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There are many unsolved problems in mathematics. Several famous problems which have recently been solved include: 1. The Pólya conjecture (disproven by Haselgrove 1958, ...

A test used to determine the statistical significance of an observation. Two main types of error can occur: 1. A type I error occurs when a false negative result is obtained ...

A transpose of a doubly indexed object is the object obtained by replacing all elements a_(ij) with a_(ji). For a second-tensor rank tensor a_(ij), the tensor transpose is ...

Angle addition formulas express trigonometric functions of sums of angles alpha+/-beta in terms of functions of alpha and beta. The fundamental formulas of angle addition in ...

A set of positive integers is called weakly triple-free if, for any integer x, the set {x,2x,3x} !subset= S. For example, all subsets of {1,2,3,4,5} are weakly triple-free ...

There are two related conjectures, each called the twin prime conjecture. The first version states that there are an infinite number of pairs of twin primes (Guy 1994, p. ...

A vector bundle is special class of fiber bundle in which the fiber is a vector space V. Technically, a little more is required; namely, if f:E->B is a bundle with fiber R^n, ...

The one-dimensional wave equation is given by (partial^2psi)/(partialx^2)=1/(v^2)(partial^2psi)/(partialt^2). (1) In order to specify a wave, the equation is subject to ...

A q-analog, also called a q-extension or q-generalization, is a mathematical expression parameterized by a quantity q that generalizes a known expression and reduces to the ...

The q-binomial coefficient is a q-analog for the binomial coefficient, also called a Gaussian coefficient or a Gaussian polynomial. A q-binomial coefficient is given by [n; ...