The course contents are divided into mandatory topics and deepening topics. The mandatory topics are all necessary for a passed grade whereas the study of deepening topics can give higher grades. Throughout the course an emphasis on sound mathematical arguments and methods of proof will be present. This means that each area of the course will be a training in sound reasoning applied to the particular subject matter of that area. For example, the study of sets will involve the study of how to prove set formulas.
The mandatory topics are:
* Elementary logic, involving basic logical connectives and the study of sound arguments and methods of proof.
* Introductory set theory, involving basic set operations.
* Functions, in particular used for the articulations of isomorphisms of graphs.
* Basic number theory (divisibility, congruences, prime numbers etc.)
* Graph theory, the isomorphism concept, trees, directed graphs, matrix representations, Eulerian circuits and paths and related properties. The usage of graphs to model properties worth reasoning about and computing possibly involving applications like finding the minimal spanning tree or the shortest path between two nodes in a weighted graph.
* Basic combinatorics including the study of the principle of multiplication, the principle of inclusion and exclusion, the binomial theorem, combinations and permutations.
The deepening topics are:
* Relations including partial orders and equivalence relations, with applications and examples from number theory including the congruence relation.
* More advanced number theory with methods of proof such as mathematical induction possibly with applications in cryptography or similar areas of interest.
* Basic discrete probability theory, event space, conditional events, and independent events.