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Let lim stand for the limit lim_(x->c), lim_(x->c^-), lim_(x->c^+), lim_(x->infty), or lim_(x->-infty), and suppose that lim f(x) and lim g(x) are both zero or are both ...

An elliptic curve of the form y^2=x^3+n for n an integer. This equation has a finite number of solutions in integers for all nonzero n. If (x,y) is a solution, it therefore ...

The regular polygon of 17 sides is called the heptadecagon, or sometimes the heptakaidecagon. Gauss proved in 1796 (when he was 19 years old) that the heptadecagon is ...

An Abelian category is a category for which the constructions and techniques of homological algebra are available. The basic examples of such categories are the category of ...

The free module of rank n over a nonzero unit ring R, usually denoted R^n, is the set of all sequences {a_1,a_2,...,a_n} that can be formed by picking n (not necessarily ...

A spectral sequence is a tool of homological algebra that has many applications in algebra, algebraic geometry, and algebraic topology. Roughly speaking, a spectral sequence ...

Two lattice points (x,y) and (x^',y^') are mutually visible if the line segment joining them contains no further lattice points. This corresponds to the requirement that ...

The Young tableau (plural, "tableaux") of a Ferrers diagram is obtained by placing the numbers 1, ..., n in the n boxes of the diagram. A "standard" Young tableau is a Young ...

Minimal surfaces are defined as surfaces with zero mean curvature. A minimal surface parametrized as x=(u,v,h(u,v)) therefore satisfies Lagrange's equation, ...

The Ackermann function is the simplest example of a well-defined total function which is computable but not primitive recursive, providing a counterexample to the belief in ...