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## Sets and Combinatorics

2019-2020

### Course Objective

After completing this course, the student
1. is able to prove identities between sets using Venn diagrams and the
algebra of sets or logical reasoning;
2. can compose sets using set operations to produce a desired set, and
conversely, determine the elements of such a composed set;
3. can work with the standard sample spaces of Probability Theory to
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. is able to construct proofs by mathematical induction and apply the
binomial and multinomial theorem in calculations.

### Course Content

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

### Teaching Methods

In each of the first three weeks: two lectures of 2 hours, and one
tutorial of 3 hours. In the fourth week: one lecture of 2 hours and one
tutorial of 2 hours before the final exam.

### Method of Assessment

Three written pretests during each of the first three tutorials, and a
written exam at the end of the course. The exam determines 75% of the
is the weighted average of the exam and the pretests (in particular, a
test). For the resit exam, the pretests are only 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. There is no resit possible for pretests only.

### Literature

Lecture Notes for the course and all additional course materials will be
provided through Canvas.

1BA

### General Information

Course Code X_400621 3 EC P3 100 English Faculty of Science dr. R. Hindriks dr. R. Hindriks

### Practical Information

You need to register for this course yourself

Last-minute registration is available for this course.

Teaching Methods Seminar, Lecture
Target audiences

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