## 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 [...]

## The 2018 South African Mathematics Olympiad — Problem 5

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 [...]

## The 2018 South African Mathematics Olympiad — Problem 4

The final round of the South African Mathematics Olympiad will be taking place on Thursday, 28 July 2019. In the week leading up to the contest, I plan to take a look at some of the problems from the senior paper from 2018. A list of all of the posts [...]

## MAM1019H fundamentals of mathematics

1.1 Relations - introduction 1.2 Relations - properties 1.3 Relations - equivalence relations

## 1.3 Relations: Equivalence relations

We know that a relation is called an Equivalence Relation when it is reflexive, symmetric AND transitive on some set A. Let's look at some examples. Example One: Let $latex a,b \in \mathbb{R}.$ Suppose we have that a is related to b (i.e. a ~ b) if $latex a - b \in [...]

## 1.2 Relations: Properties

Note: Do not confuse binary operations (+, x, -, ...) with relations. Recall the definition for a relation as: A relation R on a set A is a subset R ⊆ A × A. We often abbreviate the statement (x, y) ∈ R as xRy. For instance, the binary operation "x" has a [...]

## 1.1 Relations: Introduction

What are relations? In every day life, a person is related to their parents, siblings, cousins, teachers, friends, etc. in some way. Similarly in mathematics, mathematical objects like numbers and sets are related to one another in some way. Many relations (symbols) will be familiar already: $latex 2 <3$ $latex \pi \approx 3.14$ [...]

## The 2018 South African Mathematics Olympiad — Problem 3

The final round of the South African Mathematics Olympiad will be taking place on Thursday, 28 July 2019. In the week leading up to the contest, I plan to take a look at some of the problems from the senior paper from 2018. A list of all the posts can [...]

## The 2018 South African Mathematics Olympiad — Problem 2

The final round of the South African Mathematics Olympiad will be taking place on Thursday, 28 July 2019. In the week and half leading up the the contest, I plan to take a look at some of the problems from the senior paper in 2018, and have already written about [...]

## The South African Mathematics Olympiad problems

Introduction to the SA maths Olympiad 2018 Olympiad problem 1 2018 Olympiad problem 2 2018 Olympiad problem 3 2018 Olympiad problem 4 2018 Olympiad problem 5

## The 2018 South African Mathematics Olympiad — Problem 1

The final round of the South African Mathematics Olympiad will be taking place on Thursday, 28 July 2019. In the two weeks leading up to the contest, I plan to take a look at some of the problems from the senior paper from 2018. The first problem from the 2018 [...]