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A commutative Noetherian unit ring having only finitely many maximal ideals. A ring having the same properties except Noetherianity is called quasilocal. If K is a field, the ...

A set S and a binary operator * are said to exhibit closure if applying the binary operator to two elements S returns a value which is itself a member of S. The closure of a ...

A sheaf is a presheaf with "something" added allowing us to define things locally. This task is forbidden for presheaves in general. Specifically, a presheaf F on a ...

A pathwise-connected domain is said to be simply connected (also called 1-connected) if any simple closed curve can be shrunk to a point continuously in the set. If the ...

Simpson's paradox, also known as the amalgamation paradox, reversal paradox, or Yule-Simpson effect, is a paradox in which a statistical trend appears to be present when data ...

Given an ordinary differential equation y^'=f(x,y), the slope field for that differential equation is the vector field that takes a point (x,y) to a unit vector with slope ...

Another word for a C^infty (infinitely differentiable) manifold, also called a differentiable manifold. A smooth manifold is a topological manifold together with its ...

Spherical mirrors were a popular subject for M. C. Escher's lithographs, including "Still Life with a Spherical Mirror" (Bool et al. 1982, p. 261; Forty 2003, Plate 23), ...

A two-component complex column vector. Spinors can describe both bosons and fermions, while tensors can describe only bosons.

Stadium billiards refers to the investigation of the path of a billiard ball on a stadium-shaped billiard table, as first investigated by Bunimovich (1974).