Ishraq Al-Awamleh will be leading our Mathematics Teachers' Circle of Austin (MTCA) on the topic of "The 4-Average and Beyond."

The importance of central tendency has a long history, which in addition to covering the arithmetic mean, includes the mode, median, midrange and extends to very general setups. We will look closely at the 4-averaging process which is in addition to being an average operator, it is an extension of typical measures of central tendency.

We find unexpected discrete to continuous mean value principles that are used to analyze the normalized p-Laplacian for particular values of p. A particularly interesting case is the 4−Laplacian which is the harmonic mean between the usual Laplacian and ∞-Laplacian. We will extend this discrete averaging for polynomials in 2 dimensions to higher dimensions.