Luke Collins' Website

Luke

I give lessons on anything to do with mathematics or computer science, in Tarxien, for students who want to sit for their intermediate, A-level or undergraduate exams.

If you want some information about lessons, drop me a line:

📞+356 79 000 126
✉️(for lessons)
✉️(for anything else)

I mainly like to teach one-to-one (although group sessions can be arranged).


About Me

My name is Luke Collins, I am currently a visiting mathematics lecturer at the University of Malta. I graduated from the same university 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.

University of Malta
University of Warwick
Malta Mathematical Society

Outside of academia, I work with Simply VC, a company specialising in Blockchain development and infrastructure; and I'm also cofounder of 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.

Simply VC
LearnD
FSF

I do not have any social media accounts—if you want to get in touch, call or email me. 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.


Research

My areas of interest in mathematical research are combinatorics, graph theory and number theory.

Publications

A pair of graphs from my research
  1. Luke Collins & Irene Sciriha
    . The Walks and CDCs of Graphs with the Same Main Eigenspace. Discussiones Mathematiæ Graph Theory (in press), doi:10.7151/dmgt.2386.
  2. Luke Collins
    . The Ternary Goldbach Conjecture. Master's Dissertation in Mathematics (2020), University of Warwick, UK.
  3. Luke Collins
    . On Walks and Canonical Double Coverings of Graphs with the Same Main Eigenspace. Undergraduate Dissertation in Mathematics (2019), University of Malta, Malta.
  4. Luke Collins
    . Synthesising Safety Runtime Enforcement Monitors for μHML. Undergraduate Dissertation in Computer Science (2019), University of Malta, Malta.
  5. Luke Collins & Irene Sciriha
    . Two-graphs and NSSDs: An Algebraic Approach. Discrete Applied Mathematics (2018), 266, pp. 92–102, doi:10.1016/j.dam.2018.05.003.

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.


Teaching

Note that PDFs which are not linked yet, or have version number < 1.0, are still work-in-progress.

Notes and Exercises

MATSEC Booklet Front Page

Miscellaneous


Other Projects

Programming Projects

I have worked on various coding projects over the years, including:
Snakes Game
Tile Game
SHML Parser

Miscellaneous