This is the companion website to David Sumpter’s book Four Ways of Thinking. These pages allow you to get deeper in to the mathematics presented in the book. They are both a tour of some of the ideas that were a bit too involved to get in to the text itself and can be read as standalone mini-adventures in to mathematics. They also contain reference material for those looking to learn more. I have tried to make each section in a way that allows you to spend some time really getting in to a subject.
Each section gives links to useful background, often using high school matchs from BBC Byte Size and/or University maths from Khan Academy. These both provide good summaries of methods. Although many of the topics — maximum likelihood, chaos entropy etc. — are taught in university maths and statsitics courses, often in the second or third years, my aim is to show step-by-step how they work without advanced mathematical background. I hope this approach can be particularly useful to students (upper secondary school or early university… or maybe those thinking about studying at univesity…), teachers (looking for examples to illustrate why maths is useful) and professionals (interested in a new way of seeing maths and who want to understand a new approach), and to people who work with statistics and computing in their jobs and want to get to the bottom of the underlying mathematical ideas.
Experience with programming is required for many of the examples. Many of the examples include code in Python. I recommend you either download Anaconda and run the code in Spyder (download .py files). or upload the Python Notebook (download .ipynb files) Google Colab. Personally, I learn mathematics best when I have example applications, code to run which solves numerical examples, a graphical understanding, along with the maths itself. It is all of these which I aim to provide here.
Contents
Interactive
Complex
