# Linear Algebra and Optimisation (Autumn 2024)

#### Official course description:

##### Course info

##### Programme

##### Staff

##### Course semester

##### Exam

##### Abstract

This is a course in mathematics covering linear algebra and analysis (calculus) of functions of several variables. These are perhaps the two areas of mathematics that have found most uses in practical applications. In particular, the course equips the student with mathematical tools necessary for analysis of big data.

##### Description

Linear algebra and analysis (calculus) of functions of several variables are perhaps the two areas of mathematics that have found most uses in practical applications. In particular, the course equips the student with mathematical tools necessary for analysis of big data.

The topics covered in the linear algebra part of the course include systems of linear equations, matrices, determinants, vector spaces, bases, dimension, and eigenvectors. The topics covered in the calculus part include
partial derivatives, gradients, and Lagrange multipliers. A number of applications of the material will be
covered in the course, focusing on applications to data science.

##### Formal prerequisites

As the course is mandatory for 1st semester Data Science students mathematics corresponding to the Danish A-level with an average mark of at least 6 on the Danish 7-point marking scale is a prerequisite.##### Intended learning outcomes

After the course, the student should be able to:

- Solve systems of linear equations and multivariable optimisation problems.
- Define the basic concepts of linear algebra and multivariable calculus, e.g., eigenvalues or directional derivative.
- Compute the essential constructions of linear algebra and multivariable calculus, such as the inverse of a given matrix or the gradient of a function.
- Apply the tools of linear algebra and calculus to solve small mathematical problems.
- Construct small proofs using the axioms of vector spaces
- Construct small mathematical arguments, for example to show that a subset is a vector space

##### Learning activities

14 weeks of lectures and exercises. At the exercise sessions the students will solve and present solutions to mathematical problems. The mandatory assignments are of the form of mathematical problems. The solutions must be submitted in written form.

##### Mandatory activities

There are 6 mandatory assignments, out of which 5 must be approved for the student to qualify for the exam. The deadlines are evenly distributed over the semester (approximately one every 2 weeks), and exact dates will be posted on learnit the first week of the semester. If a mandatory assignment is not approved the first time, the student will be allowed to resubmit one week after the first deadline.The pedagogical purpose of the mandatory activities is to ensure that all students practice presenting mathematical arguments in writing and that they get feedback on this. Written formative feedback will be provided by teachers and TAs.

The student will receive the grade NA (not approved) at the ordinary exam, if the mandatory activities are not approved and the student will use an exam attempt.

##### Course literature

Ron Larson:* Elementary Linear Algebra*, International Metric Edition, 8th edition

James Stewart, Daniel K. Clegg and Saleem Watson: *Calculus: Early Transcendentals*, Metric Edition, 9th edition

##### Student Activity Budget

Estimated distribution of learning activities for the typical student- Preparation for lectures and exercises: 55%
- Lectures: 17%
- Exercises: 17%
- Assignments: 9%
- Exam with preparation: 2%

##### Ordinary exam

**Exam type:**

A: Written exam on premises, External (7-point scale)

**Exam variation:**

A33: Written exam on premises on paper with restrictions

**Exam duration:**

4 hours

**Aids allowed for the exam:**

Written and printed books and notes

Pen

E-books and/or other electronic devices

- Access to e-books, also on laptops and iPads is permitted, access to course notes as well as personal notes on laptops, iPads and the like is permitted.

##### reexam

**Exam type:**

A: Written exam on premises, External (7-point scale)

**Exam variation:**

A33: Written exam on premises on paper with restrictions

**Exam duration:**

4 hours

**Aids allowed for the exam:**

Written and printed books and notes

Pen

E-books and/or other electronic devices

- Access to e-books, also on laptops and iPads is permitted, access to course notes as well as personal notes on laptops, iPads and the like is permitted.