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A ring in the mathematical sense is a set S together with two binary operators + and * (commonly interpreted as addition and multiplication, respectively) satisfying the ...

Also called Macaulay ring, a Cohen Macaulay ring is a Noetherian commutative unit ring R in which any proper ideal I of height n contains a sequence x_1, ..., x_n of elements ...

A vector derivative is a derivative taken with respect to a vector field. Vector derivatives are extremely important in physics, where they arise throughout fluid mechanics, ...

The polynomial giving the number of colorings with m colors of a structure defined by a permutation group.

Let f be a finite real-valued function defined on an interval [a,b]. Then at every point in [a,b] except on a set of Lebesgue measure zero, either: 1. There is a finite ...

Let R be the class of expressions generated by 1. The rational numbers and the two real numbers pi and ln2, 2. The variable x, 3. The operations of addition, multiplication, ...

The edge count of a graph g, commonly denoted M(g) or E(g) and sometimes also called the edge number, is the number of edges in g. In other words, it is the cardinality of ...

The Hartley Transform is an integral transform which shares some features with the Fourier transform, but which, in the most common convention, multiplies the integral kernel ...

Jackson's theorem is a statement about the error E_n(f) of the best uniform approximation to a real function f(x) on [-1,1] by real polynomials of degree at most n. Let f(x) ...

An invariant of an elliptic curve given in the form y^2=x^3+ax+b which is closely related to the elliptic discriminant and defined by j(E)=(2^83^3a^3)/(4a^3+27b^2). The ...