The aim of the course is to become familiar with the standard methods that are used to protect digital data, when they are transmitted (internet, infrared, wireless, etc.), as well as when they are stored on some information carrier (cd, dvd, magnetic tape, hard disc, etc). The data are to be protected against random errors caused by noise, damage, impurities, and so on. To show how one can apply these codes to a public key cryptosystem and secret sharing.
Topics to be discussed are:
- Error correcting codes
- q-ary symmetric channel and the probability of correct decoding
- Systematic encoding, information sets and MDS codes
- Weight enumerator of a code
- Cyclic, Reed-Solomon, Goppa and Reed-Muller codes
- Several decoding algorithms
- NP-hard problems in coding theory
- Cryptographic systems of McEliece and Niederreiter
- Secret sharing
- Docent: Ruud Pellikaan
The aim of this course is to give a thorough introduction to the theory if Lie groups, in particular compact Lie groups and their representations.
A Lie group is a group with the additional structure of a differential manifold for which the group operation is differentiable. The name Lie group comes from the Norwegian mathematician M. Sophus Lie (1842-1899) who was the first to study these groups systematically in the context of symmetries of partial differential equations.
The theory of Lie groups plays a central role in the description of symmetries in Physics (quantum physics, elementary particles), Geometry and Topology (principal bundles), and Number Theory (automorphic forms).
- Docent: Erik van den Ban
The course is a combination of an introductory and an advanced course in set theory. The first part provides an introduction to axiomatic set theory so that the course can be followed by a student who has no background in axiomatic set theory. We will however assume mathematical maturity, including naive use of sets that is very common in mathematics.
The course will start with an introduction to axiomatic Set Theory, based on the axioms of Zermelo and Fraenkel. It will show how the generally well-known facts from naive Set Theory follows from these axioms and how modern mathematics can be embedded in Set Theory.
The second part of the course will offer combinatorial tools from Set Theory that have proved useful in infinitary situations in Algebra, Topology and Analysis.
- Docent: KP Hart