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A continuous homomorphism of a group into the nonzero complex numbers. A multiplicative character omega gives a group representation on the one-dimensional space C of complex ...

Multivariable calculus is the branch of calculus that studies functions of more than one variable. Partial derivatives and multiple integrals are the generalizations of ...

A function of more than one variable.

A polynomial in more than one variable, e.g., .

A problem is NP-hard if an algorithm for solving it can be translated into one for solving any NP-problem (nondeterministic polynomial time) problem. NP-hard therefore means ...

A negative integer is one of the integers ..., -4, -3, -2, -1 obtained by negating the positive integers. The negative integers are commonly denoted Z^-.

Any irreducible curve may be carried by a factorable Cremona transformation into one with none but ordinary singular points.

A nonempty set is a set containing one or more elements. Any set other than the empty set emptyset is therefore a nonempty set. Nonempty sets are sometimes also called ...

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 ...

A normal extension is the splitting field for a collection of polynomials. In the case of a finite algebraic extension, only one polynomial is necessary.