*Official course description, subject to change:*

### Linear Algebra and Optimisation

##### 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, Lagrange multipliers and multiple integrals. A number of applications of the material will be covered in the course, including least squares analysis and Google’s PageRank algorithm.

##### 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

##### Ordinary exam

**Exam type:**

A: Written exam on premises, external (7-trinsskala)

**Exam variation:**

A22: Written exam on premises with restrictions. Restrictions may concern which software and which books you may use.

**Exam description:**

The exam is a 4 hour written exam

1. Solutions submitted hand written on paper.

2. Access to aid in the form of books, own notes, e-books, also on laptops and iPads is permitted.

3. Use of internet including email and social media is not permitted.

4. Use of any other hardware or software such as MatLab or pocket calculators is not permitted

5. Any form of communication between students or with the outside world is not permitted.