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For {M_i}_(i in I) a family of R-modules indexed by a directed set I, let sigma_(ij):M_i->M_j i<=j be an R-module homomorphism. Call (M_i,sigma_(ij)) a direct system over I ...

int_0^pi(sin[(n+1/2)x])/(2sin(1/2x))dx=1/2pi, where the integral kernel is the Dirichlet kernel.

Discrepancy is a measure of the deviation of a point set from a uniform distribution. In general, the computation of the discrepancy of a point set is computationally ...

The length of the largest-sized square contained within the Ferrers diagram of a partition. Its size can be determined using DurfeeSquare[f] in the Wolfram Language package ...

An n×n matrix A is an elementary matrix if it differs from the n×n identity I_n by a single elementary row or column operation.

A proof which can be accomplished using only real numbers (i.e., real analysis instead of complex analysis; Hoffman 1998, pp. 92-93).

The matrix operations of 1. Interchanging two rows or columns, 2. Adding a multiple of one row or column to another, 3. Multiplying any row or column by a nonzero element.

Ellipsoidal calculus is a method for solving problems in control and estimation theory having unknown but bounded errors in terms of sets of approximating ellipsoidal-value ...

delta(r)=sqrt(r)-2alpha(r), where alpha(r) is the elliptic alpha function.

The series sumf(n) for a monotonic nonincreasing f(x) is convergent if lim_(x->infty)^_(e^xf(e^x))/(f(x))<1 and divergent if lim_(x->infty)__(e^xf(e^x))/(f(x))>1.