Combinatorics I
3 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, latin squares, 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 connections
to diofantine equations.
Prerequisites Algebra 1
Text-books:
Notes, possibly supplemented by Matroid Theory, Oxley, Oxford.