## 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 [...]

## p-values: an introduction (Part 1)

The starting point This is the first of (at least) 3 posts on p-values. p-values are everywhere in statistics- especially in fields that require experimental design. They are also pretty tricky to get your head around at first. This is because of the nature of classical (frequentist) statistics. So to [...]

## R-squared values for linear regression

What we are talking about Linear regression is a common and useful statistical tool. You will have almost certainly come across it if your studies have presented you with any sort of statistical problems. The pros of regression are that it is relatively easy to implement and that the relationship [...]

## Cantor–Schröder–Bernstein Theorem

Knowledge this posts assumes: What is a set, set cardinality, a function, an image of a function and an injective (one-to-one) function. David Hilbert imagines a hotel with an infinite number of rooms. In this hotel, each room can only be occupied by one guest, and each room is indeed [...]

## 1.6 Partitions

Recall the relation $latex \equiv \text{ mod} (4) $ on the set $latex \mathbb{ N}.$ One of the equivalence classes is $latex [0] = \{ ..., -8, -4, 0, 4, 8, ...\}$ which is equivalent to writing $latex [0] = [4] = [-4] = [8] = [-8] ...$ We could do this [...]

## Review: Calculus Reordered

Book title: Calculus Reordered: A History of the Big Ideas Author : David M. Bressoud Princeton University Press Link to the book: Calculus Reordered: A History of the Big Ideas Discussions on the history of different fields are usually dry, wordy and generally, when you are studying the field, hard [...]

## Investigating Practical Ordering of Grids

In Reinforcement Learning there is an environment known as Gridworld. In this environment you have a grid and there is an agent that learns how to find the shortest path from one cell to another. The theme of reinforcement learning is that you do not want to hard-code the rules, [...]

## 1.5 Equivalence classes (Infinite sets)

Let's find the equivalence classes of the following finite set S: Given $latex S = \{ -1, 1, 2, 3, 4 \}, $ we can form the following relation $latex R = \{ (-1, -1), (1,1), (2,2), (3,3), (4,4), (1,3), (3,1), (2,4), (4,2) \}. $ Note: writing the relation $latex [...]

## The 2018 South African Mathematics Olympiad — Problem 6

The final round of the South African Mathematics Olympiad will be taking place on Thursday, 28 July 2019. I have been writing about some of the problems from the senior paper from 2018. A list of all of the problems can be found here. Today we will look at the [...]

## On the invariant measure in special relativity

I'm writing this for my string theory class. We are basing our lectures on Zwiebach - A First Course in String Theory, and starting off with special relativity. Not everybody in the class has a physics background (pure and applied mathematics students), and so there are likely to be questions [...]

## 1.4 Equivalence classes

Let's recall the definition of an equivalence relation: A relation R on a set A is termed an equivalence relation if it is simultaneously reflexive, symmetric and transitive. Let's look at more examples: Example One: Let $latex A = \{2, 11, 17, 20\}$ be a set with the following relation: [...]