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A method of determining the maximum number of positive and negative real roots of a polynomial. For positive roots, start with the sign of the coefficient of the lowest (or ...

The expected number of real zeros E_n of a random polynomial of degree n if the coefficients are independent and distributed normally is given by E_n = ...

A polynomial with real positive coefficients and roots which are either negative or pairwise conjugate with negative real parts.

"The reals" is a common way of referring to the set of real numbers and is commonly denoted R.

The Banach-Saks theorem is a result in functional analysis which proves the existence of a "nicely-convergent" subsequence for any sequence {f_n}={f_n}_(n in Z^*) of ...

Let x be a real number, and let R be the set of positive real numbers mu for which 0<|x-p/q|<1/(q^mu) (1) has (at most) finitely many solutions p/q for p and q integers. Then ...

The Bernoulli inequality states (1+x)^n>1+nx, (1) where x>-1!=0 is a real number and n>1 an integer. This inequality can be proven by taking a Maclaurin series of (1+x)^n, ...

A functional is a real-valued function on a vector space V, usually of functions. For example, the energy functional on the unit disk D assigns a number to any differentiable ...

A dimension also called the fractal dimension, Hausdorff dimension, and Hausdorff-Besicovitch dimension in which nonintegral values are permitted. Objects whose capacity ...

The word "base" in mathematics is used to refer to a particular mathematical object that is used as a building block. The most common uses are the related concepts of the ...