# 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 Q4-5Fri 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 Q7Fri 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 1,3Fri 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 2cFri 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