Islands: research topic for students

Időtartam: 45
Technikai eszközök:

Computer, projecting possibility

Hallgatóság: max. 50-60 persons, grades 11-12.

The topic of islands will be introduced. Although the area  is new, the methods we show can be easily understood and are based on elementary (high school) mathematics.We will explain the notion of an island in details. We give motivation and the history of the topic, starting with the result of Gábor Czédli (Szeged). We give overview of the elementary methods and of the elementary results. Finally, we list some open problems.

Let a grid be given. A height is assigned to each cell of the grid. We call a fixed shaped part of the grid an island, if all of its cells are higher than its neigbouring cells. The maximum number of islands is a central question. The notion came from information theory (S. Földes, N. Singhi), however the topic became a new research area. The questions can be easily understood and investigated by students as well, improving their creativity and giving them (and us) a challenge to find new results.