1. Deal with randomness? Thanks to probability theory!

This workshop gives the pupils an introduction into the theory of probability and its basic mathematical notions and concepts. Practical exercises that the pupils carry out by themselves help them to gain a clearer understanding of how to deal with probabilities. By means of specific examples, for instance from the field of medical sciences, they also see how concepts from probability theory can help to make decisions.

The workshop covers among others the following concepts

• Basic notions (random variable, expected value, distribution)
• Bernoulli experiment and the binomial distribution
• Geometric distribution
• Conditional probability
• Examples and applications of probability theory

This workshop is suited for pupils from 3^e  onwards.
The workshop is flexible and the pace is adapted to the level of each class.

2. Finding the shortest path? Thanks to graph theory!

During this workshop, the pupils get an introduction to graph theory and learn how different theoretical concepts are used to model and solve problems that arise in daily life, for example in logistics and planning. The pupils can actively participate in the workshop and in various practical exercises, they have the opportunity to test by themselves the concepts addressed by the workshop.

The workshop covers among others:

• the problem of the seven bridges of Königsberg
• Eulerian and semi-Eulerian graphs
• weighted graphs
• Dijkstra’s algorithm to find the shortest path
• the Traveling Salesman problem
• Google’s PageRank algorithm
• applications of graph theory in daily life

This workshop is suited for pupils from 4^e  onwards.

3. Keep a secret? Thanks to Number Theory!

This mathematics workshop allow students to learn how number theory is applied to secure communications. Through practical exercises such as decryption of a coded message with a cipher wheel, the student will discover how an encryption algorithm works and understand the underlying number theory.

They will tackle different mathematical concepts:

• the Euclidean division (division with remainder)
• the greatest common divisor
• the extended Euclidean algorithm
• Fermat's little theorem
• the RSA-algorithm

If the teachers wish to prepare their classes before the workshop, corresponding materials that can be used to work with the students will be provided. (For more details see the Prerequisite tab)

This workshop is suited for pupils from 3^e  onwards.
The workshop is flexible and the pace is adapted to the level of each class.

Class level and age or participants

All the mathematics workshops are suitable for classes ranging from 3^rd to 1^st grade (in the Luxembourgish school system), meaning students aged 15 to 19.

Workshop 2 (graph theory) is also suitable for classes from the 4^th grade.

Language

The workshops can be given in Luxembourgish, French, German or English.

Time schedule

Workshops 1 and 2 (probability and graph theory) can be offered either as a full-day (6.5 hrs.) or as a half-day (3-4 hrs.) course. Workshop 3 (number theory) can only be offered as a full-day course.

The full-day workshops take place from 9:00h till 15:30h with a lunch break of one hour. During the lunch break the students can get some food from the restaurants that are located on Campus Belval and in Belval Plaza, or they can use the canteen. The lunch schedule need to be observed, so that the afternoon activities can resume on time.

Teachers who choose the half-day version of the course are free to choose their preferred starting time (can be done during registration procedure).

Location

The workshops in mathematics take place in the Maison du Savoir (MSA) on Campus Belval.

If you arrive by car or coach, take the A4 and keep it until the end, then follow the signs towards "Belval". On the campus, there are no signs to indicate the way to Maison du Savoir. Please use the map below to find your way.

If you arrive by train, the stop is "Belval Université". Our building is 10 minutes away from the train station by foot. There are also several buses that you can take to arrive on the campus.

Prerequisite

For workshop 3 (focusing on number theory), if you wish to prepare the class before the workshop, you can review or introduce the following concepts:

a) The Euclidean division (i.e. the division with remainder) and the Euclidean algorithm (for the division, the case of a negative dividend/divisor should also be considered).

b) The Greatest common divisor (gcd) of two integers and Bézout's identity that gives the gcd of two integers as a linear combination of these integers. (For example 3 = gcd(6, 15) = -12*6 + 5*15). Such a linear combination can be obtained by means of the extended Euclidean algorithm.

c) The definition of a prime number.

d) The basic rules of exponentiation.

Materials that can be used for the preparation will be provided.

Certificate

At the end of a workshop, each student receives a certificate attesting to his participation.