Sets and Combinatorics

COURSE OBJECTIVE
After completing this course, the student

1. understands the basic notions, operations and algebraic rules of set theory;
2. can prove set inclusions and set equalities in set theory;
3. can work with the standard sample spaces of Probability Theory, and compute the sizes of such sample spaces and of typical events;
4. can decide whether a given function is injective, surjective and/or bijective;
5. can determine images and preimages of sets under a given function;
6. knows how to construct proofs by mathematical induction.

COURSE CONTENT
Sets, set operations, the algebra of set theory, the laws of De Morgan, product sets and power sets, standard samples spaces of Probability Theory, basic rules of combinatorics, binomial and multinomial coefficients, binomial and multinomial theorem, cardinality and (un)countability, functions and graphs, principle of mathematical induction.

TEACHING METHODS
In each of the first three weeks: two lectures and one exercise class. In the fourth week: one lecture and one exercise class before the final exam.

TYPE OF ASSESSMENT
Written exam (75%) at the end of the course, and written pretests made in class at the end of the exercise classes (25%). The final grade is the weighted average of the exam and the pretests (a bad grade for one test can be compensated by a good grade for another tests). For the resit exam, the pretests are still taken into account if this is in the student's favour. If the average grade of the pretests is lower than that of the resit exam, only the grade of the resit exam will count.