### General Information

Course Code | X_400621 |
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Credits | 3 EC |

Period | P3 |

Course Level | 100 |

Language of Tuition | English |

Faculty | Faculty of Science |

Course Coordinator | dr. R. Hindriks |

Examiner | dr. W. Kager |

Teaching Staff |
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 |
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Target audiences

This course is also available as:

### Course Objective

After completing this course, the student1. 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 onetutorial 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 awritten exam at the end of the course. The exam determines 75% of the

grade, the pretests together determine 25% of the grade. The final grade

is the weighted average of the exam and the pretests (in particular, a

bad grade for one test can be compensated by a good grade for another

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 beprovided through Canvas.