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There are at least two distinct notions known as the Whitehead group. Given an associative ring A with unit, the Whitehead group associated to A is the commutative quotient ...

A nonzero element x of a ring for which x·y=0, where y is some other nonzero element and the multiplication x·y is the multiplication of the ring. A ring with no zero ...

A real-valued stochastic process {B(t):t>=0} is a Brownian motion which starts at x in R if the following properties are satisfied: 1. B(0)=x. 2. For all times ...

Trigonometric functions of npi/9 radians for n an integer not divisible by 3 (e.g., 40 degrees and 80 degrees) cannot be expressed in terms of sums, products, and finite root ...

Logic is the formal mathematical study of the methods, structure, and validity of mathematical deduction and proof. According to Wolfram (2002, p. 860), logic is the most ...

A random matrix is a matrix of given type and size whose entries consist of random numbers from some specified distribution. Random matrix theory is cited as one of the ...

A division algebra, also called a "division ring" or "skew field," is a ring in which every nonzero element has a multiplicative inverse, but multiplication is not ...

A group G is a finite or infinite set of elements together with a binary operation (called the group operation) that together satisfy the four fundamental properties of ...

Pre-Algebra

Suppose A and B are candidates for office and there are 2n voters, n voting for A and n for B. In how many ways can the ballots be counted so that B is never ahead of A? The ...