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In statistics, sampling is the selection and implementation of statistical observations in order to estimate properties of an underlying population. Sampling is a vital part ...

The second, or diamond, group isomorphism theorem, states that if G is a group with A,B subset= G, and A subset= N_G(B), then (A intersection B)⊴A and AB/B=A/A intersection ...

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 ...

Let A be an n×n matrix over a field F. Using the three elementary row and column operations over elements in the field, the n×n matrix xI-A with entries from the principal ...

The study of figures on the surface of a sphere (such as the spherical triangle and spherical polygon), as opposed to the type of geometry studied in plane geometry or solid ...

A figure formed by taking a series of steps of length 1, 2, ..., n, with an angle theta turn after each step. The symbol for a spirolateral is ^(a_1,...,a_k)n_theta, where ...

The extension field K of a field F is called a splitting field for the polynomial f(x) in F[x] if f(x) factors completely into linear factors in K[x] and f(x) does not factor ...

If M^n is a finite simplicial complex of dimension n>=5 that has the homotopy type of the sphere S^n and is locally piecewise linearly homeomorphic to the Euclidean space ...

A symmetric function on n variables x_1, ..., x_n is a function that is unchanged by any permutation of its variables. In most contexts, the term "symmetric function" refers ...

Let G be a group having normal subgroups H and K with H subset= K. Then K/H⊴G/H and (G/H)/(K/H)=G/K, where N⊴G indicates that N is a normal subgroup of G and G=H indicates ...