Author Archives: apgoucher

The determinant of a matrix can be regarded, most naturally, as the volume scaling factor of the corresponding linear map. However, one of the formulae for finding the determinant of a square matrix is to compute , where we sum over … Continue reading →

The connect sum of two knots is obtained by joining them together in the obvious way. There is, however, one small detail. If you define this naïvely, then you won’t necessarily obtain an unambiguous connect sum. For instance, consider the … Continue reading →

Some things have actually happened. A few of these are worth mentioning. RMM 2013 results Firstly, the results of the Romanian Master of Mathematics (RMM 2013) competition have been published. There have been two perfect scores this year (very rare … Continue reading →

Consider the Gaussian function . This gives the standard normal distribution, which has zero mean, unit variance, and points of inflection located at ±1. Note the scaling term , which is included so that the integral is 1 (necessary for a … Continue reading →

Some of you may have noticed a particularly queer post on cp4space yesterday (since deleted), which was written by an impostor. Specifically, I was hosting several people (including, but by no means limited to, the daughter of Kjartan Poskitt). I … Continue reading →

The torus is a reasonably interesting object. It can be embedded in as a quartic surface bounding a doughnut, or obtained by identifying opposite edges of a square. An intermediate between these constructions is the Clifford torus, which is the … Continue reading →