Discrete Mathematics is concerned with finite structures and their properties. It is an exciting growth area in the modern information age. Just as continuous mathematics led to major scientific developments in the 19th and 20th century, Discrete Mathematics with its various subfields such as algebra, combinatorics, computational algebra, coding theory, cryptography, discrete optimization, information theory, geometry, graph theory, machine learning, number theory, etc., underlies much of the developments in modern fields such as computer technology, communication networks and e-commerce.

The cluster Discrete Mathematics is interested in all mathematical problems of a discrete nature

Applied and Provable Security
Coding Theory and Cryptology
Discrete Algebra and Geometry
Mathematical Communication Theory

form the DM cluster.

Cryptology is the mathematical theory of protecting information against unauthorized access (confidentiality), ensuring that a message has not been altered by a third party (integrity) and really originated from the person who is claimed to be the sender (authenticity). Work in the groups in DM covers the design of systerms as well as building larger constructions and protocols, including multi-party computation. Moreover, different groups work on analyzing the security of cryptographic schemes using cryptanalysis techniques (analyzing the underlying mathematical problems) and security proofs (relating the security of schemes and protocols to the security of used building blocks). To ensure correctness of security proofs, groups also work on applying tools from formal verification to verify proofs.

Mathematical communication theory enables reliably communicating data over a possibly noisy channel, efficiently storing and retrieving them, and guaranteeing their integrity. Work in the groups in DM covers coding theory, optimization for data storage and recovery, network coding, quantum error correction, and links with cryptography in code-based cryptography, an area of post-quantum cryptography.

The third main area in DM covers discrete algebra and geometry including ,enumerative and algebraic combinatorics. Phenomena throughout mathematics and the natural sciences have discrete algebraic aspects, often along with analytical counterparts. While the latter are typically modelled using real numbers, differential equations, and numerical computations, describing the discrete-algebraic aspects involves objects like nite elds, graphs, polynomials, groups, algebras, and symbolic computations. The Discrete Algebra and Geometry (DAG) group at the TU/e develops the mathematics needed for such a description.

Publications of the DM cluster can be accessed by clicking on All publications