## Sticky Post – Read this first. Categories and Links in Mathemafrica

The navigability of Mathemafrica isn't ideal, so I have created this post which might guide you to what you are looking for. Here are a number of different categories of post which you might like to take a look at: First year mathematics notes and resources (particularly for the University [...]

## Visual Differential Geometry and Forms – a mathematical drama in five acts, by Tristan Needham – a review

NB. I was sent this book as a review copy. From Princeton University Press Studying physics, some two decades ago at The University of Bristol, I found the majority of what we covered relatively intuitive. Even the arcane world of quantum mechanics, while impossible to truly visualise, is, [...]

## CRL Task 5: Learning Causal Models

We've now come to one of the most vital aspects of this theory - how can we learn causal models? Learning models is often an exceptionally computationally intensive process, so getting this right is crucial. We now develop some mathematical results which guarantee bounds on our learning. We'll start by [...]

## CRL Task 3: Counterfactual Decision Making

In the previous blog post we discussed some theory of how to select optimal and possibly optimal interventions in a causal framework. For those interested in the decision science, this blog post may be more inspiring. This next task involves applying counterfactual quantities to boost learning performance. This is clearly [...]

## CRL Task 2: Interventions – When and Where?

In the previous blog post we discussed the gorey details of generalised policy learning - the first task of CRL. We went into some very detailed mathematical description of dynamic treatment regimes and generalised modes of learning for data processing agents. The next task is a bit more conceptual and [...]

## CRL Task 1: Generalised Policy Learning

In the previous blog post we developed some ideas and theory needed to discuss a causal approach to reinforcement learning. We formalised notions of multi-armed bandits (MABs), Markov Decision Processes (MDPs), and some causal notions. In this blog post we'll finally get to developing some causal reinforcement learning ideas. The [...]

## Preliminaries for CRL

In the previous blog post we discussed and motivated the need for a causal approach to reinforcement learning. We argued that reinforcement learning naturally falls on the interventional rung of the ladder of causation. In this blog post we'll develop some ideas necessary for understanding the material covered in this [...]

## Causal Reinforcement Learning: A Primer

As part of any honours degree at the University of Cape Town, one is obliged to write a thesis 'droning' on about some topic. Luckily for me, applied mathematics can pertain to pretty much anything of interest. Lo and behold, my thesis on merging causality and reinforcement learning. This was [...]

## Covid-19 tests: probabilities

Bayes' Theorem is applied to medical tests, to calculate the probability of being infected with a virus, given a positive or negative test result. What drives the uncertainty is false negative results, or false positive results. In this article, I give a practical outline as to how one can interpret [...]

## A challenging limit

This post comes mostly from the youtube video by BlackPenRedPen found here: https://www.youtube.com/watch?v=89d5f8WUf1Y&t=3s This in turn comes from Brilliant.com - details and links can be found in the original video In this post we will have a look at a complicated-looking limit that has an interesting solution. Here it is: $latex [...]

## Parrondos Paradox

Introduction In this post we will have a look at Parrondos paradox. In a paper* entitled "Information Entropy and Parrondo's Discrete-Time Ratchet"** the authors demonstrate a situation where, by switching between 2 losing strategies, we can create a winning strategy. Setup The setup to this paradox is as follows: We [...]