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The mathematical study of knots. Knot theory considers questions such as the following: 1. Given a tangled loop of string, is it really knotted or can it, with enough ...

The theory of non-uniformly hyperbolic diffeomorphisms.

The study of the nature and properties of bifurcations.

Erdős proved that there exist at least one prime of the form 4k+1 and at least one prime of the form 4k+3 between n and 2n for all n>6.

The branch of algebraic topology which deals with homotopy groups. Homotopy methods can be used to solve systems of polynomials by embedding the polynomials in a family of ...

The problem of forecasting future values X_(t+tau) (tau>0) of a weakly stationary process {X_t} from the known values X_s (s<=t).

The study of sampling

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

The theory of classifying problems based on how difficult they are to solve. A problem is assigned to the P-problem (polynomial-time) class if the number of steps needed to ...

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.