Course: Combinatorics: Strategies and Methods for Counting

The factorial of a natural (n) is the natural number [n!=ntimes (n-1)cdotstimes 2times 1] The factorial appears in several combinatorial formulas: why?

We are already familiar wit sequences, sets, collections. How do we count them? We see here one of the most powerful tools in combinatorics: the Multiplication Principle. Be careful: its …

How to model into mathematical terms a counting problem of distribution of indistinguishable objects? We see here the notion of composition and howit is related to that of collection.

The number of partitions that can be formed with a set containing a given number (k) of elements is the (k)-th Bell number. Let us discover how it is related …

What are the main mathematical objects that we are going to be able to count? Sequences, sets and collections will be the main characters of the MOOC.

How to model into mathematical terms a counting problem of distribution of distinguishable objects? We see here the notion of sharing and how it is related to that of sequence.

Subdividing a group of (k) students into (n) study groups produces what we call a (n)-partition of the sets of students. The number of these subdivisions is the Stirling number …

Why and how difficult may it be to count the number of elements of a set?

Let’s present the team. In the videos you’ll meet Alberto and Carlo , professors of mathematics at the University of Padova (Italy). You can click ‘Follow’ on the profile to …