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The number of elements in a group G, denoted |G|. If the order of a group is a finite number, the group is said to be a finite group. The order of an element g of a finite ...

An invertible knot is a knot that can be deformed via an ambient isotopy into itself but with the orientation reversed. A knot that is not invertible is said to be ...

A formal logic developed by Alonzo Church and Stephen Kleene to address the computable number problem. In the lambda calculus, lambda is defined as the abstraction operator. ...

The series for the inverse tangent, tan^(-1)x=x-1/3x^3+1/5x^5+.... Plugging in x=1 gives Gregory's formula 1/4pi=1-1/3+1/5-1/7+1/9-.... This series is intimately connected ...

A one-person game played on a rectangular lattice of lamps which can be turned on and off. A move consists of flipping a "switch" inside one of the squares, thereby toggling ...

The longest increasing scattered subsequence is the longest subsequence of increasing terms, where intervening nonincreasing terms may be dropped. Finding the largest ...

Let G=(V,E) be a (not necessarily simple) undirected edge-weighted graph with nonnegative weights. A cut C of G is any nontrivial subset of V, and the weight of the cut is ...

Presburger arithmetic is the first-order theory of the natural numbers containing addition but no multiplication. It is therefore not as powerful as Peano arithmetic. ...

Isolated resonances in a dynamical system can cause considerable distortion of preserved tori in their neighborhood, but they do not introduce any chaos into a system. ...

The rook numbers r_k^((m,n)) of an m×n board are the number of subsets of size k such that no two elements have the same first or second coordinate. In other word, it is the ...