## 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 [...]

## Simpson’s Paradox

Introduction A key consideration when analysing stratified data is how the behaviour of each category differs and how these differences might influence the overall observations about the data. For example, a data set might be split into one large category that dictates the overall behaviour or there may be a [...]

## What is mathematics?

Below you find some thoughts on this wide question, I encourage you to think about. What is your vision of mathematics? It will be most probably the result of your own experience with the subject, traumas that happened along the way and realizing that, could make you more conscious about [...]

## Reasoning and making sense: a pillar of mathematics?

An essential part of learning mathematics is about reasoning and making sense. What does this exactly mean? When a student is given a problem, he needs to make sense of it, from his level of perceptive which is unique to each individual. This will come with big struggle, and the [...]

## The Wisdom of the Crowds

This content comes primarily from the notes of Mark Herbster (contributed to by Massi Pontil and John Shawe-Taylor) of University College London. Introduction The Wisdom of the Crowds, or majority rule and related ideas tend to come up pretty often. Democracy is based (partly) on the majority of people being able [...]

## Automatic Differentiation

Much of this content is based on lecture slides from slides from Professor David Barber at University College London: resources relating to this can be found at: www.cs.ucl.ac.uk/staff/D.Barber/brml What is Autodiff? Autodiff, or Automatic Differentiation, is a method of determining the exact derivative of a function with respect to its inputs. [...]

## Captain Raymond Holt vs Claude Shannon

Overview In this post I am going to introduce a pretty famous riddle, made popular recently by the police sitcom Brooklyn Nine-Nine as well as the idea of the entropy of a probability distribution, made popular by Claude Shannon. Then I am going to go through a solution that is [...]

## What did you expect? Some notes on the Expectation operator.

Introduction A significant amount of focus in statistics is on making inference about the averages or means of phenomena. For example, we might be interested in the average number of goals scored per game by a football team, or the average global temperature or the average cost of a house [...]

## The Gradient Vector

Introduction In this post we introduce two important concepts in multivariate calculus: the gradient vector and the directional derivative. These both extend the idea of the derivative of a function of one variable, each in a different way. The aim of this post is to clarify what these concepts are, [...]

## The (Central) Cauchy distribution

The core of this post comes from Mathematical Statistics and Data Analysis by John A. Rice which is a useful resource for subjects such as UCT's STA2004F. Introduction The Cauchy distribution has a number of interesting properties and is considered a pathological (badly behaved) distribution. What is interesting about it is that [...]

## K-means: Intuitions, Maths and Percy Tau

Much of this content is based on lecture slides from slides from Professor David Barber at University College London: resources relating to this can be found at: www.cs.ucl.ac.uk/staff/D.Barber/brml The K-means algorithm The K-means algorithm is one of the simplest unsupervised learning* algorithms. The aim of the K-means algorithm is, given a [...]