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An operator A^~ such that A^~^2=A^~ or an element of an algebra x such that x^2=x.

Topological lower bounds in terms of Betti numbers for the number of critical points form a smooth function on a smooth manifold.

A strong inequality in which a is not only less than b, but much less (by some convention) is denoted a<<b.

A mathematical object S is said to be multiplicatively closed if a,b in S implies that ab in S.

The symbol p^e∥n means, for p a prime, that p^e|n, but p^(e+1)n.

A reflexive relation.

Euclidean n-space is denoted R^n.

The robustness of a given outcome to small changes in initial conditions or small random fluctuations. Chaos is an example of a process which is not stable.

The hundred-dollar, hundred-digits challenge problems are a set of ten problems in numerical analysis published in the January/February 2002 issue of SIAM News ...

Newton's method, also called the Newton-Raphson method, is a root-finding algorithm that uses the first few terms of the Taylor series of a function f(x) in the vicinity of a ...