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If f(z) is meromorphic in a region R enclosed by a contour gamma, let N be the number of complex roots of f(z) in gamma, and P be the number of poles in gamma, with each zero ...

A function f(x) is said to have bounded variation if, over the closed interval x in [a,b], there exists an M such that |f(x_1)-f(a)|+|f(x_2)-f(x_1)|+... +|f(b)-f(x_(n-1))|<=M ...

According to Pólya, the Cartesian pattern is the resolution method for arithmetical or geometrical problems based on equations. The first step is to translate the question ...

A circle is the set of points in a plane that are equidistant from a given point O. The distance r from the center is called the radius, and the point O is called the center. ...

A constructive proof is a proof that directly provides a specific example, or which gives an algorithm for producing an example. Constructive proofs are also called ...

Does there exist an algorithm for deciding whether or not a specific mathematical assertion does or does not have a proof? The decision problem is also known as the ...

A handle is a topological structure which can be thought of as the object produced by puncturing a surface twice, attaching a zip around each puncture travelling in opposite ...

The Cartesian product of a countable infinity of copies of the interval [0,1]. It can be denoted [0,1]^(aleph_0) or [0,1]^omega, where aleph_0 and omega are the first ...

If a subgroup H of G has a group representation phi:H×W->W, then there is a unique induced representation of G on a vector space V. The original space W is contained in V, ...

A law is a mathematical statement which always holds true. Whereas "laws" in physics are generally experimental observations backed up by theoretical underpinning, laws in ...