• Course code:63536B
  • Credits:6
  • Semester: winter
  • Contents

Each year the lecturer is a visiting professor from other universities.

The course will be held  by: Michael Lang

The course is intended for established visiting researchers and lecturers and for experts in computer and information science which will introduce students to topics that are interesting due to recent theoretical findings and methodological breakthroughs or for their applicative value, and are as such not included into the existing curriculum.

The specific contents of the course are determined yearly.

 

The course will include selected advanced topics in:

  • Latin squares (orthogonal arrays, conjugates and isomorphism, partial and incomplete Latin squares, counting Latin squares, the Evans conjecture)
  • Hadamard matrices, Reed-Muller codes (Hadamard matrices and conference matrices, recursive constructions, Payley matrices, Williamson's method, excess of a Hadamard matrix, first order Reed-Muller codes)
  • Designs (the Erdös-De Bruijn theorem, Steiner systems, Hadamard designs, counting, incidence matrices, the Wilson-Petrenjuk theorem, symmetric designs, projective planes, derived and residual designs, the Bruck-Ryser-Chowla theorem, constructions of Steiner triple systems, write-once memories)
  • Codes and designs (terminology of coding theory, the Hamming bound, the Singleton bound, weight enumerators and MacWilliams’ theorem, the Assmus-Mattson theorem, symmetry codes, the Golay codes, codes from projective planes)
  • Strongly regular graphs and partial geometries (the Bose-Mesner algebra, eigenvalues, the integrality conditions, quasisymmetric designs, the Krein condition, the absolute bound, uniqueness theorems, partial geometries, examples)
  • Orthogonal Latin squares (pairwise orthogonal Latin squares and nets, Euler's conjecture, the Bose-Parker-Shrikhande theorem, asymptotic existence, orthogonal arrays and transversal designs, difference methods, orthogonal subsquares)
  • Projective and combinatorial geometries (projective and affine geometries, duality, Pasch's axiom, Desargues’ theorem, combinatorial geometries, lattices, Greene's theorem)
  • Gaussian numbers and q-analogues (chains in the lattice of subspaces, q-analogue of Sperner's theorem, interoperation of the coefficients of the Gaussian polynomials, spreads)

 

Objectives and competences:

The goal of the course is to introduce basic theoretical ideas as well as practical implementations of new methods and technologies in the field of computer and information science.

 

Intended learning outcomes:

Knowledge and understanding: A broader overview and understanding of the field of study, and of up to date methods and concepts.

Application: Applying current approaches and techniques from the specific field of computer and information science.

Reflection: Understanding the advantages of the chosen approaches in computer and information science in solving specific practical tasks.

Transferable skills: Solving complex problems, designing complex systems.

 

Learning and teaching methods:

Lectures, lab exercises

 

Assessment:

Type (examination, oral, coursework, project):

  • Continuing (homework, midterm exams, project work)
  • Final (written and oral exam)

Grading: 6-10 pass, 1-5 fail.

  • Study programmes
  • Distribution of hours per semester
45
hours
lectures
30
hours
tutorials