Discrete mathematics is the study of objects and structures that are fundamentally discrete - made up of distinct and separated parts - as opposed to continuous.

Developing mathematics to describe structures limited to integers

This area of mathematics that has become increasingly important in recent decades, in part due to the advent of computers, and in part because of the recent ubiquity of large discrete (social, biological, ecological etc.) networks.

Discrete mathematics has many real-world applications in areas such as logistics, engineering, cryptography, computer algorithms, computer vision and relational databases. Applications vary from finding an optimal railway schedule, securing your privacy in WhatsApp, or protecting your data on a memory device against physical damage.

Describing the algebraic and geometric aspects of discrete structures in mathematics and its application areas involves objects such as finite fields, graphs, (zero sets of) polynomials, groups, algebras, and symbolic computations. The Discrete Algebra and Geometry group at TU/e develops the mathematics needed for such a description. The group plays a leading role in algebraic graph theory, combinatorics, finite and incidence geometry, group theory, discrete Lie theory and applied algebra. Team members are active in the fields of computer algebra, interactive mathematics, and applied and discrete aspects of algebraic geometry.

Recent research themes include the study of simple groups and simple Lie algebras by geometric methods, of special subsets in finite projective planes (or spaces), and of solving large systems of polynomial equations with symmetry. The group is also involved in innovation of (mathematics) education, for which it develops, experiments with and implements new forms. This includes open source software for interactive (mathematical) documents on the web, and research into the set-up of such documents and their use. The group offers this software and other open source tools for education to the larger TU/e community and beyond (e.g. 4TU.AMI institute). These activities resulted in the company Sowiso, specialized in digital testing of mathematics.

The group collaborates closely with researchers from the University of Ghent, University of Birmingham, University of Bern, Eötvös Loránd University of Budapest and 4TU.AMI (the mathematics institute of Delft University of Technology, University of Twente, Wageningen University and TU/e). Within TU/e’s mathematics department, the team is closely connected to the Coding & Cryptology group, and the Discrete Optimization group.