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A branch of mathematics that is a sort of generalization of calculus. Calculus of variations seeks to find the path, curve, surface, etc., for which a given function has a ...

The term "characteristic" has many different uses in mathematics. In general, it refers to some property that inherently describes a given mathematical object, for example ...

A topological space decomposes into its connected components. The connectedness relation between two pairs of points satisfies transitivity, i.e., if a∼b and b∼c then a∼c. ...

A connected graph is graph that is connected in the sense of a topological space, i.e., there is a path from any point to any other point in the graph. A graph that is not ...

A space D is connected if any two points in D can be connected by a curve lying wholly within D. A space is 0-connected (a.k.a. pathwise-connected) if every map from a ...

First-passage percolation is a time-dependent generalization of discrete Bernoulli percolation in which each graph edge e of Z^d is assigned a nonnegative random variable ...

A continuous transformation from one function to another. A homotopy between two functions f and g from a space X to a space Y is a continuous map G from X×[0,1]|->Y such ...

A tree with a finite number of branches at each fork and with a finite number of leaves at the end of each branch is called a finitely branching tree. König's lemma states ...

A lion and a man in a closed arena have equal maximum speeds. What tactics should the lion employ to be sure of his meal? This problem was stated by Rado in 1925 (Littlewood ...

A maximally nonhamiltonian graph is a nonhamiltonian graph G for which G+e is Hamiltonian for each edge e in the graph complement of G^_, i.e., every two nonadjacent vertices ...