Mathematics for Computer Science

• Logics: Statements, arguments, basic proof theory. Mathematical induction.
• Set theory and discrete functions.
• Number theory: Divisibility and congruence, Euclid's algorithm, Diffie-Hellman as application.
• 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.

The course will give students knowledge of how mathematics is used in solving problems in computer science. It also provides a foundation for further specialization in mathematics and computer science. The course puts emphasis on 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 graph isomorphisms.
• 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 equivalence relations, paths in graphs and graph isomorphisms
• apply algorithms to smaller examples,
• apply basic concepts and methods from number theory related to divisibility, including Euclid's algorithm
• apply congruences calculations and perform Diffie-Hellman key exchange

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.

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.