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An unhappy number is a number that is not happy, i.e., a number n such that iterating this sum-of-squared-digits map starting with n never reaches the number 1. The first few ...

Measure theory is the study of measures. It generalizes the intuitive notions of length, area, and volume. The earliest and most important examples are Jordan measure and ...

The mathematical study of the properties of the formal mathematical structures called graphs.

The theory of non-uniformly hyperbolic diffeomorphisms.

A slightly archaic term for a computer-generated random number. The prefix pseudo- is used to distinguish this type of number from a "truly" random number generated by a ...

An analytic refinement of results from complex analysis such as those codified by Picard's little theorem, Picard's great theorem, and the Weierstrass-Casorati theorem.

Let a knot K be n-embeddable. Then its tunnel number is a knot invariant which is related to n.

The study of designs and, in particular, necessary and sufficient conditions for the existence of a block design.

The Narayan number N(n,k) for n=1, 2, ... and k=1, ..., n gives a solution to several counting problems in combinatorics. For example, N(n,k) gives the number of expressions ...

The Hajós number h(G) of a graph G is the maximum k such that G contains a subdivision of the complete graph K_k.