Attempting to acquaint with advanced math texts can be daunting sometimes – it is easy to be deterred by their density and the notation they may include. The authors of these articles have been in the same situation themselves. They thus articulate ideas not in their most compact form, but in a way that any reader can understand. Through our advanced math articles, we hope that you, the readers, are able to familiarize yourself with the recurring themes of mathematics regardless of whether or not you possess intensive background knowledge on the subject matter.

If one takes a circle and compare the length of its circumference to that of its diameter, you get pi. This constant has a surprising number of applications outside geometry, notably in infinite series of simple fractions.... Read More