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
• Fermat’s little theorem
• fast modular exponentiation
• 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.

This workshop can be offered in Luxembourgish, French, German and English.

The 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.

If you wish to prepare the class before the workshop, you can review or introduce the following concepts:

• 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).
• 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.
• The definition of a prime number.
• The basic rules of exponentiation.

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

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

If you arrive by train, the stop is “Belval Université”. The MSA 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.

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.

This workshop is offered either as a full-day (6.5 hrs.) or as a half-day (3-4 hrs.) 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.

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

This workshop can be offered in Luxembourgish, French, German and English.

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

If you arrive by train, the stop is “Belval Université”. The MSA 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.

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.

This workshop can be offered in Luxembourgish, French, German and English.

This workshop is offered either as a full-day (6.5 hrs.) or as a half-day (3-4 hrs.) 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.

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

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

If you arrive by train, the stop is “Belval Université”. The MSA 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.

The concept of classifying objects, that is of grouping them into different categories according to certain criteria, plays an important role in many sciences. For example, in biology organisms are classified based on common characteristics and evolutionary relationships. In mathematics exactly the same happens, and many mathematicians are concerned about the classification of mathematical objects.

This workshop gives an introduction into the concept of classification and illustrates its importance in science and mathematics. Through specific examples, such as numbers, geometric shapes, graphs or knots, the pupils see how mathematical objects can be classified and further learn how so-called invariant properties can be used to distinguish objects.

This workshop is suited for pupils from 3^e onwards.

This workshop is offered as a half-day (ca. 3.5 hrs.) course. Teachers are free to choose their preferred starting time (can be done during registration procedure).

This workshop can be offered in Luxembourgish, French, German and English.

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

If you arrive by train, the stop is “Belval Université”. The MSA 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.

This workshop gives students an overview of mathematical modelling and shows them how real-world problems can be modelled and solved using mathematics.

The workshop is divided into two parts, the first of which focuses on linear optimization. Students learn how to formulate a linear optimization problem and how a problem with two variables can be solved graphically. They then learn about the simplex algorithm, which can be used in the general case. The second part is devoted to the modelling of growth processes, and deals in particular with the SIR model, which is used to model the spread of an epidemic in a given population.

The workshop covers, among other things

• Introduction to mathematical modelling
• Examples of linear optimisation problems
• Graphical resolution of a two-variable problem (using GeoGebra)
• The simplex algorithm
• Introduction to modelling growth processes
• Linear, exponential and logistic growth
• The SIR model with implementation in GeoGebra

This workshop is suited for students from 3ème onwards. For the part on the simplex algorithm, it is advantageous if students already have some knowledge in manipulating systems of linear equations.

This workshop can be offered in Luxembourgish, French, German and English.

This workshop is offered either as a full-day (6.5 hrs.) or as a half-day (3-4 hrs.) 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.

Teachers that choose the half-day version of the course must choose one of the two parts of the workshop (i.e. optimization or population dynamics). They are free to choose their preferred starting time (can be done during registration procedure).

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

If you arrive by train, the stop is “Belval Université”. The MSA 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.