Algebra, Functions and Modelling

Lessons are not given in the academic year 2025-2026.

This course gives an introduction to properties of functions of one variable, and an introduction to differential equations. Using mathematics to describe extra-mathematical situations (modelling) is a central topic. Use of digital tools, including programming, will be included. Aspects related to teaching algebra and functions will also be included.

After having completed the course, the candidate is expected to have acquired learning outcome, defined as knowledge, skills and general competence as specified below:

Knowledge

The candidate has

• basic knowledge of modelling as a way of working in mathematics,
• good knowledge of important functions, such as polynomials, rational functions, trigonometric functions, exponential and logarithmic functions, and their properties,
• basic knowledge of differentiation and integration, and applications of these concepts,
• basic knowledge of differential equations and their applications,
• basic knowledge of numerical solutions of algebraic equations and differential equations.
• basic knowledge of sequences and series.

Skills

The candidate is able to

• use integration and differentiation to analyse properties of functions,
• model situations from nature and society using mathematical concepts and methods, and assess the validity of these models,
• solve problems using both algebraic and numerical techniques, and use digital tools, including simple programming, in this work,
• assess whether results obtained using digital techniques are reasonable.

General competence

The candidate has acquired

• a good basis for studying more advance mathematical courses,
• good knowledge about mathematical topics and use of digital aids, relevant for teaching mathematics in grades 8-13.

The teaching is concentrated in seminars, accompanied by Internet based tutoring. Printed and digital learning resources are available as books, articles and videos.