Meet Ross Pure, a third year Engineering student from the College of Engineering and Computer Sciences. A mathematics problem Ross solved as part of his second year R and D project was recently published. The publication is a program written in the Mathematica programming language. Its function is calculating distance distributions used in the modelling of wireless networks, and can also be applied in other areas such as forestry, mathematics, operations research, and material sciences.
Ross, what are you studying at ANU?
My degree is B Engineering (R&D)/ B Science, majoring in electronic and communication systems, and mathematics.
What is your favourite spot on campus?
Anywhere there's somewhere to sit down outside in nice surroundings, like around the trees in University Avenue.
You like it because....
If it's nice weather and a nice time of day it can put you into a really good frame of mind.
If you were free for an afternoon, what would you do?
Hang out with some friends if they are free. Otherwise I'd relax at home by reading a book or playing piano.
Tell us about your research project.
What I completed was for my R&D project in my second year. My supervisor was Salman Durrani, a senior lecturer in the Research School of Engineering, and the scope of the project was originally just to write a program to calculate the distance distributions for triangles by implementing a method described in a paper. The paper also suggested a way to utilise their method to also compute the distributions for arbitrary polygons, which I ended up attempting. After initial attempts I found their suggestion difficult, so I came up with an alternative method for generalising their result by modifying slightly a well-known mathematical theorem.
How did you solve it? What led you to being able to solve it?
I can't remember the exact train of thought that lead to what I did, but I remember thinking "there has to be an easier way to do this". In my opinion my method is a much more natural generalisation because it uses the main idea developed in the paper, and so familiarity with this idea would have definitely helped.
What was the most challenging part about solving the problem?
As with all research problems it is difficult to know whether your current approach is going to work if you are trying something new, so choosing a path to go down and when to stop going down that path when it doesn't look promising can be difficult.
Have you done anything like this before?
I have not completed any other research projects, although I will be doing at least another one before I finish my degree. I can only hope that my experiences for future projects are as good as my first one.
To those out there who have faced or will face complex maths problems in future, either in their studies or in life, what advice would you have for them with tackling them and coming up with a solution?
Sometimes the thing that will get you to a solution the quickest is taking a break. Clear your head and come back fresh.
Originally published here.