ELE 3781 Mathematics elective

Course description for ELE 3781 Mathematics elective, an elective course in mathematics for BSc Business Analytics. It covers linear algebra and matrix methods, complex numbers, optimisation in several variables, differential and difference equations and optimal control theory. Python will be used to implement mathematical models.
Parts of the course will be identical to and taught together with GRA6035 Mathematics, a core course in the MSc Business/Finance program. Certain mathematical topics (like complex numbers and optimal control theory) and the Python topics are included in ELE3781, but not in GRA6035.

Reading material

[ME] Simon, Blume, Mathematics for Economists, International Student Edition, Norton 1994 - main textbook for maths
[PA] McKinney, Python for Data Analysis, 2nd Edition, O'Reilly 2018 - main textbook for Python
[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

One week home exam (counts for 20%), and 3h written final exam (counts for 80%). There are re-take exams in the spring semester. Both exams must be passed.
This course will start in Autumn 2020 and no previous exams exist. Previous exam problems in GRA 6035 with solutions are relevant for this course (in particular the final exams).

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 08-10 + 1h video lecture (weekly), Thu 13-15 + 1h video lecture (three sessions), Plenary sessions: Mon 17-20 (four sessions). In plenary sessions, I will solve selected problems. See the lecture plan below for details.
TA sessions: Mon 1700-1845 (weekly). In exercise sessions, you will work with problems, and teaching assistants (TA's) 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 - Live stream B2-040 - Python code
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
Thu Sep 03: 1300-1445, A2-030	Lecture A: NumPy and NDarrays. Complex numbers.	[PA] 4.1 - 4.8, [ME] A3.1 - A3.5 Alternative: [E] Ch. A.1 - A.3	Problem set A - 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
Thu Oct 01: 1300-1445, B2-040	Lecture B: Non-negative matrices and applications		Problem set B - 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 16: 0800-0945, A1-040	Lecture 9: Envelope Theorems.	[ME] 19.2 - 19.3, (19.4 - 19.6)	Problem set 9 - Solutions
Oct 19 - Oct 26	Midterm exam - Solution	Home exam (with programming in python)
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, C1-060	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
Thu Nov 05: 1300-1445, B2-040	Lecture C: Optimal control theory. Portfolio optimization.	Notes on optimal portfolio theory	Problem set C - Solutions
Fri Nov 06: 0800-0945, A1-040	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, grade pass/fail