# Linear Algebra and Optimisation (Autumn 2024)

#### Official course description, subject to change:

##### 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

##### Ordinary exam

**Exam type:**

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

**Exam variation:**

A33: Written exam on premises on paper with restrictions