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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 ...

Every irrational number x has an approximation constant c(x) defined by c(x)=lim inf_(q->infty)q|qx-p|, where p=nint(qx) is the nearest integer to qx and lim inf is the ...

The Bôcher Memorial Prize is awarded by the American Mathematical Society every five years for notable research in analysis that has appeared in a recognized North American ...

The Byzantine generals problem considers a computer with many programs running, some of them possibly unfriendly, and asks how the computer can function properly. More ...

For any system that seeks to minimize a function, only seven different local forms of catastrophe "typically" occur for four or fewer variables: 1. Fold catastrophe, 2. Cusp ...

The characteristic equation is the equation which is solved to find a matrix's eigenvalues, also called the characteristic polynomial. For a general k×k matrix A, the ...

A Gaussian quadrature-like formula for numerical estimation of integrals. It uses weighting function W(x)=1 in the interval [-1,1] and forces all the weights to be equal. The ...

Chió pivotal condensation is a method for evaluating an n×n determinant in terms of (n-1)×(n-1) determinants. It also leads to some remarkable determinant identities (Eves ...

A subset S of a topological space X is compact if for every open cover of S there exists a finite subcover of S.

A number which can be computed to any number of digits desired by a Turing machine. Surprisingly, most irrationals are not computable numbers!