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Given a set P of primes, a field K is called a class field if it is a maximal normal extension of the rationals which splits all of the primes in P, and if P is the maximal ...

All closed surfaces, despite their seemingly diverse forms, are topologically equivalent to spheres with some number of handles or cross-caps. The traditional proof follows ...

Determining the length of a country's coastline is not as simple as it first appears, as first considered by L. F. Richardson (1881-1953) and sometimes known as the ...

The coheight of a proper ideal I of a commutative Noetherian unit ring R is the Krull dimension of the quotient ring R/I. The coheight is related to the height of I by the ...

The colon is the symbol ":". It is used in a number of different ways in mathematics. 1. To denote ratio or odds, as in 2:1 (voiced "two to one"). 2. To mean such that in ...

Combinatorial matrix theory is a rich branch of mathematics that combines combinatorics, graph theory, and linear algebra. It includes the theory of matrices with prescribed ...

Let K subset V subset S^3 be a knot that is geometrically essential in a standard embedding of the solid torus V in the three-sphere S^3. Let K_1 subset S^3 be another knot ...

A set of orthogonal functions {phi_n(x)} is termed complete in the closed interval x in [a,b] if, for every piecewise continuous function f(x) in the interval, the minimum ...

The expected number of trials needed to collect a complete set of n different objects when picked at random with repetition is nH_n (Havil 2003, p. 131). For n=1, 2, ..., the ...

A completely monotonic function is a function f(x) such that (-1)^(-n)f^((n))(x)>=0 for n=0, 1, 2, .... Such functions occur in areas such as probability theory (Feller ...