## 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 [...]

## Relativity, The Special and General Theory, 100th anniversary edition – by Albert Einstein

NB. I was sent this book as a review copy. From Princeton University Press. In 1917, two years after publishing his work on The General Theory of Relativity, Einstein published a popular science account of both The Special, and General Theories of relativity. It is with some embarrassment [...]

## Using Math To Tell A Lie

A more appropriate heading for this would be "How a logical truth can be a lexical lie", but hey, gotta have that clickbaity title. But nevertheless, I will frame this article as if I am addressing the title. Apparently, sociologists/psychologists classify lies with a three tier system; primary, secondary, and [...]

## Data Visualization, a practical introduction – by Kieran Healy, a review

NB. I was sent this book as a review copy. From Princeton University Press. I'm not an expert on the R programming language, but I have dabbled, which meant that while this book is perhaps aimed at slightly more advanced users (I've used it a half a dozen [...]

## Linear Algebra for the Memes

I recently saw a post on Quora asking what people generally find exciting about Linear Algebra, and it really took me back, since Linear Algebra was the first thing in the more modern part of mathematics that I fell in love with, thanks to Dr Erwin. I decided to write [...]

## All you’ve ever wanted to know about absolute values (and weren’t afraid to ask)

I've been getting a lot of questions about absolute values, and so I thought I would try and clarify things here as much as possible. I'll give some basic definitions and intuition, and then go through some examples, from easier to harder. The absolute value function is just....a function. You [...]

## How to Fall Slower Than Gravity And Other Everyday (and Not So Everyday) Uses of Mathematics and Physical Reasoning – by Paul J. Nahin, a review

NB. I was sent this book as a review copy. From Princeton University Press. This book is without a doubt the most enjoyable, stimulating book of mathematical physics (and occasionally more pure branches of maths) puzzles that I have ever read. It's essentially a series of cleverly, and occasionally [...]

## Millions, Billions, Zillions – Defending Yourself in a World of Too Many Numbers – by Brian W. Kernighan, a review

NB. I was sent this book as a review copy. From Princeton University Press. I have to admit that I was skeptical about this book when I first saw it, and even on browsing through it became more so (read on for the but...). I count myself as [...]

## The Mathematics of Secrets – by Joshua Holden, a review

NB. I was sent this book as a review copy. From Princeton University Press. This is an extremely clearly, well-written book covering a lot of ground in the mathematics of cyphers. It starts from the very basics with simple transposition cyphers and goes all the way through to [...]

## 1.2 Properties of Groups

Recall the definition of a group: A set G is "upgraded" into a group if it satisfied the following axioms under one binary operation (*) : Closure: $latex \forall x, y \in G, x*y \in G $ Associativity: $latex \forall x, y, z \in G, (x*y)*z = x*(y*z)$ Identity: $latex \exists e \in G, [...]

## 1.1 Groups Introduction

Binary operations are operations such as addition, subtraction, multiplication, division, modulus etc. that are applied to two quantities. example 1: $latex 2+5 $ is an example of an expression with addition as the binary operation example 2: Let f and g be functions defined on sets A to B. Then the [...]