# Mathematics: what you can count on

## Mathematics: What you can count on

Students discover the other side of math

The 9th grade of a German high school: Graduation and university or an apprenticeship seem a long way off. Few students at this age know what career they want to pursue later on in life. IT companies in Paderborn thought that a bit of career guidance would be a good idea and decided to offer their support. Companies like OPTANO give pupils the opportunity to gain a brief insight into the day-to-day work of math, IT, science and technology professions. As a lot of mathematicians, analysts, optimizers and software developers work at OPTANO, the students learnt first-hand about how math is behind a lot of things we take for granted every day.

#### Welcome to OPTANO

In June 2023 we had the pleasure of welcoming 30 Paderborn high school students to our company. Our experts, Dr. Sven Flake and Dr. Philip Kühl, clearly demonstrated that math is not just the dry theory that is taught at school. After a brief introduction into the world of mathematical optimization, the pupils were encouraged to be active. They divided themselves into groups and, based on real-life tasks, they had to solve two classic optimization problems.

#### The Indiana Jones Knapsack Problem

First, the students had to solve the Indiana Jones problem – better known as the knapsack problem. This is a combinatorial optimization problem which we depicted as follows: Indiana Jones is carrying a knapsack with a maximum load capacity on one of his adventures. In a cave he finds various objects like statues, masks and ancient stone tablets. Each object has been labelled with its weight and value. The goal is to pack the best combination of objects in the knapsack to achieve the highest total value while not exceeding the load capacity of the knapsack. The tricky task meant that some of the pupils had to take out their calculators…

#### The shortest bus trip or the Traveling Salesman Problem

The Travelling Salesman Problem is also a combinatorial optimization problem. We are confronted with this problem in logistics in our day-to-day lives; for example delivery services, planning routes to for breakdown services or when meeting clients and making timetables – and this is what our young visitors had to do next.

Their task was to plan the optimal route based on the following: A school bus sets out from the school and picks up students at different stops to bring them to OPTANO and then back to school again. The idea of the task is to choose the best order of the stops so that the entire route is as short as possible. To make the task easier, the bus was to allowed to travel as the crow flies. To enable this, the bus in our example could fly – which is, of course, a big exception.

Equipped with a map and some thread, the students got down to work. They tried out a lot of routes and there was a lot of intensive debate in each group.

#### It's all so easy with optimization software

Later on, our colleague, Phillip, revealed the solutions to the tasks and also showed the pupils how complex such problems can become when there are more than just a handful of objects as in our knapsack problem, or when the Traveling Salesman problem involves far more stops than our bus trip. Here, a degree of complexity has been reached which requires the deployment of optimization software such as OPTANO in order to find a reliable solution – one that can be obtained at the touch of a button, as proven in our software demonstration.

#### And what's next?

Unfortunately it will take a few years until our visitors can actually join us as colleagues at OPTANO. We hope, however, that we were able to show them just how cool math can be, that they understand how it is all around us, whether we realize it or not, and that it often makes our working lives a lot easier. Perhaps the visit helped some of the students decide which career they would like to pursue later. As some of them even enquired about doing an internship with us, we assume that we had certainly piqued their interest.

#### An OPTANO mug as a keepsake

At the end of the day our HR team, which was responsible for making the day such a success, gave each pupil a small leaving gift: an OPTANO mug filled with candy. Maybe some of the students will take the mug with them when they go to university and move into shared accommodation in a few years. And maybe it will remind them that OPTANO is a really cool and interesting place to work.

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