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 Lecture 1-14). 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 2021/22.

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
• [PA] McKinney, Python for Data Analysis, 2nd Edition, O'Reilly 2018

Exams

• One week home exam (counts for 20%), and 3h written final exam (counts for 80%). Both exams must be passed.
• Previous final exam problems with solutions.

Lecture plan

• This is the lecture plan for the autumn 2022. Lecture 1-14: Fri 14-17 in A1-040 (weekly). Lecture A-C: Mon 12-15 in C2-095 (three sessions). See plan below for details.
• Office hours: Mon 12-14 and Fri 10-12 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).
• 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.
• Lecture plan for ELE3781:

  Date:	Topic:	Reading:	Exercises:
  	Python code
  Mon Sep 12: 12-15, B2-085	Lecture A: NumPy and NDarrays. Complex numbers.	[E] A.1 - A.5 [PA] 4.1 - 4.8	Problem set A: Wed 16-18 B2-085
  Mon Oct 10: 12-15, B2-085	Lecture B: Non-negative matrices and applications	[E] 4.4	Problem set B: Wed 16-18 B2-085
  Mon Oct 24: 12-15, B2-085	Lecture C: Time series and portfolio optimization.	[E] 6.7	Problem set C: Wed 16-18 B2-085
  Oct 24-31	Midterm exam - Solutions	Home exam (with Python)

• Common lecture plan for GRA6035 and ELE3781:

  Date:	Topic:	Reading:	Exercises:
  Aug 08 - Aug 10	FORK 1003: Preparatory course in Mathematics, Economics and Econometrics
  Fri Aug 26: 14-17, 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 02: 14-17, A1-040	Lecture 2: Vectors and Linear Independence. Vector spaces.	[E] 2.1 - 2.4, 2.6 - 2.7	Problem set 2: Mon 16-18, C2-010/020/030/D1-065
  Fri Sep 09: 14-17, 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 16: 14-17, A1-040	Lecture 4: Eigenvalues and eigenvectors. Diagonalization. Markov chains.	[E] 4.1 - 4.4	Problem set 4
  Mon Sep 19: 16-19, A1-040	Plenary Session 1: Problems from Lecture 1-4	Key problems 2.2, 2.3a, 2.4ef, 3.1, 3.3, 3.4, 4.3, 4.4, 4.5 [E] 4.8b Midterm 01/2022 Q4-5
  Fri Sep 23: 14-17, A1-040	Lecture 5: Definiteness of quadratic forms. Markov chains.	[E] 2.5, 4.4 - 4.6	Problem set 5: Mon 16-18, C2-010/020/030/D1-065
  Fri Sep 30: 14-17, A1-040	Lecture 6: Unconstrained Optimization.	[E] 5.1 - 5.5, 5.7	Problem set 6: Mon 16-18, C2-010/020/030/D1-065
  Fri Oct 07: 14-17, A1-040	Lecture 7: Constrained Optimization. Lagrange problems.	[E] 6.1 - 6.4, 6.6	Problem set 7
  Mon Oct 10: 16-19, A1-040	Plenary Session 2: Problems from Lecture 4-6 + Midterm exam problems	Key problems 6.1, 6.2a, 6.3c, 6.5b Midterm Mock midterm 10/2022 Q2,4-11,14,17,19,21-22 Midterm 01/2020 Q7
  Fri Oct 14: 09-10	Midterm exam for GRA6035 - Solutions - Results	All material from Lecture 1 - Lecture 6 is relevant for the midterm exam.
  Fri Oct 14: 14-17, 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 21: 14-17, A1-040	Lecture 9: Matrix methods and optimization	[E] 5.6, 6.7	Problem set 9: Mon 16-18, C2-010/020/030/D1-065
  Fri Oct 28: 14-17, A1-040	Lecture 10: First order differential equations.	[E] 7.1 - 7.7	Problem set 10
  Mon Oct 31: 16-19, A1-040	Plenary Session 3: Problems from Lecture 7-9	Key problems 7.3, 7.4, 8.1, 8.2, 9.1 - 9.4 [E] 6.3 - 6.5 Final exams 11/2017 3-4, 11/2018 3-4, 01/2019 5, 11/2019 4, 01/2022 3, 04/2022 1,3
  Fri Nov 04: 14-17, A1-040	Lecture 11: Stability. Second order differential equations.	[E] 7.8 - 7.10	Problem set 11: Mon 16-18, C2-010/020/030/D1-065
  Fri Nov 11: 14-17, A1-040	Lecture 12: Systems of differential equations.	[E] 9.1 - 9.3	Problem set 12
  Mon Nov 14: 16-19, A1-040	Plenary Session 4: Problems from Lecture 10-12	Key problems 10.2c, 10.3b, 10.4c, 11.2d, 11.3, 12.1a, 12.3 Final exams 04/2022 2ad, 01/2022 1,2c 01/2020 3a, 12/2015 2c
  Fri Nov 18: 14-17, A1-040	Lecture 13: Difference equations. Systems of difference equations.	[E] 8.1 - 8.4, 9.4 - 9.5	Problem set 13: Mon 16-18, C2-010/020/030/D1-065
  Fri Nov 25: 14-17, A1-040	Lecture 14: Revision, exam problems from final exam 12/2021		Extra exercise session: Mon 16-18, D1-065
  Wed Nov 30: 14-17	Final exam for GRA6035 and ELE3781 - Solutions - Results for GRA6035
  Jan 09 2023: 09-12	Final exam (retake for GRA6035) - Solutions
  Jan 09 2023: 17-18	Midterm exam (retake for GRA6035) - Solutions