**Workshop 1: "Magical tricks with a mathematical background", by Prof. Dr. Ehrhard Behrends, **Department of Mathematics and Computer Science, Freie Universitat Berlin, Germany

I happens every now and then that a mathematical fact can be transformed into a surprising mathematical trick. Examples can be found in many areas of mathematics (elementary number theory, combinatorics, theory of invariants, probability, ...), and in this interactive workshop some of them will be explained.

**Workshop 2: "Mathematical Magic Tricks", by Prof. Dr. Michael Lambrou, **Department of Mathematics, University of Crete, Greece

The workshop will focus on some interesting number guessing tricks and will discuss the mathematics behind them. All the tricks performed need prearranged equipment, such as cards or dice with sets of numbers printed on them. The workshop will be "hands on" and students will learn how to construct the necessary equipment and understand why the tricks work. The mathematics dicussed comes from various fields such as elementary Number Theory or Combinatorics.

**Workshop 3: "Proofs without words", by Prof. Sava Grozdev, **VUZF University, Sofia, Bulgaria

Click here to download the Workshop 3 Description

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**Workshop 4: "Making Mathematics fun and easier to learn, using cartoons and funny stories", by Dr Sotos Voskarides, **Department of Electrical Engineering, Computer Engineering and Informatics, Cyprus University of Technology, President of Cyprus Cartoonists Association, Cyprus

Funny stories enriched with funny drawings, humorous cartoons and comics are the main tools to be used in this workshop whose aims are: (i) to convey mathematical ideas in a unique relaxing, easy and funny way, (ii) to show how much happiness and fun students (and also teachers) can get during the learning process of Mathematics by using cartoons and humor, (iii) to improve dramatically student’s motivation in learning Mathematics and (iv) to make learning of Mathematics more attractive and enjoyable for everybody.

This method can be an alternative option to teachers to convert to real happiness and satisfaction the anxiety and the negative approach of some of their students inherited maybe from their past or older students or relatives or teachers or in some cases from all the above.

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**Workshop 5: "Isogonal Transformation revisited with GeoGebra", by Peter Kortesi, **University of Miskolc, Miskolc, Hungary

The symmedian lines and the symmedian point of given triangle present interesting properties. Part of these properties can be formulated in a more general context for isogonals. In a triangle the isogonal of a line passing through one of the vertices of the triangle is a line symmetric to the bisector of the given angle. It can be proven that the three isogonals of three concurrent lines which pass through the three vertices of the triangle, are concurrent. This property serves as definition for the isogonal transformation, the image of a given point in this transformation will be the intersection point of the three isogonals of the three lines which pass through the given point and the vertices of the triangle. The workshop is aimed to present some of the properties of the isogonal transformations, and to visualise them using GeoGebra.

**Workshop 6: "Mathematics in the service of Cryprography and Cryptanalysis", by Marija Bosnjak, **Tehnicka Skola Pozega, Croatia

Cryptography is a scientific discipline that studies the methods for sending messages in a form that only those whom are intended can read it. It will be presented classical and modern cryptography and cryptanalysis. We will try to explain to which extent math is behind it all and give examples.

Students will have a chance to encode and decode words and whole sentences using the methods of encryption and decryption.

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Workshop 7: "The Ring Lemma", by Professor Mats Andersson, Senior Lecturer Samuel Bengmark, Professor Torbjörn Lundh and PhD Student Anders Karlsson, **

**Chalmers University of Technology, Sweden**

Click here to download the Workshop 7 Description

**Workshop 8: "Random Trees as Models of Evolution", by Serik Sagitov, Department of Mathematical Sciences, Chalmers and University of Gothenburg, Sweden**

Charles Darwin's Tree of Life shows that all species on Earth are related and that they evolved from a common ancestor. Many details of the tree of life are not known and therefore it is relevant to view it as a random tree. At another level, the gene trees connecting the gene copies of different individuals within a single species can also be treated as random trees. During this interactive lecture we will together build from scratch a few basic mathematical models of random trees that play an important role in modern Population and Evolutionary Genetics.

**Workshop 9: "Hyperbolic Geometry", by Ulf Persson, Department of Mathematical Sciences, Chalmers and University of Gothenburg, Sweden**

What is most obvious? 1 + 1 = 2 or that the angular sum of a triangle is (or if you prefer 180?). I guess most of you could not imagine a world in which the first was not true, while the second statement is different. It is surprising and far from obvious, although there is a very simple argument for it, based on a very reasonable principle that lies behind all Euclidean geometry, the so called Parallel Postulate. But is it true, and if so can we prove it using even more foundational principles? Euclid assumed it was true, giving no arguments, but asserting it as an axiom. People tried in vain over a period of several thousand years to prove it, but to no avail. In the beginning of the 19th century three mathematicians had the courage to deny it and thus explore the possibilities of alternate geometries, so called non-Euclidean geometries. In the talk we will describe the strange world of Hyperbolic Geometry (with occasional references to the much more imaginable Spherical Geometry) where the angular sums of triangles do not add up to π, where perimeters of circle grow exponentially, where you can only see small parts of spheres, where indeed the limits of large spheres are no longer planes, but something intermediate. And in which the starry sky would change noticeable when you walk on the ground. It is a strange world, but nevertheless it has physical interpretations via Special Relativity Theory.