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Let V be a real vector space (e.g., the real continuous functions C(I) on a closed interval I, two-dimensional Euclidean space R^2, the twice differentiable real functions ...

Probability is the branch of mathematics that studies the possible outcomes of given events together with the outcomes' relative likelihoods and distributions. In common ...

In order to find integers x and y such that x^2=y^2 (mod n) (1) (a modified form of Fermat's factorization method), in which case there is a 50% chance that GCD(n,x-y) is a ...

If isosceles triangles with apex angles 2kpi/n are erected on the sides of an arbitrary n-gon A_0, and if this process is repeated with the n-gon A_1 formed by the free ...

The proof theories of propositional calculus and first-order logic are often referred to as classical logic. Intuitionistic propositional logic can be described as classical ...

A root-finding algorithm which converges to a complex root from any starting position. To motivate the formula, consider an nth order polynomial and its derivatives, P_n(x) = ...

Abstract algebra is the set of advanced topics of algebra that deal with abstract algebraic structures rather than the usual number systems. The most important of these ...

There are essentially three types of Fisher-Tippett extreme value distributions. The most common is the type I distribution, which are sometimes referred to as Gumbel types ...

The Paris-Harrington theorem is a strengthening of the finite Ramsey's theorem by requiring that the homogeneous set be large enough so that cardH>=minH. Clearly, the ...

In order to recover all Fourier components of a periodic waveform, it is necessary to use a sampling rate nu at least twice the highest waveform frequency. The Nyquist ...