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 note we show that if the areal mean-value theorem holds for a plane domain (subject to a mild regularity condition) for all integrable harmonic functions, then the domain must be a disk. It is ...

Since \(x+7\not= 0\) for all \(x\in [-1,2]\) it follows that the function \(g\text{,}\) as a rational function, is continuous on the closed interval \([-1,2]\) and ...