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The Monty Hall problem is named for its similarity to the Let's Make a Deal television game show hosted by Monty Hall. The problem is stated as follows. Assume that a room is ...

A noncayley graph is a graph which is not a Cayley graph. All graphs that are not vertex-transitive are noncayley graphs. However, some vertex-transitive graph are noncayley. ...

A normalized form of the cumulative normal distribution function giving the probability that a variate assumes a value in the range [0,x], ...

The Penrose triangle, also called the tribar (Cerf), tri-bar (Ernst 1987), impossible tribar (Pappas 1989, p. 13), or impossible triangle, is an impossible figure published ...

Define a valid "coloring" to occur when no two faces with a common edge share the same color. Given two colors, there is a single way to color an octahedron (Ball and Coxeter ...

A primitive polynomial is a polynomial that generates all elements of an extension field from a base field. Primitive polynomials are also irreducible polynomials. For any ...

A projective module generalizes the concept of the free module. A module M over a nonzero unit ring R is projective iff it is a direct summand of a free module, i.e., of some ...

The rising factorial x^((n)), sometimes also denoted <x>_n (Comtet 1974, p. 6) or x^(n^_) (Graham et al. 1994, p. 48), is defined by x^((n))=x(x+1)...(x+n-1). (1) This ...

The sporadic groups are the 26 finite simple groups that do not fit into any of the four infinite families of finite simple groups (i.e., the cyclic groups of prime order, ...

The word "surface" is an important term in mathematics and is used in many ways. The most common and straightforward use of the word is to denote a two-dimensional ...