Search Results for ""

Let n be an integer variable which tends to infinity and let x be a continuous variable tending to some limit. Also, let phi(n) or phi(x) be a positive function and f(n) or ...

A permutation problem invented by Cayley. Let the numbers 1, 2, ..., n be written on a set of cards, and shuffle this deck of cards. Now, start counting using the top card. ...

Hadamard matrices H_n can be constructed using finite field GF(p^m) when p=4l-1 and m is odd. Pick a representation r relatively prime to p. Then by coloring white ...

Universal algebra studies common properties of all algebraic structures, including groups, rings, fields, lattices, etc. A universal algebra is a pair A=(A,(f_i^A)_(i in I)), ...

The volume of a solid body is the amount of "space" it occupies. Volume has units of length cubed (i.e., cm^3, m^3, in^3, etc.) For example, the volume of a box (cuboid) of ...

The absolute difference of two numbers n_1 and n_2 is |n_1-n_2|, where the minus sign denotes subtraction and |x| denotes the absolute value.

If f is continuous on a closed interval [a,b], then there is at least one number x^* in [a,b] such that int_a^bf(x)dx=f(x^*)(b-a). The average value of the function (f^_) on ...

The ratio C of the largest to smallest singular value in the singular value decomposition of a matrix. The base-b logarithm of C is an estimate of how many base-b digits are ...

A dependent variable is a variable whose value depends on the values of one or more other independent variables. This notion comes up regularly in a variety of contexts. In ...

Let f be differentiable on the open interval (a,b) and continuous on the closed interval [a,b]. Then if f(a)=f(b), then there is at least one point c in (a,b) where f^'(c)=0. ...