Imagine you’re trying to escape from a large room with only one exit. To make matters worse, you’re blindfolded and wander around at random, searching for the door.
While I hope this never happens to anyone, finding the average time required to escape the room is actually a field of study in mathematics. Over this past summer I spent my time researching and studying this class of problem, known as a mean first passage time or narrow escape problem.
I have tried to solve this problem using computer models rather than exact mathematical solutions. By making approximations about the governing equations and using many repeating computations, I was able to come up with meaningful results. These types of problems are useful in modelling a variety of different real-world processes like neuron dynamics, financial markets and search algorithms.
During my research I learnt to work independently, record my ideas, get help when I needed it, consult multiple different sources, ask tough questions, not to give up when you get stuck, plan out your day and make time to relax and unwind. It was a massive learning experience!
Professor Tony Roberts was a fantastic supervisor. I became curious about these problems during one of his lectures when I realised just how passionate and excited he got over maths problems. Seeing how someone very experienced in the field approached a problem was an invaluable learning opportunity. I’m very grateful for the support and mentoring he provided over the six-week project.
After presenting my research at AMSIConnect in Melbourne, I realised that communicating mathematics is something I really enjoy doing. I have also spent four years working with high-school students as part of the University of Queensland’s Outreach program.
This year I decided to combine those two interests and start a small business—Lambda Learning—which encourages secondary students to get involved with and excited about maths. So far, I’ve been able to deliver three presentations in schools with several more planned before the end of the year, with the hope to reach more and more students.
When I was in middle school I wasn’t good at maths. I didn’t think it was useful and I wasn’t that interested in studying it. Luckily for me, I had excellent teachers who helped me discover my innate curiosity and taught me that if I applied myself, I could do well at mathematics.
That’s the message I share with students, that the mathematical sciences are useful in so many different areas, and that you don’t have to be a genius to get involved in them.
In addition to my work in high schools, my honours research focuses on energy transitions. To reduce carbon emissions in the energy sector, Australia and the world are transitioning away from fossil fuels to more renewable energy sources. Wind and solar are the leading candidates to help do that, but they are inherently different from current power-generation methods, both in the way they generate electricity and when they do so. This has massive implications for Australia’s power system, electricity market, energy policy and economy.
I’m a firm believer that the mathematical sciences have a key role to play in helping to make informed, data-based decisions about these issues. That is my goal with my research, to use the mathematical and critical-thinking skills I have developed to help make sense of the current energy landscape. In five years’ time I’d love to be either finishing a PhD in this area, or working for a renewable-energy consulting company, applying all the skills that I am learning.