Department of Mathematics

Heubach number

Here are two integers whose squares have lots of 9s. The averages of the digits in these squares are 8.25 and 8.275. Can you find a square with greater digit average? See M. Dufour and S. Heubach, Squares with Large Digit Average, Crux Mathematicorum, Vol. 46, No. 8 (2020), pp. 384 - 389


The Math Department office is closed indefinitely because of the corona virus pandemic.

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Events

Pasadena City College, Pi Day. March 14, 2:00-5:00pm. Click to enlarge the flyer below.

Pi Day

problems solving

News

Just Published: Hichem Hajaiej (with coauthors Slim Ibrahim and Nader Masmoudi) just published Ground State Solutions of the Complex Gross Pitaevskii Equation Associated to Exciton-Polariton Bose-Einstein Condensates, in the Journal de Mathématiques Pures et Appliquées

HajaiejBose-Einstein condensates ( BEC) arise in many fields. They were proposed by two physicists Bose and Einstein, as they offer a unique and attractive macroscopic nature. However, a considerable obstacle in the study of (BEC) is the very low temperature required to create the condensate. In 2013, a new type of BEC has been suggested by a group of physicists. It does not require a low-temperature environment. In this paper, we validated their model mathematically. The underlying partial differential equation has a very rich and new structure. We shed some light on the equation but there are many other interesting aspects worth investigating. They can be the subject of a research project for graduate students.

Professor Hichem Hajaiej works on applied partial differential equations arising in quantum mechanics, optics, medicine. He also has research papers on biophysics, superfluid, wind energy, and forensics of plane crashes.