23.9)	Problem set 4 - Solutions
Mon Sep 14: 1700-1945, A1-040	Plenary Session 1: Problems from Lecture 1-4	Key Pb 1.3, 3.3c, 3.4b, 4.1cdf, 4.2de, 4.3, 4.4 [E] 2.11, 3.13, 3.15
Fri Sep 18: 0800-0945, A1-040	Lecture 5: Non-negative matrices. Definiteness of quadratic forms.	[ME] 13.1 - 13.5, 16.1 - 16.4, 23.8, (Google's Pagerank algorithm )	Problem set 5 - Solutions
Fri Sep 25: 0800-0945, A1-040	Lecture 6: Unconstrained Optimization.	[ME] 14.1 - 14.4, 14.8, 17.1 - 17.5, 30.1	Problem set 6 - Solutions
Fri Oct 02: 0800-0945, 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 05: 1700-1945, A1-040	Plenary Session 2: Problems from Lecture 4-6 + Midterm exam 10/2018	Key Pb 6.3a,6.4be [WB] 4.3b, 4.11, 5.7, 5.13, 5.14, 6.4, 6.5 Midterm Exam 01/2018 Q5, 10/2018 Q8
Fri Oct 09: 0800-0945, A1-040	Lecture 8: Constrained Optimization. Second Order Conditions.	[ME] 19.1, (19.4)	Problem set 8 - Solutions
Fri Oct 09: 1300-1400	Mock midterm exam - Solutions	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 16: 0800-0945, A1-040	Lecture 9: Envelope Theorems.	[ME] 19.2 - 19.3, (19.4 - 19.6)	Problem set 9 - Solutions
Fri Oct 23: 0800-0945, A1-040	Lecture 10: First order differential equations.	[ME] 24.1 - 24.2, (24.4 - 24.6) Alternative: [E] 9.1-9.7	Problem set 10 - Solutions
Mon Oct 26: 1700-1945, A1-040	Plenary Session 3: Problems from Lecture 7-9	Key problems 7.3b, 7.4, 8.1b, 8.2d, 8.3b, 9.2, 9.3a [WB] 7.9, 8.7, 8.12-13 Final Exam 2018/11 3-4
Fri Oct 30: 0800-0945	Lecture 11: Stability. Second order differential equations.	[ME] 24.1 - 24.3, (24.4 - 24.6) Alternative: [E] 9.8 - 9.10	Problem set 11 - Solutions
Fri Nov 06: 0800-0945	Lecture 12: Systems of differential equations and difference equations.	[ME] 23.2	Problem set 12 - Solutions
Fri Nov 13	Lecture 13: Final exam 11/2019.
Thu Nov 19	Plenary Session 4: Problems from Lecture 10-12	Key problems 10.4c, 11.1c, 12.3 [E] 9.14, 9.18 [WB] 10.8cd, 11.8, 12.7
Fri Nov 20	Lecture 14: Review of important topics for the final exam.

	Information about the exam - Notes from Zoom
Mon Jan 18: 0900-1200	Final exam 18/01/2021 - Solutions	Home exam, with grade pass/fail

Wed Mar 17: 1700-1800	Zoom session: Exam revision (see message/link/video on It's Learning)
Fri Mar 19: 0900-1215	Final exam 19/03/2021 (retake) - Solutions