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The term "integral" can refer to a number of different concepts in mathematics. The most common meaning is the the fundamenetal object of calculus corresponding to summing ...

An ordinary differential equation (frequently called an "ODE," "diff eq," or "diffy Q") is an equality involving a function and its derivatives. An ODE of order n is an ...

Define the packing density eta of a packing of spheres to be the fraction of a volume filled by the spheres. In three dimensions, there are three periodic packings for ...

The Legendre differential equation is the second-order ordinary differential equation (1-x^2)(d^2y)/(dx^2)-2x(dy)/(dx)+l(l+1)y=0, (1) which can be rewritten ...

A linear recurrence equation is a recurrence equation on a sequence of numbers {x_n} expressing x_n as a first-degree polynomial in x_k with k<n. For example ...

The roots (sometimes also called "zeros") of an equation f(x)=0 are the values of x for which the equation is satisfied. Roots x which belong to certain sets are usually ...

Given a polynomial p(x)=a_nx^n+a_(n-1)x^(n-1)+...+a_1x+a_0 (1) of degree n with roots alpha_i, i=1, ..., n and a polynomial q(x)=b_mx^m+b_(m-1)x^(m-1)+...+b_1x+b_0 (2) of ...

In August 2002, M. Agrawal and colleagues announced a deterministic algorithm for determining if a number is prime that runs in polynomial time (Agrawal et al. 2004). While ...

In general, polynomial equations higher than fourth degree are incapable of algebraic solution in terms of a finite number of additions, subtractions, multiplications, ...

An algorithm that can be used to factor a polynomial f over the integers. The algorithm proceeds by first factoring f modulo a suitable prime p via Berlekamp's method and ...