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The mathematical study of abstract computing machines (especially Turing machines) and the analysis of algorithms used by such machines. A connection between automata theory ...

A formal mathematical theory which introduces "components at infinity" by defining a new type of divisor class group of integers of a number field. The divisor class group is ...

The branch of mathematics which formalizes a number of algebraic properties of collections of transformations between mathematical objects (such as binary relations, groups, ...

A branch of game theory dealing with strategies to maximize the outcome of a given process in the face of uncertain conditions.

A branch of topology dealing with topological invariants of manifolds.

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 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).