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Liam Harris

The mathematics team at USW is fantastic; they are very passionate about teaching as well as research and have always made me feel welcome. So, when I completed my undergraduate degree here I knew I had to stay to do a PhD.

It has been hard, I do not think you can get through a PhD without wanting to quit at least once! At those times, I always said to myself well if you think it is too hard you are probably doing some good work. But mostly it has been rewarding, you continue to learn so much during a PhD you are constantly challenged its stressful but exhilarating.

I have had excellent support from my supervisors both of whom have mentored and guided me throughout the process (and they are continuing to do so!). The courses/sessions provided by USW’s graduate research office were something I greatly appreciated. I entered into the PhD with aspirations of becoming a lecturer and researcher and I have been lucky enough to work as a lecturer alongside my PhD. 

My area of maths is called combinatorics; essentially, it is the area of mathematics concerned with counting. My PhD looked at the solutions to various chess problems, on various types of “board”. I focused on the bishop piece and the problems of independence and of domination 
Independence asks for a maximal placement of a given chess piece such that no piece in the placement can move to the position of another in a single chess move.

Domination asks for a minimum placement of a given chess piece such that: every square of the board is either occupied by a piece in the placement, or at least one piece in the placement is positioned such that it could move to that square in a single chess move.

I have always loved Combinatorics, ever since I studied it in the second year of my undergraduate Maths degree. Chess problems have fascinated me for a long time too and this PhD was a chance to continue working on similar problems to those I looked at in my undergrad dissertation. It may seem a bit pointless to some but mathematics is always a source of surprising connections and it is not difficult to relate real world counting problems to (seemingly) abstract ones.

Liam Harris, Maths PhD

Dr Liam Harris was awarded his PhD in 2019 and is now working as a Mathematics lecturer at USW. He is a member of the algebra and combinatorics research group.