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Comprehensive encyclopedia of mathematics with 13,000 detailed entries. Continually updated, extensively illustrated, and with interactive examples.

The term "null graph" is used both to refer to any empty graph and to the empty graph on 0 nodes. Because of the conflicting usage, it is probably best to avoid use of the ...

The first example discovered of a map from a higher-dimensional sphere to a lower-dimensional sphere which is not null-homotopic. Its discovery was a shock to the ...

Given a function f(x_1,...,x_n) defined on a domain U, the graph of f is defined as the set of points (which often form a curve or surface) showing the values taken by f over ...

Martin Gardner (1975) played an April Fool's joke by asserting that the map of 110 regions illustrated above (left figure) required five colors and constitutes a ...

In August 2002, M. Agrawal and colleagues announced a deterministic algorithm for determining if a number is prime that runs in polynomial time (Agrawal et al. 2004). While ...

Nonstandard analysis is a branch of mathematical logic which introduces hyperreal numbers to allow for the existence of "genuine infinitesimals," which are numbers that are ...

The four-color theorem states that any map in a plane can be colored using four-colors in such a way that regions sharing a common boundary (other than a single point) do not ...