Atsuji has internally characterized those metric spaces X for which each real-valued continuous function on X is uniformly continuous as follows: (1) the set X' of limit points of X is compact, and (2 ...

If you have trouble remembering how to graph different mathematical functions, these simple figures with their dancing arms can help. At the very least, they’ll make you think of math every time you ...

The Monthly publishes articles, as well as notes and other features, about mathematics and the profession. Its readers span a broad spectrum of mathematical interests, and include professional ...

In this part you do not have to sketch the graph and you may even be given the sketch of the graph to start with. For a quadratic equation of the form \(y = k{(x - a)^2} + b\), the following diagram ...