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Geometry which depends only on the first four of Euclid's postulates and not on the parallel postulate. Euclid himself used only the first four postulates for the first 28 ...

An Achilles number is a positive integer that is powerful (in the sense that each prime factor occurs with exponent greater than one) but imperfect (in the sense that the ...

An Abelian variety which is canonically attached to an algebraic variety which is the solution to a certain universal problem. The Albanese variety is dual to the Picard ...

The use of techniques from algebra, topology, and geometry in the solution of combinatorial problems, or the use of combinatorial methods to attack problems in these areas ...

A transformation in which vectors are transformed in a fixed coordinate system. In contrast, a transformation in which the coordinate system is changed, leaving vectors in ...

Given a property P, if P(x)∼x as x->infty (so, using asymptotic notation, the number of numbers less than x not satisfying the property P is o(x), where o(x) is one of the ...

The alternative hypothesis is the hypothesis used in hypothesis testing that is contrary to the null hypothesis. It is usually taken to be that the observations are the ...

A definable set, also called a Souslin set.

An anyon is a projective representation of a Lie group.

The nonconservation of adiabatic invariants which arises in systems with three or more degrees of freedom.