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Mathematics is a broad-ranging field of study in which the properties and interactions of idealized objects are examined. Whereas mathematics began merely as a calculational ...

There are several regular mathematics competitions available to students. The International Mathematical Olympiad is perhaps the largest, while the William Lowell Putnam ...

(d^2V)/(dv^2)+[a-2qcos(2v)]V=0 (1) (Abramowitz and Stegun 1972; Zwillinger 1997, p. 125), having solution y=C_1C(a,q,v)+C_2S(a,q,v), (2) where C(a,q,v) and S(a,q,v) are ...

The power series that defines the exponential map e^x also defines a map between matrices. In particular, exp(A) = e^(A) (1) = sum_(n=0)^(infty)(A^n)/(n!) (2) = ...

The minimal polynomial of a matrix A is the monic polynomial in A of smallest degree n such that p(A)=sum_(i=0)^nc_iA^i=0. (1) The minimal polynomial divides any polynomial q ...

The product C of two matrices A and B is defined as c_(ik)=a_(ij)b_(jk), (1) where j is summed over for all possible values of i and k and the notation above uses the ...

Given a square complex or real matrix A, a matrix norm ||A|| is a nonnegative number associated with A having the properties 1. ||A||>0 when A!=0 and ||A||=0 iff A=0, 2. ...

A maximal clique is a clique that cannot be extended by including one more adjacent vertex, meaning it is not a subset of a larger clique. A maximum clique (i.e., clique of ...

A maximal independent vertex set of a graph is an independent vertex set that cannot be expanded to another independent vertex set by addition of any vertex in the graph. A ...

A deconvolution algorithm (sometimes abbreviated MEM) which functions by minimizing a smoothness function ("entropy") in an image. Maximum entropy is also called the ...