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If a is an element of a field F over the prime field P, then the set of all rational functions of a with coefficients in P is a field derived from P by adjunction of a.

A connected graph G is said to be t-tough if, for every integer k>1, G cannot be split into k different connected components by the removal of fewer than tk vertices. The ...

A locally finite space is one for which every point of a given space has a neighborhood that meets only finitely many elements of any cover.

Numerical minimization is implemented NMinimize[f, vars].

An n-manifold which cannot be "nontrivially" decomposed into other n-manifolds.

A quantity which transforms like a tensor except for a scalar factor of a Jacobian.

Calculus I

A wide variety of large numbers crop up in mathematics. Some are contrived, but some actually arise in proofs. Often, it is possible to prove existence theorems by deriving ...

Define the first Brocard point as the interior point Omega of a triangle for which the angles ∠OmegaAB, ∠OmegaBC, and ∠OmegaCA are equal to an angle omega. Similarly, define ...

There are certain optimization problems that become unmanageable using combinatorial methods as the number of objects becomes large. A typical example is the traveling ...