ELE 3781 Mathematics elective

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 2023/24.

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 semester 2024. Lecture 1-14 will consist of a 3h lecture in A1-040 (Fri 12-15).
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 and Fri 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 05 - Aug 07	FORK 1003: Preparatory course in Mathematics, Economics and Econometrics
Fri Aug 23: 12-15, A1-040	Lecture 1: Linear systems and Gaussian elimination. Rank.	[E] 1.1 - 1.6	Problem set 1: Fri 16-18 D1-065 + Mon 16-18, C2-010/D1-065
Fri Aug 30: 12-15, A1-040	Lecture 2: Vectors spaces. Span and linear Independence. Orthogonal projection.	[E] 2.1 - 2.7	Problem set 2: Fri 16-18 D1-065 + Mon 16-18, C2-010/D1-065
Fri Sep 06: 12-15, A1-040	Lecture 3: Matrices, determinants and minors.	[E] 3.1 - 3.4	Problem set 3: Fri 16-18 D1-065 + Mon 16-18, C2-010/D1-065
Fri Sep 13: 12-15, A1-040	Lecture 4: Eigenvalues and eigenvectors. Diagonalization. Powers.	[E] 4.1 - 4.4	Problem set 4: Fri 16-18 D1-065
Mon Sep 16: 16-19, A1-040	Plenary Session 1: Problems from Lecture 1-4 Key problems 1.4, 2.1bdf, 2.3, 2.4cd, 2.5bc, 3.2bc, 3.3b, 3.4b, 4.1def, 4.2, 4.3, 4.4, 4.5 Midterm 01/'20 Q4,Q8, 10/'22 Q6,Q8
Fri Sep 20: 12-15, A1-040	Lecture 5: Markov chains. Definiteness of quadratic forms. Orthogonal diagonalization.	[E] 2.5, 4.4 - 4.6	Problem set 5: Fri 16-18 D1-065 + Mon 16-18, C2-010/D1-065
Fri Sep 27: 12-15, A1-040	Lecture 6: Orthogonal diagonalization. Unconstrained Optimization. Convexity.	[E] 5.1 - 5.6	Problem set 6: Fri 16-18 D1-065 + Mon 16-18, C2-010/D1-065
Fri Oct 04: 10-11	Mock Midterm Exam - Solutions
Fri Oct 04: 12-15, A1-040	Lecture 7: Constrained Optimization. Lagrange problems.	[E] 6.1 - 6.4	Problem set 7: Fri 16-18 D1-065
Mon Oct 07: 16-19, A1-040	Plenary Session 2: Problems from Lecture 5-7 Key problems 5.1cde, 5.2d, 5.3, 5.4bc, 5.5bf, 6.2b, 6.3cd, 6.4bce, 6.5ab, 7.1d, 7.2b, 7.3b, 7.4d
Fri Oct 11: 12-15, A1-040	Lecture 8: Kuhn-Tucker problems.	[E] 6.5	Problem set 8: Fri 16-18 D1-065 + Mon 16-18, C2-010/D1-065
Fri Oct 18: 12-15, A1-040	Lecture 9: Envelope theorems. Minimum variance portfolio.	[E] 5.7, 6.6 - 6.7	Problem set 9: Fri 16-18 D1-065 + Mon 16-18, C2-010/D1-065
Fri Oct 25: 12-15, A1-040	Lecture 10: First order differential equations.	[E] 7.1 - 7.7	Problem set 10: Fri C2-020/16-18 D1-065
Thu Oct 31: 16-19, A1-040	Plenary Session 3: Problems from Lecture 8-10 Key problems 8.1b, 8.2, 9.1c, 9.2bc, 10.2c, 10.3c, 10.4bc Exam problems 01/'24 Q4e, 01/'22 Q3
Fri Nov 01: 12-15, A1-040	Lecture 11: Stability. Second order differential equations.	[E] 7.8 - 7.10	Problem set 11: Fri 16-18 Fri C2-020/D1-065 + Mon 16-18, C2-010/D1-065
Fri Nov 08: 12-15, A1-040	Lecture 12: Systems of differential equations.	[E] 9.1 - 9.3	Problem set 12: Fri 16-18 Fri C2-020/D1-065
Mon Nov 11: 16-19, A1-040	Plenary Session 4: Problems from Lecture 11-12 + Exam problems Key problems 11.3c, 12.2ab, 12.3, 12.4bc, 12.5be Exam problems 01/'24 Q1d, Q3d, 11/'19 Q4bc 11/'18 Q2c,Q5
Fri Nov 15: 12-15, A1-040	Lecture 13: Difference equations. Systems of difference equations.	[E] 8.1 - 8.4, 9.4 - 9.5	Problem set 13: Fri 16-18 Fri C2-020/D1-065 + Mon 16-18, C2-010/D1-065
Fri Nov 22: 12-15, A1-040	Lecture 14: Revision, Exam problems: Final exam 11/2023		Extra exercise session: Fri C2-020/16-18 D1-065
Mon Nov 25: 09-14	Final exam for GRA6035 and ELE3781

Jan 2025 (date/time TBA)	Final exam (retake for GRA6035)