The Joys and Frustrations of Mathematical Modelling

By Marcus Pensa, Monash University

During my time researching as an AMSI scholar, I experienced both the joys and frustration of mathematic research. I also quickly learnt that computers are an inescapable part of mathematical modelling.

My project involved modelling the movement of molecules in cells. I was interested in how much of a given molecule reaches the surface of the cell, if that molecule is produced at a single point within the cell. One of the calculations involved in this modelling was dividing a very large number (>10^300) by another very large number, which gives a quotient (answer) that has a manageable size. Unfortunately, the computer program that we were using, Matlab, could not handle the individual very large numbers and we had to approximate our quotient using a novel approach. It was quite confronting running into a technological limitation which up until that point only existed in my mind as a theoretical barrier which I would never have to deal with. One method I devised did what I wanted it to, but it did so very slowly due to being computationally expensive. Again, I was grappling with the restraints of computational technology. In the end, we were able to apply the work of others, a description of the quotient which has been known for over 30 years, and this saved the day! I thought it was quite beautiful how the latest technology coupled with classic techniques and discovery all came together to solve a new biologically motivated problem.

At times it was frustrating that there was no answer sheet, but it was always exciting to be working on a problem which no one knows the answer to. I am grateful that with my supervisor’s support, I was able to overcome some hurdles and make progress. I have also gained an appreciation that for mathematics in today’s day and age, coding is no different from calculus or algebra in the sense that these are all tools in a mathematician’s toolbox. Each needs to be understood to stop us using trying to use a screwdriver to put in a nail, or at least to help us understand why it’s not working after we start trying.

Marcus Pensa was one of the recipients of a 2017/18 AMSI Vacation Research Scholarship.

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