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An abstract vector space of dimension n over a field k is the set of all formal expressions a_1v_1+a_2v_2+...+a_nv_n, (1) where {v_1,v_2,...,v_n} is a given set of n objects ...

An operator defined on a set S which takes two elements from S as inputs and returns a single element of S. Binary operators are called compositions by Rosenfeld (1968). Sets ...

The successive square method is an algorithm to compute a^b in a finite field GF(p). The first step is to decompose b in successive powers of two, b=sum_(i)delta_i2^i, (1) ...

In the field of percolation theory, the term percolation threshold is used to denote the probability which "marks the arrival" (Grimmett 1999) of an infinite connected ...

A factor of a polynomial P(x) of degree n is a polynomial Q(x) of degree less than n which can be multiplied by another polynomial R(x) of degree less than n to yield P(x), ...

"Chaos" is a tricky thing to define. In fact, it is much easier to list properties that a system described as "chaotic" has rather than to give a precise definition of chaos. ...

The number 163 is very important in number theory, since d=163 is the largest number such that the imaginary quadratic field Q(sqrt(-d)) has class number h(-d)=1. It also ...

Let A be a matrix with the elementary divisors of its characteristic matrix expressed as powers of its irreducible polynomials in the field F[lambda], and consider an ...

Let E be a linear space over a field K. Then the vector space tensor product tensor _(lambda=1)^(k)E is called a tensor space of degree k. More specifically, a tensor space ...

The smallest positive composite number and the first even perfect square. Four is the smallest even number appearing in a Pythagorean triple: 3, 4, 5. In the numerology of ...