Course content

• Logics: Statements, arguments, basic proof theory. Mathematical induction.
• Set theory and discrete functions.
• Number theory: Divisibility and congruence, Euclid's algorithm, RSA and/or Diffie-Hellman as applications.
• Graph theory: Important types of graphs, graph isomorphy, trees. Graph theoretical algorithms, such as Prim's and Dijkstra's algorithms.
• Combinatorics: Counting results related to quantities, functions and graphs.

Learning outcome

The course will give students knowledge of how mathematics is used in solving problems in computer science. It will also provide a foundation for further specialisation in mathematics and computer science. The course emphasises applications.

Knowledge: The candidate should demonstrate knowledge of the following

• concepts in logic of statements.
• common forms of mathematical proofs, including mathematical induction.
• basic set theory.
• discrete functions and relations.
• concepts and algorithms related to graphs, including trees and graphisomorphism.
• concepts, methods and results in number theory, modular calculus and cryptography.

Skills: The candidate can

• apply basic concepts, results and methods from the theory of statements and arguments, for example determine whether an argument is valid or invalid and determine whether two statements are equivalent
• construct simple mathematical proofs, including inductive proofs
• apply basic concepts and results related to set theory, discrete functions and relations, and can represent these in different ways
• apply basic concepts and results related to graphs, including paths in graphs and graphisomorphism
• apply algorithms to smaller examples,
• apply basic concepts and methods from number theory related to divisibility, including Euclid's algorithm
• apply congruences calculations and work with Diffie-Hellman key exchange and/or RSA.

General competence: The candidate

• can communicate about and by means of mathematics, and use relevant mathematical notation
• can use mathematics to model and solve theoretical and practical problems in situations relevant to their own field, in academic and professional contexts.

Learning methods and activities

Lectures and exercises. Exercises will be based on assignments in a digital assessment system. Exercises and learning videos for self-study will be available as a supplement to the lectures.

Compulsory assignments: at least 75% of the exercises must be approved for admission to the exam. The number of obligatory assignments and weighting will be announced at the start of the semester.

Compulsory assignments

• Obligatorisk arbeidskrav

Specific conditions

Recommended previous knowledge

Mathematics from secondary education

Course materials

Recommended literature will be published at the beginning of semester.

Credit reductions