The Austrian Mathematics Olympiad is a series of competitions and preparatory courses for school pupils in 7th and sometimes 6th grade. Further information on the Olympiad can be found here.
The Department of Mathematics runs a variety of activities for school pupils interested in maths. These include:
We are also happy to visit schools to give interesting lectures on maths or give a lecture for school classes coming to our university. These lectures are suitable for pupils in 6th grade and above (taken as an elective, for instance) and cover a wide variety of topics, including well-known mathematical puzzles and recent research.
A list of topics can be found below. If you are interested in finding out more, just get in touch!
For anyone with a particular interest in finding out about day-to-day mathematical research activities, they have the option of spending a month during the summer holidays (usually in July/August) on a holiday research placement in the department. Further details about this and information about the organisational process can be found here.
School pupils interested in finding out more about studying maths at university have the opportunity to do just that! Within the framework of the student union’s Degree programme tasters scheme, it is possible for pupils to attend individual lecture units, in which (for the most part) contents are dealt with that don’t have any particular requirements. Each semester, we usually offer one or two such lecture units for our Bachelor’s in Technical Mathematics. Details about the programme and registration can be found here.
There is also the SchülerInnen an die Hochschulen university visit programme, which is run by the Austrian Research and Support Centre for the Gifted and Talented (ÖZBF). Further details about this programme can be found here.
School visits: available lectures (selection)
Sorting algorithms are some of the best-studied in the field: so imagine the surprise when a new, faster-than-anticipated sorting algorithm was introduced for Java in 2009. This lecture reports on a current study (with Aumüller, Dietzfelbinger, Krenn and Prodinger), in which dual-pivot Quicksort is analysed precisely for the first time, and presents an outlook on multi-pivot Quicksort (work-in-progress with Daniel Krenn).
Digit expansions in elliptic curve cryptography
When encrypting sensitive data (for example online), one-way functions are often used; these are functions that can be quickly calculated, but the reversal of which is extremely difficult for attackers to calculate. In order to increase security, larger parameter values must be chosen, but this must not increase the calculating time excessively. One approach to speed up the calculations involves digit expansions with negative digits.
Fixing little mistakes: Check digits and coding...or: how to understand IBAN
When entering a long series of numbers such as an ISBN, EAN or IBAN, it’s easy to make a mistake. The numbers can be mixed up or perhaps left out altogether. For this reason, these series of numbers usually contain one or more “check digits”, which are able to identify these sorts of errors. Similar processes are also used when saving data on hard disks or USB sticks, in order to protect against technical defects. In this workshop, the mathematical procedures that are used for these types of check digits are presented, and these are then tried out in practice with the help of examples.
Mathematical optimisation in practice
Abstract: Satalia (NP Complete) is a successful British technology company with a focus in the fields of mathematical optimisation and artificial intelligence. Satalia is currently financing a long-term research project with the Department of Mathematics at the Alpen-Adria-Universität Klagenfurt. Within the framework of this project, Philipp Hungerländer and his team are working on various projects, including with one of the world’s largest supermarket chains and one of the world’s biggest auditing companies. This involves the implementation of their mathematical research results for the improvement of a wide range of economic processes in the fields of logistics and personnel planning.
Inverse problems in acoustics
In various technical and medical applications, acoustic waves are used, for example in ultrasound images from inside our bodies. Acoustic noise can, however, also become very unpleasant. Inverse problems, which are practical problems in which the causes for desired or observed effects need to be calculated, appear in a variety of acoustic applications, from the optimal design of medical ultrasound devices to the reconstruction of noise sources from indirect microphone measurements. In this lecture, we cover a wide variety of topics, from applications from our current research to relevant brain teasers for school pupils.
The dynamics of love
Mathematics is known to be both an aesthetic and a useful science. Instead of demonstrating this with the well-known applications from physics, life sciences or engineering, this lecture is dedicated to romantic relations. We present mathematical models based on differential equations that can be used to predict the evolution of romances and discuss them.