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Consider n intersecting circles. The maximal number of regions into which these divide the plane are N(n)=n^2-n+2, giving values for n=1, 2, ... of 2, 4, 8, 14, 22, 32, 44, ...

A theory of constructing initial conditions that provides safe convergence of a numerical root-finding algorithm for an equation f(z)=0. Point estimation theory treats ...

The truth of an infinite sequence of propositions P_i for i=1, ..., infty is established if (1) P_1 is true, and (2) P_k implies P_(k+1) for all k. This principle is ...

A pseudograph is a non-simple graph in which both graph loops and multiple edges are permitted (Zwillinger 2003, p. 220).

A type of cryptography in which the encoding key is revealed without compromising the encoded message. The two best-known methods are the knapsack problem and RSA encryption.

The William Lowell Putnam Mathematics Competition is an annual mathematics contest open to North American college students administered by the Mathematical Association of ...

A random permutation is a permutation containing a fixed number n of a random selection from a given set of elements. There are two main algorithms for constructing random ...

A conjecture due to M. S. Robertson in 1936 which treats a univalent power series containing only odd powers within the unit disk. This conjecture implies the Bieberbach ...

Searching refers to locating a given element or an element satisfying certain conditions from some (usually ordered or partially ordered) table, list, tree, etc.

A sorting algorithm which makes n passes over a set of n elements, in each pass selecting the smallest element and deleting it from the set. This algorithm has running time ...