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The "mathematical paradigm" is a term that may be applied to the fundamental idea that events in the world can be described by mathematical equations, and that solutions to ...

A function f:X->R is measurable if, for every real number a, the set {x in X:f(x)>a} is measurable. When X=R with Lebesgue measure, or more generally any Borel measure, then ...

A nonnegative function g(x,y) describing the "distance" between neighboring points for a given set. A metric satisfies the triangle inequality g(x,y)+g(y,z)>=g(x,z) (1) and ...

Let K be a number field and let O be an order in K. Then the set of equivalence classes of invertible fractional ideals of O forms a multiplicative Abelian group called the ...

A quotient ring (also called a residue-class ring) is a ring that is the quotient of a ring A and one of its ideals a, denoted A/a. For example, when the ring A is Z (the ...

In the directed graph above, pick any vertex and follow the arrows in sequence blue-red-red three times. You will finish at the green vertex. Similarly, follow the sequence ...

Given a circular table of diameter 9 feet, which is the minimal number of planks (each 1 foot wide and length greater than 9 feet) needed in order to completely cover the ...

Universality is the property of being able to perform different tasks with the same underlying construction just by being programmed in a different way. Universal systems are ...

The term Bol loop refers to either of two classes of algebraic loops satisfying the so-called Bol identities. In particular, a left Bol loop is an algebraic loop L which, for ...

A problem listed in a fall issue of Gazeta Matematică in the mid-1970s posed the question if x_1>0 and x_(n+1)=(1+1/(x_n))^n (1) for n=1, 2, ..., then are there any values ...