Lecture: Wednesday 14:00-15:30 (V 302)
Labor: Wednesday 16:00-17:30 (V 302)
Vorlesungsankündigung [HTML]
References:
The book contains more material than required for the first familiarity with combinatorial methods -- it gives a comprehensive enough description of all modern combinatorics. In lectures we will concentrate on most basic methods and results with most elegant proofs -- those which (according to Paul Erdös) could be published in The Book.
Prerequisites:
The course is self-contained. It assumes certain mathematical maturity
but no prerequisite combinatorics. Knowledge of the elements of
linear algebra and elementary probability theory at
undergraduate
level can be helpful but is not necessary: all the necessary stuff will
be introduced during the lecture.
Goals:
The goal of this course is to train your ``combinatorial way of thinking'',
which should help later when dealing with more realistic things, like algorithms
and programs for concrete problems. We will start with most basic combinatorial
principles (selections with and without repetitions, double counting, pigeonhole
principle, the inclusion-exclusion principle, etc.) and finish with most
powerful tools (linear algebra method and the probabilistic method). You
will be surprised how with a mere knowledge of the concepts of linear independence
and discrete probability, completely unexpected connections can be made
between Algebra, Probability and Combinatorics.
Homework:
There will be no written exercises. Instead, you will try to
solve them during the week, and then present the solution(s) in a labor
(on a purely voluntary basis). In case of difficulties, we will try to
find a solution together. Exercises will be mainly from the book.
The "Schein":
No formal requirements. Active presence in lectures and in labor will
be enough.