Introduction to mathematics

The course provides an introduction to mathematical structures and computational science models, mathematical terminology, and ways of thinking. The topics are motivated by both theoretical and applied examples.

The aim of the course is to prepare students for further studies in mathematics. This is achieved, among other things, through topics in mathematical analysis beyond what is presented in the introductory course. For example, the real numbers are introduced from the ground up. At the same time, students will be trained in conducting rigorous mathematical arguments, both orally and in writing. Another goal is to provide an initial introduction to computational science methods, based on the mathematical tools students have from upper secondary school, supplemented with selected topics from the introductory course that can be taken in parallel.

Upon completion of the course, the student should have the following learning outcomes defined in terms of knowledge, skills, and general competence:

Knowledge
The student:

• understands fundamental properties of integers, rational numbers, and real numbers, including induction proofs, field axioms, the completeness axiom, and the construction of the real numbers
• understands the foundations of mathematical analysis
• is familiar with standard techniques in computational science

Skills
The student:

• masters basic numerical methods
• masters fundamental number systems and basic mathematical analysis

General Competence
The student:

• can view simple realistic problems from a mathematical perspective and model and solve them
• is capable of analytical thinking, both in concrete and more abstract situations
• can carry out simple mathematical arguments and present them clearly and systematically using appropriate notation and terminology, both orally and in writing