Author: Mark Rosin
Welcome to this fourth Data Storytelling Lab workshop, Intro to Mathematical Modeling & Visualization in Python.
About: We tend to think of data as descriptive. The result of a census or transcripts or sales figures, for example. In scientific contexts, data are how we describe the world. They are the result of experiments and measuring naturally occurring phenomena, for example, the levels anthropogenic carbon dioxide in the atmosphere or the results of a vaccine trial.
However, with the right tools, we can also create data that extrapolates from a state of limited knowledge to a fuller understanding. We can even generate data that makes predictions about future scenarios. This is known as mathematical modelling. It is the use of mathematics to model a scenario using well defined equations, and the solving of these equations to generate data about that scenario. Sometimes this can be done using pencil and paper, but increasingly these mathematical models can only be solved on a computer. The results of simulation are a core part of not only science (think climate modelling, drug discovery, engineering, physics), but also finance, weather modelling, business, and running government. The results given by these models are known as simulation data.
In this notebook we take a look at a simple model for describing the dynamics of a population. Let's start with a simple example—exponential growth—and proceed from there.
In this session we'll introduce the concept of mathematical modelling through a simple, but rich, test case. Please navigate to the python notebook to follow along.
- Understand that a wide range of phenomena can be approximated by a mathematical model.
- Recognize that data can be both an input and an output from a mathematical model.
- Identify the key components of a model: data, variables, parameters, and update rules.
We will be working entirely in a single Google Colab notebook. This requies an internet connection and a google account (your Pratt email is powered by Google and will suffice). To edit the notebook, make your own copy and save it to your drive.
- Wigner, E. P. (1960). The unreasonable effectiveness of mathematics in the natural sciences. Mathematics and science, 13, 1-14.
- Daniel Lawson and Glenn Marion (2008). An Introduction to Mathematical Modelling, Glenn Marion, Bioinformatics and Statistics Scotland