by Dr Kamil Erguler
Climate and One Health Group
CARE-C - The Cyprus Institute
This tutorial series introduces mathematical modelling through hands-on examples. You are encouraged to try them yourself, change the configuration, and get a feel for how things work. You can find the tutorials in this folder, arranged in a roughly logical order.
The series also serves as a reference guide for myself, so I will keep adding to it and updating it as I find more material worth mentioning, remembering, or explaining more clearly.
I will use generative AI tools where useful: to improve the clarity of the presentation, to exchange ideas, and to brainstorm alternative ways of explaining concepts. Just so you know.
Some unseful resources:
If you have comments, suggestions, requests for topics, or questions that need clarification, I would be very happy to hear from you. You can reach me at:
k.erguler [at] cyi.ac.cy
Now fasten your seatbelts and prepare for take-off.
Chapter 1: Model and parameter inference
Wait! Where are we going?
Our first step is to understand that, no matter how complex mathematics may become, it is still simpler than life itself. When we say there is a 50–50 chance of getting heads in a coin toss, we are already using a grossly stripped-down version of reality. We are not thinking about the exact shape and weight of the coin, the force of the throw, air friction, wind, bumpy surfaces, tiny imperfections in the coin, or the possibility of a cheating player. Instead, we imagine a much simpler mathematical object: something with two possible outcomes, each with equal probability. This simplified idea helps us form an expectation in our minds, so that we can understand and play the game in real life. The more carefully our model captures the important features of the real situation, the closer our expectations may come to the real world.
This will all become clearer as we move on, but for now, I’ll leave you with Conway’s Game of Life. In 1970, the British mathematician John Horton Conway invented this cellular automaton to demonstrate how simple rules can generate surprisingly complex behaviour, even in a highly idealised world. The game takes place on a grid of cells, each of which can be either alive or dead. At each step, the state of every cell is updated according to only a few rules, based on the number of neighbouring live cells. Although the rules are very simple, the patterns that appear can be remarkably rich, sometimes looking almost as if they have purpose or organisation. For a deeper philosophical introduction to cellular automata, check this out.
library(IRdisplay)
IRdisplay::display_html('
<iframe
src="https://veclim.com/files/games/game_of_life.html?v=3"
width="870"
height="660"
style="border: none;">
</iframe>
')