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An algorithm similar to Neville's algorithm for constructing the Lagrange interpolating polynomial. Let f(x|x_0,x_1,...,x_k) be the unique polynomial of kth polynomial order ...

A branch point whose neighborhood of values wrap around the range a finite number of times p as their complex arguments theta varies from 0 to a multiple of 2pi is called an ...

Given a ship with a known constant direction and speed v, what course should be taken by a chase ship in pursuit (traveling at speed V) in order to intercept the other ship ...

The backward difference is a finite difference defined by del _p=del f_p=f_p-f_(p-1). (1) Higher order differences are obtained by repeated operations of the backward ...

(dy)/(dx)+p(x)y=q(x)y^n. (1) Let v=y^(1-n) for n!=1. Then (dv)/(dx)=(1-n)y^(-n)(dy)/(dx). (2) Rewriting (1) gives y^(-n)(dy)/(dx) = q(x)-p(x)y^(1-n) (3) = q(x)-vp(x). (4) ...

The blow-up lemma essentially says that regular pairs in Szemerédi's regularity lemma behave like complete bipartite graphs from the point of view of embedding bounded degree ...

A roll of two 6s (the highest roll possible) on a pair of 6-sided dice. The probability of rolling boxcars in a single roll of two dice is 1/36, or 2.777...%. In order to ...

There are at least two theorems known as Chebyshev's theorem. The first is Bertrand's postulate, proposed by Bertrand in 1845 and proved by Chebyshev using elementary methods ...

The finite simple groups of Lie-type. They include four families of linear simple groups: PSL(n,q) (the projective special linear group), PSU(n,q) (the projective special ...

The classification theorem of finite simple groups, also known as the "enormous theorem," which states that the finite simple groups can be classified completely into 1. ...