Teacher resources and professional development across the curriculum
Teacher professional development and classroom resources across the curriculum
The identification of a "one-to-one" correspondence--enables us to enumerate a set that may be difficult to count in terms of another set that is more easily counted.
A graph in which every node is connected to every other node is called a complete graph.
A de Bruijn sequence is the shortest string that contains all possible permutations of a particular length from a given set.
A Hamilton cycle is a path that visits every node in a graph and ends where it began.
An arrangement where order matters.
Of central importance in Ramsey Theory, and in combinatorics in general, is the "pigeonhole principle," also known as Dirichlet's box. This principle simply states that we cannot fit n+1 pigeons into n pigeonholes in such a way that only one pigeon is placed in each hole, with no pigeons left over.
Ramsey Theory reveals why we tend to find structure in seemingly random sets. Ramsey numbers indicate how big a set must be to guarantee the existence of certain minimal structures.