Course content

The course gives an introduction to mathematical logic and set theory, and elementary number theory with modular arithmetic. Other central topics are: Sequences, recurrence relations, mathematical induction and combinatorial counting methods with applications. Moreover, the course gives an introduction to the theory of relations, graphs and trees, as well as formal languages, grammars and finite automata.

Learning outcome

1. Knowledge. The student has a basic knowledge of mathematical logic, set theory and combinatorial counting methods. The student is familiar with elementary number theory, including the chinese remainder theorem and Fermat's little theorem. The student has knowledge of recursion an induction, as well as relations, graphs and trees. The student also has basic knowledge of formal languages, grammars and finite automata.

2. Skills. The student is able to make practical use of elementary logic and set theory, can apply Euclid's algorithm, and is proficient in modular arithmetic. The student can solve systems of linear congruences using the chinese remainder theorem, can write simple proofs using induction, and is able to recognize, understand and apply concepts such as relations, graphs and trees in applications, for example in information technology. Moreover, the student is able to apply combinatorial counting methods to solve practical problems, and can make practical use of finite automata.

Learning methods and activities

Lectures, compulsory exercises, mid-semester examination. Portfolio assessment is the basis for the grade awarded in the course. This portfolio comprises a written final examination (80%) and the semester assignment (20%). The results for the constituent parts are to be given in %-points, while the grade for the whole portfolio (the course grade) is given by the letter grading system. The mid-semester examination only counts if it has a positive effect on the total assessment. Retake of examination may be given as an oral examination.

Compulsory assignments

• Exercises

Recommended previous knowledge

None.

Course materials

Will be announced at the start of the semester.

Credit reductions