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The edge chromatic number, sometimes also called the chromatic index, of a graph G is fewest number of colors necessary to color each edge of G such that no two edges ...

In physics, the word entropy has important physical implications as the amount of "disorder" of a system. In mathematics, a more abstract definition is used. The (Shannon) ...

A field is any set of elements that satisfies the field axioms for both addition and multiplication and is a commutative division algebra. An archaic name for a field is ...

A set X whose elements can be numbered through from 1 to n, for some positive integer n. The number n is called the cardinal number of the set, and is often denoted |X| or ...

A subset E of a topological space S is said to be of first category in S if E can be written as the countable union of subsets which are nowhere dense in S, i.e., if E is ...

Steiner gave and Droz-Farny (1901) proved that if equal circles are drawn about the vertices of a triangle (dashed circles in the above figure), they cut the lines joining ...

Fisher's exact test is a statistical test used to determine if there are nonrandom associations between two categorical variables. Let there exist two such variables X and Y, ...

Given a system of ordinary differential equations of the form d/(dt)[x; y; v_x; v_y]=-[0 0 -1 0; 0 0 0 -1; Phi_(xx)(t) Phi_(yx)(t) 0 0; Phi_(xy)(t) Phi_(yy)(t) 0 0][x; y; ...

The Floyd-Warshall algorithm, also variously known as Floyd's algorithm, the Roy-Floyd algorithm, the Roy-Warshall algorithm, or the WFI algorithm, is an algorithm for ...

Let two players each have a finite number of pennies (say, n_1 for player one and n_2 for player two). Now, flip one of the pennies (from either player), with each player ...