ELE 3781 Mathematics elective 2023/24

Course description for ELE 3781 Mathematics elective, an elective course in mathematics for BSc Data Science for Business. It covers linear algebra and matrix methods, optimisation in several variables, and differential and difference equations (identical to and taught together with GRA6035 Mathematics).
For material from last year's course, see ELE 3781 Mathematics elective 2022/23.

Reading material

[E] Eriksen, Graduate Mathematics for Business, Economics and Finance, Cappelen Damm 2021 - List of corrections
[EP] Eriksen, Graduate Mathematics for Business, Economics and Finance - Problems and solutions, Cappelen Damm 2021 - List of corrections

Exams

A 5h written final exam (counts for 100%).
Previous final exam problems with solutions.

Lecture plan

This is the lecture plan for the autumn 2023. Lecture 1-14 will consist of a 3h lecture in A1-040 (Fri 12-15). See plan below for details.
Office hours: Mon 12-14 and Fri 10-12 at my office B3y-085. I have an open door policy, which means that you may come to my office at other times (no appointment needed).
Plenary sessions: Mon 16-19 (four sessions). In plenary sessions, I will solve selected problems. See the lecture plan below for details.
Exercise sessions: Mon 16-18 (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 07 - Aug 09	FORK 1003: Preparatory course in Mathematics, Economics and Econometrics
Fri Aug 25: 12-15, A1-040	Lecture 1: Linear systems and Gaussian elimination. Rank.	[E] 1.1 - 1.6	Problem set 1: Mon 16-18, C2-010/020/030/D1-065
Fri Sep 01: 12-15, A1-040	Lecture 2: Vectors and vector spaces. Linear Independence, bases and dimension.	[E] 2.1 - 2.4, 2.6 - 2.7	Problem set 2: Mon 16-18, C2-010/020/030/D1-065
Fri Sep 08: 12-15, A1-040	Lecture 3: Matrices, determinants and minors.	[E] 3.1 - 3.4	Problem set 3: Mon 16-18, C2-010/020/030/D1-065
Fri Sep 15: 12-15, A1-040	Lecture 4: Eigenvalues and eigenvectors. Diagonalization. Powers.	[E] 4.1 - 4.4	Problem set 4
Mon Sep 18: 16-19, A1-040	Plenary Session 1: Problems from Lecture 1-4	Key problems 2.1bdf, 2.2, 2.4, 3.3bc, 3.4bc, 4.1def, 4.2d, 4.3, 4.4b, 4.5b [E] 2.7, 2.14 Midterm 10/2022 Q7
Fri Sep 22: 12-15, A1-040	Lecture 5: Markov chains. Definiteness of quadratic forms. Orthogonal diagonalization.	[E] 2.5, 4.4 - 4.6	Problem set 5: Mon 16-18, C2-010/020/030/D1-065
Fri Sep 29: 12-15, A1-040	Lecture 6: Ortogonal diagonalization. Unconstrained Optimization. Convexity.	[E] 5.1 - 5.6	Problem set 6: Mon 16-18, C2-010/020/030/D1-065
Fri Oct 06: 12-15, A1-040	Lecture 7: Constrained Optimization. Lagrange problems.	[E] 6.1 - 6.4	Problem set 7
Mon Oct 09: 16-19, A1-040	Plenary Session 2: Problems from Lecture 5-7 + Midterm exam problems	Key problems 5.1e, 5.2de, 5.3cd, 5.4, 5.5bc, 6.1, 6.2, 6.3, 6.4, 6.5, 7.2b
Thu Oct 12: 17-18	Mock midterm exam - Solutions	All material from Lecture 1-6 is relevant for the mock midterm exam
Fri Oct 13: 12-15, A1-040	Lecture 8: Kuhn-Tucker problems. Envelope Theorems.	[E] 6.5 - 6.6	Problem set 8: Mon 16-18, C2-010/020/030/D1-065
Fri Oct 20: 12-15, A1-040	Lecture 9: Envelope Theorems. Matrix methods. Note on Minimum variance portfolios	[E] 5.6, 6.6 - 6.7	Problem set 9: Fri 16-18 D1-065, Mon 16-18, C2-010/020/D1-065
Fri Oct 27: 12-15, A1-040	Lecture 10: First order differential equations.	[E] 7.1 - 7.7	Problem set 10: Fri 16-18 D1-065
Mon Oct 30: 16-19, A1-040	Plenary Session 3: Problems from Lecture 7-9	Key problems 7.1, 7.3b, 7.4, 8.1b, 8.2, 9.2, 9.3, 9.4 Final exam 04/2022 Q3
Fri Nov 03: 12-15, A1-040	Lecture 11: Stability. Second order differential equations.	[E] 7.8 - 7.10	Problem set 11: Fri 16-18 D1-065, Mon 16-18, C2-010/020/030/D1-065
Fri Nov 10: 12-15, A1-040	Lecture 12: Systems of differential equations.	[E] 9.1 - 9.3	Problem set 12: Fri 16-18 D1-065
Mon Nov 13: 16-19, A1-040	Plenary Session 4: Problems from Lecture 10-12	Key problems 10.1c, 10.2bc, 10.3, 10.4, 11.1c, 11.2bcd, 11.3, 12.1c, 12.4 Final exam 12/2021 Q2
Fri Nov 17: 12-15, A1-040	Lecture 13: Difference equations. Systems of difference equations.	[E] 8.1 - 8.4, 9.4 - 9.5	Problem set 13 - Solutions: Fri 16-18 D1-065, Mon 16-18, C2-010/020/030/D1-065
Fri Nov 24: 12-15, A1-040	Lecture 14: Revision, Final exam 11/2022		Extra exercise session: Fri 16-18 D1-065
Mon Nov 27: 14-16	Extra exercise session (Room A2 Blue 1 / Blue 4)
Tue Nov 28: 09-14	Final exam for GRA6035 and ELE3781 - Solutions - Results

Wed Jan 10: 09-14	Final exam (retake for GRA6035) - Solutions