## 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 [...]

## 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 [...]

## Taking a pipe round a corner corridor optimisation question

You have a corridor which has an L-shape in it. The corridor looks like this: where a and b are the widths of the sections of the corridor. The question is to find the longest pipe that can be carried down this corridor. The word pipe here just means something [...]

## Prove that for every positive integer n, 9^n – 8n -1 is divisible by 64.

Prove that for every positive integer $latex n$, $latex 9^n-8n-1$ is divisible by 64. This question screams proof by induction, so we start with the base case, which in this case is $latex n=1$: $latex 9^1-8-1$ which is indeed divisible by 64. Now, let's assume that it holds true for [...]

## A tricky complex numbers problem

The question is as follows: If $latex \frac{\pi}{6}\in arg(z+a)$ and $latex \frac{2\pi}{3}\in arg(z-a)$ and $latex a\in \mathbb{R}$, find $latex z$. So, let's think about the information given and what we are trying to find. We want to find the complex number $latex z$ which satisfies this slightly strange set of [...]

## Using polynomials to solve differential equations

One of the aims of MAM1000W isn't just to teach you individual mathematical topics, but over time to allow you to see the links between these subjects. Sometimes we do this explicitly, and sometimes you should notice the connections yourself simply by seeing one topic pop up in the middle [...]