Luke Collins' Website
My name is Luke Collins, I am currently a visiting mathematics lecturer at the University of Malta, as well as a Heilbronn doctoral student at UCL, under the joint supervision of Alexey Pokrovskiy and Shoham Letzter.
I graduated from the University of Malta with a first class double honours in Mathematics and Computer Science, and completed a Master's degree in Mathematics at the University of Warwick, graduating with distinction. My main research interests lie in graph theory, combinatorics, and number theory. Recently, I re-established the Malta Mathematical Society, and run it with the help of a group of dedicated undergraduates from the University of Malta.
Outside of academia, I was a researcher at Simply VC, a company specialising in Blockchain development and infrastructure; and I also cofounded the mobile app company LearnD. In my spare time, I enjoy listening to classical music, playing the piano, doing (ethical) hacking and practising Brazilian jiu-jitsu. I like reading about history, politics, theology and philosophy.
I don't really use social media—if you want to get in touch, email me at luke (at) collins (dot) mt. I am a member and supporter of the Free Software Foundation, a movement which advocates for users' rights to study the source code of programs executing on their machine. I make use of Arch Linux, and always run free (libre) whenever possible.
My areas of interest in mathematical research are combinatorics, graph theory and number theory.
My Erdős number is ⩽ 3 because of the chain: L. Collins (me) → I. Sciriha → C. Godsil → P. Erdős.
- Luke Collins & Irene Sciriha. The Walks and CDCs of Graphs with the Same Main Eigenspace. Discussiones Mathematiæ Graph Theory (in press),
- Luke Collins. The Ternary Goldbach Conjecture. Master's Dissertation in Mathematics (2020), University of Warwick, UK.
- Luke Collins. On Walks and Canonical Double Coverings of Graphs with the Same Main Eigenspace. Undergraduate Dissertation in Mathematics (2019), University of Malta, Malta.
- Luke Collins. Synthesising Safety Runtime Enforcement Monitors for μHML. Undergraduate Dissertation in Computer Science (2019), University of Malta, Malta.
- Luke Collins & Irene Sciriha. Two-graphs and NSSDs: An Algebraic Approach. Discrete Applied Mathematics (2018), 266, pp. 92–102,
Walks and CDCs
Recently I've been doing quite a bit of research related to walks and an operation called the canonical double cover (CDC) of a graph. Read more about this research here.
I give some courses at the University of Malta. Some of the resources I've prepared for the courses can be found in this section.
Notes and Exercises
Note that PDFs which are not linked yet, or have version number < 1.0, are still work-in-progress.
- Courses I'm teaching this year at the University of Malta: CHE1215, CHE1217 and TET1013.
- LaTeX Course I delivered for the Doctoral School
- Master's level algorithms course I delivered for IDEA Academy:
- Undergraduate and Postgraduate Notes
- Pure Mathematics at A-level and Intermediate
- MATSEC formulæ exam booklet: A4 version | A5 printable version
- Complete list of O-level plane geometry theorems
I occasionally give private tuition for anything related to mathematics and computer science. If you would like me to tutor you, email me at luke (at) collins (dot) mt.
- Here is a tool for visualising the effect of 2×2 matrices: matrix visualiser.
- Here is a tool to draw automata diagrams: automaton designer.
- Here is a tool for generating truth tables: truth table generator.
Programming ProjectsI have worked on various coding projects over the years, including:
- a multiplayer snakes game written in C,
- a multiplayer tile game written in Java,
- a compiler for a custom Turing complete language written in C++,
- a logic parser and normaliser written in Haskell.