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Fermat's last theorem is a theorem first proposed by Fermat in the form of a note scribbled in the margin of his copy of the ancient Greek text Arithmetica by Diophantus. The ...

A cubic equation is an equation involving a cubic polynomial, i.e., one of the form a_3x^3+a_2x^2+a_1x+a_0=0. Since a_3!=0 (or else the polynomial would be quadratic and not ...

Given a differential operator D on the space of differential forms, an eigenform is a form alpha such that Dalpha=lambdaalpha (1) for some constant lambda. For example, on ...

Expanded notation is the term given in elementary mathematics education for the expansion of a positive integer in the form sum_(k)b_k10^k, i.e., as a sum of appropriate ...

Two closed simply connected 4-manifolds are homeomorphic iff they have the same bilinear form beta and the same Kirby-Siebenmann invariant kappa. Any beta can be realized by ...

A diagonal matrix is a square matrix A of the form a_(ij)=c_idelta_(ij), (1) where delta_(ij) is the Kronecker delta, c_i are constants, and i,j=1, 2, ..., n, with no implied ...

A power is an exponent to which a given quantity is raised. The expression x^a is therefore known as "x to the ath power." A number of powers of x are plotted above (cf. ...

A differential of the form df=P(x,y)dx+Q(x,y)dy (1) is exact (also called a total differential) if intdf is path-independent. This will be true if ...

A relation expressing a sum potentially involving binomial coefficients, factorials, rational functions, and power functions in terms of a simple result. Thanks to results by ...

The Kähler potential is a real-valued function f on a Kähler manifold for which the Kähler form omega can be written as omega=ipartialpartial^_f. Here, the operators ...