## 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 [...]

## Cartesian product

We know we can use binary operations to add two numbers, x and y: $latex x+y, x-y, x \times y, x \div y. $ Furthermore there are other operations such as $latex \sqrt{x}$ or any other root and exponents. Operations can involve other mathematical objects other than numbers, such as sets. $latex def^n$ Given two [...]

## 3. power sets

Recall powers (or exponents) of numbers: $latex 2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32$ Similarly, sets have the power operation to create new sets. $latex def^n$ If A is a set, then the power set of A is another set denoted as $latex \mathbb{ P }(A) = \text{ set [...]

## 2. Subsets

https://giphy.com/gifs/infinite-boxes-vG1Dgq3JRXLMc Consider a set $latex A = \{2, 3, 7\} \text{ and } B = \{2, 3, 4, 5, 6, 7\}.$ Note that every element in set A is also found in set B, however, the reverse is not true (B contains elements 4, 5 and 6 [...]

## Reverse Mathematics – By John Stillwell, a review

NB. I was sent this book as a review copy. From Princeton University Press I'm not sure I've read a mathematics book which was so hard to review, not because of the quality of the book (which is superb), but because the way of thinking is in some senses so [...]

## Singalakha’s guide to plotting rational functions

To sketch the graph of a function $latex k(x)=\frac{f(x)}{g(x)}$: Find the intercepts: X-intercepts, set y=0 (there can be multiple) Y-intercept, set x=0 (there can be only one) Factorise the numerator and denominator if possible: Sign table: determine where the function is negative and where it is positive Find the Vertical [...]

## My vlogging channel

Hi all, I'm not sure if it counts as vlogging, or making maths videos regularly fits into a slightly more niche category, but anyway, I wanted to advertise some videos that I've been putting up recently. I'm doing this in an attempt to find a different communication channel with my [...]

## 1. Sets

If like me, you've spent most of your mathematical high school years introduced to basic sets at the beginning of the year from Grades 8 to 12, then I think you'd agree that sets was one of the quickest and easiest sections we traditionally did. We would quickly recap the [...]

## A quick introduction to writing mathematics in WordPress using LaTeX

Here are a couple of very useful links about writing mathematics, for new authors of this blog: LaTeX for wordpress Equations in LaTeX in wordpress (and links in that same page, which are very useful). I will update this as I find more useful material. Generally I like to use [...]

## A Whimsical Introduction to Graph Theory (1)

Part 1 - What are Graphs? Mathematics is full of fascinating ideas and concepts. These can, however, be very challenging to tackle and make sense of, especially when you are put under pressure to answer questions about them! In this post, and those to come, I hope to share some [...]

## e-day – A mathematical holiday celebrated on February 7th

Today, February 7th, 2018, is called e-day because e is approximately 2.718, and this date is written 2/7/18 in some parts of the world. e, also called Euler’s Number after the Swiss mathematician Leonhard Euler, is a very important constant that comes up in many different places in mathematics. The numer e was discovered by the Swiss [...]