In this blog post, we have spoken to Robert Johnson, Senior Lecturer in Pure Mathematics and Head of the Combinatorics research group. He told us about his own academic journey, from Cambridge University to the School of Maths, as well as his teaching style and his research interests. He also told us what it takes, in his opinion, to be an excellent maths student.
What is good about working at the School of Maths?
It is hard to pick one thing, as I genuinely enjoy most parts of my job. I find the School a very friendly, collaborative place to work and feel at home here. Not only are my colleagues great mathematicians and teachers, but they are also enthusiastic about new ideas and go out of their way to share them and help out in all sorts of ways.
Tell us about your academic journey.
I have always taken the approach of doing what I enjoy and seeing where it leads. During my undergraduate degree at Cambridge, combinatorics particularly appealed to me as an area full of easy to state but compelling questions that need creative mathematical arguments to solve. This, together with some inspiring lecturers, encouraged me to choose this area for my PhD (also at Cambridge). After that, I spent one year at LSE before joining QMUL in 2004, and have been here since. I have recently taken over as Head of the Combinatorics research group. This made me think about how my research fits with the rest of the group, in particular the more applied areas of combinatorial optimisation, and how to build connections with other research groups.
What does your research focus on?
My research is in combinatorics, which is the mathematics of discrete structures such as graphs (networks), permutations, and collections of finite sets. A particular focus is extremal combinatorics, which considers questions about the largest combinatorial structure satisfying a certain property. A simple example of such a question (which is not difficult to answer) would be how many subsets of a finite set can you find such that any two of them have a non-empty intersection? One current project involves looking at problems of this type about permutations rather than sets. I am a pure mathematician so my main motivation is intrinsic mathematical appeal but some of my work is inspired by applications. For example, a question in statistics was the stimulus for a recent project on constructing graphs that are richly connected according to a metric based on electrical resistance.
What is your teaching style like?
I try to convey why things are the way they are and to put ideas into some kind of mathematical narrative rather than presenting them as isolated facts. I am particularly keen on teaching skills and ways of thinking as well as knowledge. For instance, a large part of the first-year module I have taught for the last few years is about how to understand, learn and come up with mathematical proofs. I do make my modules challenging, but I always do my best to create a supportive atmosphere in classes and to be kind to students - that is particularly important, given the unusual demands last year has put on us all.
What makes a great maths student in your opinion?
Anyone who is enthusiastic about maths, either for its own sake or as a tool to understand the world. Picking up new mathematical concepts and ways of thinking takes time and effort, so patience and persistence are great virtues to have. It helps to enjoy the feeling of being stuck into a problem and wrestling a solution out of it, rather like the enjoyment of finally cracking a difficult puzzle.