# Lectures and Workshops

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## Delta robots - Štefko Miklavič

Delta robots were invented in the early 1980s by profesor Reymond Clevel's research team from Ecole Polytechnique Federale de Lausanne, Switzerland. Their light construction gives them two properties highly valued in robotics: speed and precision. This makes them highly praised both in industry and some other areas, such as medicine. But when directing a delta robot we encounter a purely mathematical problem, solvable with some basic tools of space geometry. During the lecture we will first explore the structure and workings of the delta robot and then try to solve the before mentioned problem of how to direct them.

## Graphs are everywhere - Ademir Hujdurović

Have you ever thought about a travelling salesman, who needs to visit several cities where he sells his products? How can he optimise his trip? Or what about a postman who wishes to travel along every road in a city in order to deliver letters, with the least possible distance. Or a telecommunications company which is trying to lay out cables in a new neighbourhood along roads to have connection to every house and want to optimise their costs. On this lecture we will see how these and similar situations can be modelled by graphs and we will discuss methods of solving such problems.

## Isometries and similarities of the plane - István Kovács

In the lecture we will discuss two classical types of transformations of the plane. Isometries are the transformations that preserve the distance between the points, whereas the similarities are those, which change the distance by the same factor. All these transformations can be further divided to two classes

depending on whether they also preserve the orientation of the plane. It will be shown that every isometry can be written as the product of at most three reflections, and depending on the number and position of these reflections, we obtain the translations, rotations and slides. It will also be shown that the similarities consist of the isometries, central stretches, rotational stretches and axial stretches. As an application, we will also discuss some classical objects, such as Euler line, Euler circle and Simson line.

## Mathematics of strategic behaviour - Aljaž Ule

Mathematics is an important element of analyses prepared by experts in economics. Have you ever asked yourself how these experts actually develop a good mathematical model of people? In the workshop we will present a few basic models of human decision-making, competition and cooperation, and discover how a good analysis relies on mathematics, psychology, social sciences and a bit of biology.

## Paradoxa in probability - Mihael Perman

In probability theory there appear certain problems that seemingly lead to contradicting conclusions, though it is not immediately obvious why it is so. Mostly, paradoxes arise because of incomplete information or ambiguous definitions. When faced from the right viewpoint they mostly disappear. We will visit some of the classic paradoxes such as Bertrand paradox, the paradox of prison and other similar ones, then a bit more complicated paradoxes such as the Martingale strategy paradox and the St. Petersburg paradox.

## Slide-Together Geometric Constructions - Mary Servatius (project work only)

The five platonic solids have been studied and admired for thousands of years. In this project we will explore the concepts of regularity, duality, and the golden ratio by building the contemporary models of George Hart with ruler and compass. While the focus of this project is to build geometric intuition, the exploration will lead us to some classical results from Geometry.

## Trading on stock exchanges - Rado Pezdir

Students will learn fundamental concepts of stock trading and finance using web trading platform +500. Although the focus of workshop will be on trading itself some theoretical concepts will be explained as well i.e. fundamental and technical analysis and how quantitative modelling is done. We will also apply some statistical concepts such as Brownian motion (using excel) to forecast movement of stock prices and test our predictions on real world data.