Let K be a field of characteristic 0 and let n be a natural number. Let Γ be a subgroup of the multiplicative group (K*) n of finite rank r. Given a1,..., an ∈ K* write A(a1,..., an, Γ) for the number ...

Some important points to revise from the chapter are: • An equation of the form ax + by + c = 0, where a, b and c are real numbers, such that a and b are not both zero, is called a linear equation in ...

By harnessing randomness, a new algorithm achieves a fundamentally novel — and faster — way of performing one of the most basic computations in math and computer science.

But what if you could use your smartphone to solve equations by pointing the camera at the problem in your textbook instead of using a graphing calculator? That is the idea behind PhotoMath.