Workshop 1

Non-constructive Theorems in Problem Solving

Prof. Sava Grozdev

Bulgarian Academy of Sciences 



The Curriculum of Mathematical Olympiads comprises the so-called non-constructive theorems and we shall discuss them in more details during the Workshop. These are theorems of existence but they do not provide an algorithm to find what is claimed to exist. We shall give the theorems without proof but with illustrations of their application, formulating problems and discussing their solutions. Among the theorems to be considered are: the Fundamental Theorem of Algebra, Bolzano and Weierstrass theorems on continuous functions, Lagrange growth theorem, Cantor theorem, Chinese remainder theorem, Thue Lemma, Dirichlet theorem for infinite arithmetic progression, Bachet theorem, Dirichlet principle.  


Workshop 2

The Passage from Recreational Mathematics to Pure Mathematics

Professor Michael Lambrou

Department of Mathematics, University of Crete



In the workshop we will discuss the idea of making mathematics attractive by using material from recreational mathematics. In particular, we will discuss various intriguing "impossibility proofs" drawn from recreational mathematics and build up to a similar topic in serious mathematics.


Workshop  3 (80 minutes)

  Introduction into elementary coding theory 

Professor  Dr. Guenter Toerner

Professor Törner Anne

Universitaet Duisburg-Essen 



Coding theory is the study of methods for efficient and accurate transfer of information from one place to another. The mathematical theory behind is about 60 years old, however its questions and preliminary answers can be traced back to ancient times. Many fields of mathematics such as linear algebra, ring theory, geometry and algebraical geometry have contributed essentially to the still engrowing theory within discrete mathematics. There are numerous applications developing methods for e.g. computer science, information theory, astronomy and astronautics. 


The workshop (80 minutes) will introduce into this topic and will reveal the high importance of coding theory for modern communication. First models can be understood even at school level. So the lecturer is anticipating an interesting auditorium and is welcoming all participants. 


Workshop 4


Professor Peter Kortesi

University of Miskolc 



The flexagons can be considered as a type of topologiocal model. They are figures made from a sheet of paper, but end up having surprising properties, like many faces appearing by flexing them. The first flexagon description - the tri-tetrafleaxgon - appeared in 1897 (Albert Hopkins: Magic Stage Illusions and Scientific Diversions) and it was very popular. The creation of the hexa-hexaflexagon in 1934 by Arthur Stone initiated mathematical interest in these figures. Three friends B. Tuckerman, R. Feyhman, and J. Tukey studied the properties of the hexa-hexaflexagons, and developed a complete mathematical theory for them. A number of scientific papers appeared (M.Gardner in Scientific American, 1956, O.C. Oakley and R.T. Wisner in The American Mathematical Monthly, 1957). The tetra-flexagons are rectangular flexagons. The simplest of them is the tri-tetraflexagon, where tri- indicates the number of faces, and tetra the form of the figure. We will study the contruction of the tetra-tetraflexagons, and hexa-tetraflexagons. Recently in the article:The combinatorics of all regular flexagons, (McLean et all. , European Journal of Combinatorics Volume 31 Issue 1, January, 2010) a regular flexagon is given as one that contains 9n equilateral triangular regions on a straight strip of paper. The flexagon is said to have order 3n because you can color 3n of the faces with 3n different colors. An other family of regular flexagons to be studied are the hexaflexagons, we will experiment the hexa-hexaflexagons, nona-and dodeca-hexaflexagons, and discover a bit of their mathematics.


Workshop 5: 60 min

The role of counter examples in overcoming the errors in mathematics

Gagatsis Athanasios, University of Cyprus

Philippou Andreas, CMS

Timotheou Savas, CMS

European Mathematical Society
Munich Re
National and Kapodistrian University
Hellenic Mathematical Society