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Logic is the formal mathematical study of the methods, structure, and validity of mathematical deduction and proof. According to Wolfram (2002, p. 860), logic is the most ...

The line R[s]=1/2 in the complex plane on which the Riemann hypothesis asserts that all nontrivial (complex) Riemann zeta function zeros lie. The plot above shows the first ...

A tag system in which a list of n tag rules (each of a special form) is applied to a system in sequential order and then starting again from the first rule. In a cyclic tag ...

A cylindrical projection of points on a unit sphere centered at O consists of extending the line OS for each point S until it intersects a cylinder tangent to the sphere at ...

Let O be an incidence geometry, i.e., a set with a symmetric, reflexive binary relation I. Let e and f be elements of O. Let an incidence plane be an incidence geometry whose ...

A square matrix is called Hermitian if it is self-adjoint. Therefore, a Hermitian matrix A=(a_(ij)) is defined as one for which A=A^(H), (1) where A^(H) denotes the conjugate ...

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

A system of curvilinear coordinates in which two sets of coordinate surfaces are obtained by revolving the curves of the elliptic cylindrical coordinates about the y-axis ...

Determination of whether predicate P(x_1,...,x_n) is true or false for any given values of x_1, ..., x_n is called its decision problem. The decision problem for predicate ...

A cellular automaton is a collection of "colored" cells on a grid of specified shape that evolves through a number of discrete time steps according to a set of rules based on ...