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A braid is an intertwining of some number of strings attached to top and bottom "bars" such that each string never "turns back up." In other words, the path of each string in ...

Let f:M|->N be a map between two compact, connected, oriented n-dimensional manifolds without boundary. Then f induces a homomorphism f_* from the homology groups H_n(M) to ...

Chevalley's theorem, also known as the Chevalley-Waring theorem, states that if f is a polynomial in F[x_1,...,x_n], where F is a finite field of field characteristic p, and ...

All closed surfaces, despite their seemingly diverse forms, are topologically equivalent to spheres with some number of handles or cross-caps. The traditional proof follows ...

Combinatorial geometry is a blending of principles from the areas of combinatorics and geometry. It deals with combinations and arrangements of geometric objects and with ...

There are at least two meanings on the word congruent in mathematics. Two geometric figures are said to be congruent if one can be transformed into the other by an isometry ...

Given an expression involving known constants, integration in finite terms, computation of limits, etc., the constant problem is the determination of if the expression is ...

The proposal originally made by Georg Cantor that there is no infinite set with a cardinal number between that of the "small" infinite set of integers aleph_0 and the "large" ...

The phrase "convergence in mean" is used in several branches of mathematics to refer to a number of different types of sequential convergence. In functional analysis, ...

A notation for polyhedra which begins by specifying a "seed" polyhedron using a capital letter. The Platonic solids are denoted T (tetrahedron), O (octahedron), C (cube), I ...