Experimental Mathematics Lab
The Experimental Mathematics Lab promotes and coordinates experimental activities in mathematics at the University of Luxembourg.
We are all accustomed to the idea of experiments in physics, chemistry or biology. But mathematics can be done at an equally experimental level, often using computational methods. This applies to statistics, algebra, analysis, geometry, and other flavours of mathematics. It includes visualising complex mathematical objects, using computers to work with examples that go beyond what is possible using pen and paper and finding patterns in complicated data.
Even in highly abstract areas of mathematics the value of experimentation has increased dramatically in recent years, with computers, programming languages and computer algebra systems getting stronger and easier to use.
Projects for students
The Experimental Mathematics Lab (EML) was created in June 2014. It allows students at all levels (Bachelor, Master and PhD) enrolled at the University of Luxembourg to carry out original projects for their thesis, helping them to develop their understanding of mathematics but also their programming and modeling capabilities. With this laboratory, students can:
- develop new visualization tools and new images (or even movies or 3d printouts) of mathematical objects,
- develop modules for computing on mathematical notions, to be used either independently or as libraries for existing mathematical computing environment,
- make advances in mathematical questions, when progress can be made by applying computational tools—for instance for classification, for finding patterns or when a counter-example can be searched for.
We believe that participating in such computational mathematics projects can be an important addition to the “traditional” teaching of mathematics. One reason is that it gives students the opportunity to interact in a very practical way with elaborate mathematical notions, to the point where it often allows them to discover a new way to do and think about mathematics. Another is that it helps them develop programming skills that are useful well beyond their studies.