Last modified: 20 Jan 2023 16:02
Combinatorics is the branch of mathematics concerned with counting. This includes counting structures of a given kind (enumerative combinatorics), deciding when certain criteria can be met, finding "largest", "smallest", or "optimal" objects (external combinatorics and combinatorial optimization), and applying algebraic techniques to combinatorial problems (algebraic combinatorics). The course is recommended to students of mathematics and computing science.
|Second Sub Session
|15 credits (7.5 ECTS credits)
* Induction * Growth rates * Subsets and binomial coefficients (subsets of fixed size, properties of binomial coefficients, the binomial therem) * Partitions and Bell numbers * Counting with symmetry * Recurrences * Generating functions * Derangements * Principle of inclusion-exclusion * Extermal problems * The Pigeonhole Principle * Ramsey theory * Graph theory
Information on contact teaching time is available from the course guide.
There are no assessments for this course.
Best of (resit exam mark) or (resit exam mark combined with CA marks).
|To be able to operate with elementary counting functions and magnitudes
|To be able to count partitions
|Apply Ramsey theory and colouring problems
|To be able to recognise and count different types of selections
|To be able to apply Euler's theorem to polyhedra
|Understand graphs and trees
|Understand prinicple of inclusion and exclusion
|Understand generating functions and formal power series
|Apply generating functions
|To be able to use binomial coefficients