ELE 3781 Mathematics elective

Course description for ELE 3781 Mathematics elective, an elective course in mathematics for BSc Business Analytics.
This course covers linear algebra and matrix methods, optimisation in several variables, and differential and difference equations (identical to and taught together with GRA6035 Mathematics)
It also covers complex numbers and implementation of mathematical models in Python (Lecture A-C)
For material from last year's course, see ELE 3781 Mathematics elective 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
[PA] McKinney, Python for Data Analysis, 2nd Edition, O'Reilly 2018
[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 was first offered in 2020/21 and few 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 the lecture plan for the autumn 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).
Lectures: Fri 08-10 + 1h video lecture (weekly), Wed 15-17 + 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), Wed 15-17 (three sessions). 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:
	Python code
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
Wed Sep 08: 1500-1645, B2-040	Lecture A: NumPy and NDarrays. Complex numbers.	[E] A.1 - A.5 [PA] 4.1 - 4.8	Problem set A: Wed 01/09 15-17, B2-080
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
Wed Sep 29: 1500-1645, C2-040	Lecture B: Non-negative matrices and applications	[E] 4.4	Problem set B: Wed 06/10 15-17, B2-080
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 5-6 + 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 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
Wed Oct 20: 1500-1645, B2-040	Lecture C: Time series and portfolio optimization.	[E] 6.7	Problem set C: Wed 27/10 15-17, B2-080
Oct 25 - Nov 01	Midterm exam - Solutions	Home exam (with programming in python)
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.	[E] 7.1 - 7.7	Problem set 10
Mon Nov 01: 1700-1945, A1-040	Plenary Session 3: Problems from Lecture 7-9	Key problems 7.1bd, 8.1ab, 9.1, 9.2b, 9.3, 9.4 Final Exam 11/2019 Q4, 06/2018 Q4
Fri Nov 05: 0800-0945, A1-040	Lecture 11: Stability. Second order differential equations.	[E] 7.8 - 7.10	Problem set 11: Mon 17-19, C2-010/020/030/D1-065
Fri Nov 12: 0800-0945, A1-040	Lecture 12: Systems of differential equations.	[E] 9.1 - 9.3	Problem set 12: Mon 17-19, C2-010/020/030/D1-065
Fri Nov 19: 0800-0945, A1-040	Lecture 13: Difference equations. Systems of difference equations.	[E] 8.1 - 8.4, 9.4 - 9.5	Problem set 13
Mon Nov 22: 1700-1945, C1-010	Plenary Session 4: Problems from Lecture 10-13	Key problems 10.2b, 10.3b, 10.4b, 11.1b, 11.2cd, 12.2b, 12.4bc, 13.1d, 13.3a Final Exam 01/2020 2b,3b 11/2019 3b 01/2019 2b
Fri Nov 26: 1500-1745, A1-040	Lecture 14: Revision, exam problems: Final exam 11/2019 1-4, 2021/01 2,3b		Extra TA session: Mon 17-19, D1-065/CU1-067
Thu Dec 02: 0900-1200	Final exam - Solutions