# Studying Mathematics in Germany

Mathematics is when arithmetic stops and thought begins

An article by Daniel Kastner

## That is what it’s about

Mathematicians solve problems and prove or disprove assumptions that arise in everyday life. "Mathematics is a living subject," says Herold Dehling, spokesman for the Conference of Mathematical Departments and professor at the University of Bochum. Again and again, mathematicians develop new theses and develop them further. Like Peter Scholze, a 31-year-old mathematician from Bonn, who received the Fields Medal in 2018 for his reflections on "perfectoid spaces", the "Nobel Prize” in the field of Mathematics. In fact, maths is not a mere science of numbers, but it sets logical rules and provides the "language" with which other natural sciences can communicate. In a world that is becoming more and more complex and increasingly shaped by numbers and data, the area of work for mathematicians is growing. Mathematics plays an important role in the development of smartphones, self-driving cars or artificial intelligence, insurance rates, logistics or traffic planning. "Those who study maths have the best job opportunities," says Herald Dehling.

## This is how the course runs

Everything is based on analysis and linear algebra. For two to three semesters, students engage in basic lectures with differential and integral calculus, linear systems of equations, matrices and vector spaces. They learn to master the precise logic of the subject and, for example, to distinguish between "necessary" and "sufficient" conditions. Many universities also require programming internships - above all, it is important to prove mathematically that a program does what it should do. Stochastics and numerical analysis are added in the second academic year. Partial differential equations are also examined, as well as mathematical modelling. In doing so, students must find the best solutions to various problems, such as how they can optimally manage timetables in a transport network, and when, and where they have to deploy how many trains and how much staff to use. In the third year, they attend specialization modules such as cryptography or number theory. Most universities also have a minor subject, such as physics, computer science or even philosophy. It is advisable to do an internship during the mathematics course - for example with a statistics office, in a bank, with an insurance company or a management consultancy.

## Typical questions raised within the subject

- How can information be encrypted so that it is difficult to crack the code?
- What distinguishes finite- and infinite-dimensional vector spaces?
- Why can the number of real numbers not be counted?
- Why are there infinitely many prime numbers?
- What does a coin toss have to do with the Gaussian bell curve?
- Which function gives the best approximation to given measured values?
- How to calculate the premium of a life insurance?

## The subject suits you,...

...if you enjoy abstract thinking. Those who study maths must solve tasks that seem unsolvable at first glance. That requires passion and discipline. Although you do not have many lectures at the beginning, you spend a lot of time working on exercise sheets. "Especially in the first year, mathematics is an extremely hard course," says Herald Dehling. He recommends joining together with others in a study group and attending a maths pre-course before beginning the course. Unlike in school, it is rarely about concrete calculation examples. Instead, you're dealing with definitions and proofs, and with a formula language of variables, constants, and functions.

## Is there a numerus clausus?

Only about one fifth of the degree programs are occupied by an NC. In teaching professions there are sometimes NCs in the area of grade 2 or 3.