Dynamical systems allow us to formulate mathematical models that can help us to describe real-world phenomena. From chemical reactions, to structural components of your home, through to even the mathematics of emotion, I enjoy learning how to understand these things mathematically! Implicit in these sorts of studies, I also get the chance to use numerical methods, analysis, computing, statistics and optimization skills. I love to see the Mathematics and Statistics that I have learned (and now teach to students) come alive in the real world.
I have come to discover that some models can be used for predictive purposes when done inversely. That is, starting with an answer and working toward some other part of a mathematical model. For instance, I have explored the use of such inverse problems in ecological modelling for the preservation of fish colonies when faced with the possibility of drought, or detecting the contraction of a disease in the body based purely on current x-rays.
In addition to my discipline-based research, teaching is a huge part of my life. As the instructor of a number of entry-level mathematics and statistics courses, I am constantly looking to bridge gaps between high school and University Calculus. I aim to make this transition as smooth as possible, while improving student learning and experience. As a backbone to so many different disciplines, I strive to motivate the study of Mathematics and Statistics beyond textbook problems and the classroom and open the eyes of students to their many real-world applications and uses.