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Separation of variables is a method of solving ordinary and partial differential equations. For an ordinary differential equation (dy)/(dx)=g(x)f(y), (1) where f(y)is nonzero ...

A Taylor series is a series expansion of a function about a point. A one-dimensional Taylor series is an expansion of a real function f(x) about a point x=a is given by (1) ...

The smallest number of times u(K) a knot K must be passed through itself to untie it. Lower bounds can be computed using relatively straightforward techniques, but it is in ...

Yahtzee is a game played with five 6-sided dice. Players take turns rolling the dice, and trying to get certain types of rolls, each with an assigned point value, as ...

Pre-Calculus

A mechanical counting device consisting of a frame holding a series of parallel rods on each of which beads are strung. Each bead represents a counting unit, and each rod a ...

The abundance of a number n, sometimes also called the abundancy (a term which in this work, is reserved for a different but related quantity), is the quantity ...

Adams' method is a numerical method for solving linear first-order ordinary differential equations of the form (dy)/(dx)=f(x,y). (1) Let h=x_(n+1)-x_n (2) be the step ...

In identical experiments, an Allais paradox occurs when the addition of an independent event influences choice behavior. Consider the choices in the following table (Kahneman ...

Andrica's conjecture states that, for p_n the nth prime number, the inequality A_n=sqrt(p_(n+1))-sqrt(p_n)<1 holds, where the discrete function A_n is plotted above. The ...