## Mathematics and Science are the keys to unlocking Africa’s potential

Angelina Lutambi was born into a peasant family in Tanzania’s Dodoma region, where HIV/AIDS has decimated much of the population. Her future could easily have been bleak – but Angelina had a keen aptitude for maths. She financed her own schooling by selling cold drinks with her siblings and was awarded a grant to study at the University of Dar Es Salaam.

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## How Many Languages Do You Speak?

I’m not sure how, but it’s been a month since my last post. It feels like it was just the other day that I was working on its first draft… Since my first blog dealt with the language of Mathematics, I thought I might continue the language theme for now as it is something that really interests me.

Let me start by asking you this: How often do you take being a First Language English speaker for granted? (Has this thought ever even crossed your mind?) Have you ever traveled to a foreign country and needed to communicate and found it difficult? Were you frustrated by this? What happens when you don’t have a very good grasp of a particular Language, would you want to speak it? Or read it? Or perhaps worse still, write it?

Well, I think this is the challenge that a number of learners face and they are often left feeling frustrated and misunderstood in their classrooms, particularly in South Africa, where we have 11 official languages.…

By | February 22nd, 2016|English, Fun|4 Comments

## How to reduce the fear of mathematics

I sat this morning reading a little of The Book of Life, by Krishnamurti – something which I like to browse through and ponder from time to time. This morning’s meditation somehow felt very apt as I attempt to get almost 800 students to enjoy mathematics, and learn its techniques as well as its beauty. The meditation was the following:

How is the state of attention to be brought about? It cannot be cultivated through persuasion, comparison, reward or punishment, all of which are forms of coercion. The elimination of fear is the beginning of attention. Fear must exist as long as there is an urge to be or to become, which is the pursuit of success, with all its frustrations and tortuous contradictions. You can’t teach concentration, but attention cannot be taught just as you cannot possibly teach freedom from fear; but we can begin to discover the causes that produce fear, and in understanding these causes there is the elimination of fear.

## First week of lectures

So the first week of lectures has ended. In MAM1000 we have only dealt with sets and functions thus far, but in great detail using set builder and interval notation. In our first tutorial we have even started using parametric equations. The Modulus(Absolute value) Function had been added by the end of the week as well. Modulus function is nice to work with as the answer coming out of it must always be positive. If a variable (x) is shown in modulus it must be its non-negative version for example: if x in itself has a negative value then the value of x after modulus has been applied will be -x as this will then be a positive number. Similarly if x is positive then the output will be x. |x| is how modulus is written. We have now also learned that |x+y|<=|x|+|y|, this is called the Triangle inequality and is very important for future use.…

## Absolute values and inequalities

Things that I learnt today. Emphasis on the I, I couldn’t make for MAM1000W today.

• Absolute value definition
• Properties of absolute values
• Rules for inequalities

Absolute value

The absolute value of a number represents the distance between that number and $0$ on the real number line. Absolute value of a number $n$ is denoted by $|n|$ which is equal to $\sqrt{n^{2}}$ which is from the distance formula. Since it is the distance between $0$ and $n$ Hence $|n|=n$ if $n \geq 0$ and $|n|=-n$ if $n < 0$

Properties of Absolute values

1. $|nm| = |n||m|$
2. $|\frac{n}{m}| = \frac{|n|}{|m|}, (m \neq 0)$
3. $|n^{m}| = |n|^{m}$

Let $n > 0$ then

1. $|m| = n \iff m = \pm{n}$
2. $|m| < n \iff -n < m < n$
3. $|m| > n \iff m > n, m < -n$

Rules for inequalities

1. if $n then $n+p
2. if $n and $p then $n+p
3. if $n and $p>0$ then $np
4. if $n and $p<0$ then $np>mp$
5. if $0 then $\frac{1}{n}>\frac{1}{m}$
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## Lecture 2: Sets

List of the things I learnt today

• Definition of a set
• Different ways of representing a set
• Different kinds of sets
• Intervals
• Combinations of sets
• Set notation in functions

Definition of a set

A set is a collection of objects

Different ways of representing a set

Sets of objects are usually denoted by uppercase letters e.g.

let $\mathit{A}$ be the set of all odd numbers.The objects contained in a set are called elements which are denoted by lowercase letters e.g. $\mathit{a}$ is an element of $\mathit{A}$.

A set can be represented in two ways:

1.List

$\mathit{A}=\{a, b, c, d\}$

The set above is an finite list, you can count the number of elements.

$\mathit{B}=\{a, b, c, d,... t\}$

Is also a finite list. It’s important to present enough elements to produce a sequence if the use of ellipses is implemented for shorthand purposes.

$\mathit{C}=\{1, 2, 3, 5, 8,... \}$

This is an infinite set, you cannot count the number of elements in the set.

2. Set Builder Notation

$\mathit{D}=\{e \in \mathbb{R} : \mathit{C} (e) \}$

In the example above $e$ is an element in the set $\mathbb{R}$ where $\mathit{C} (e)$ is a characteristic of the elements which are specific to set $\mathit{D}$ or you can replace “:” with”|”.…

## Lecture 1: Ways to represent a function.

So today we basically learnt about different ways to represent a function and we defined what a function is in detail.

First things first, what is a function?

A function is a rule that assigns each element x ( x being any independent variable ) in a set A exactly one element, f(x) ( f(x) being a dependent variable ) in a set B.

From that definition of a function we can now distinguish the different types of ways to represent a function.

I only know four ways, maybe there’s more… idk

1. algebraically, with the use of an equation
2. graphs
3. tables
4. or just in words

So we also learnt how to test if a graph represents a function. To do that you have to use the vertical line test. which means that anywhere within the domain of the graph if an x value has more than one f(x) value assigned to it then that graph does not represent a function.…

# Gravitational waves: will the global south provide the next pulse of gravity research?

A little over a century ago, on 25 November 1915, Albert Einstein published a paper entitled “Die Feldgleichungen der Gravitation”. Its contents would change the world forever.

Like any good scientific theory, Einstein’s General Relativity not only explained the shortcomings of its predecessor, in this case Newtonian gravity, it also made predictions of new and unexpected phenomena. These included the bending of light by massive objects, the existence of black holes, the slowing down of time in strong gravitational fields and the very framework for the cosmology of the universe. All of these have withstood a century of intense scrutiny. But for 100 years one particular prediction in Einstein’s theory of Gravity eluded the most ingenious testing.

That changed on 11 February 2016 with the news that gravitational waves have been discovered.…

## The Equation of Everything

Salahdin Daouairi unlocks a numerical model puzzle based on a finite discrete system that is key to understanding and interpreting physical laws of the universe. Read more here.

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## You’re (probably) a Bayesian – whether you like it or not!

Statisticians have long been separated into two camps as to how they philosophically interpret their trade. These schools of thought are usually called Frequentists and Bayesians.

Frequentists believe that a probability, $p\in[0~ 1]$, associated with a specific possible outcome of an observable occurrence or process, is simply telling you that, could you observe this occurrence (or process) infinitely many times, the fraction of such observations that would yield that specific outcome is $p$ . Using the age-old coin toss example: tossing the coin is the occurrence or process and recording a Heads or Tails are the two observation. The number 0.5 $\left(P(\text{Tails})=0.5=P(\text{Heads})\right)$ tells a Frequentist that, in the pursuit of infinitely many coin tosses, the ratio of Heads recorded to the number of tosses performed asymptotically approaches 0.5. And that’s all! The value should not be interpreted as the most likely outcome for the next observation or sample taken from the process (though I’ve always wondered how a Frequentist would gamble…).…