3-4 hours of lectures per week.
Lecturer
Jørgen Brandt
Content
This is an introduction to a number of central topics in combinatorial mathematics. Some of the main topics are: Matroids and transversal theory, as a generalisation of linear independce from linear algebra, with applications in networks, completion of latin squares, existence of 0-1 matrices. Ramsey theory that shows that total disorder is impossible. The theory of balanced incomplete block designs. This covers finite affine and projective planes ( -finite geometries), the existence of orthogonal latin squares (a problem going back to a conjecture of Euler) and has connections to diofantine equations.
Prerequisites
Algebra 1.
Literature
J.H. van Lint & R.M. Wilson, A Course in Combinatorics, 2.ed., Cambridge, 2001.
Jørgen Brandt Noter.
Evaluation
Students who do not intend to take a degree in Mathematics or Statistics from the University of Aarhus, but wish to earn credits for a 2.dels course from the Department of Mathematics, should indicate at the beginning of the course that they wish to be examined.
The form of examination for these students will be active participation together with oral or written contributions.
Credits
10 ECTS
Semester
Spring 2003