#whatmaths

[whatmaths-blog]

Welcome!

Welcome to the first post of WHATMaths!

WHATMaths hopes to provide a quick explanation of some mathematical concepts, along with a lesson presentation and some related worksheets.

We hope our resources will be helpful, whether you want to use our resources to teach your class or yourself. To help, we will always state the minimum level of maths qualifications needed to understand each topic, but we aim to stick to between GCSE level and the beginning of a maths degree - i.e. anyone who isn’t in maths further education. Above all else we want maths to be accessible, not just loved by those in academia!

After each post you can find links off to our resources which you can download and share.

Happy learning!

[whatmaths-blog]

Algebraic Division

Level: GCSEs and above (this is an introduction into the techniques of dividing algebraic expressions)

About:

Algebraic Division is the process of dividing one polynomial by another. 

It is the generalised version of the arithmetic technique of long division, which you will have learnt earlier, and it is a useful tool as it allows you break down complex algebraic problems into more simple expressions. 

For a step-by-step guide of how to do this, with some helpful hints and key definitions, check out our lesson and exercises below!

Lesson resources:

Presentation

Task sheets: 1, 2, 3

[whatmaths-blog]

Complex Numbers

Level: GCSEs and above (this is only an introduction to imaginary and complex numbers, and sticks to the basic operations of addition, subtraction, multiplication, and division that does not involve complex conjugates, i.e. dividends with a real factor)

About:

A complex number is a number which can be expressed in real and imaginary parts, which looks like a + bi, where a and b are both real numbers, and i is the imaginary unit such that i2 = -1. Here, a is the real part and bi is the imaginary part. 

Adding, subtracting, multiplying and dividing with complex numbers works similar to the same operations on algebraic expressions except instead of an unknown variable x or y, we work with i. 

Try our lesson and examples below and you'll get the hang of it!

Lesson resources:

Presentation

Task Sheets: 1, 2, 3

[whatmaths-blog]

The Pigeonhole Principle (an intro)

Level: A-Level Mathematics and above (this is only an introduction to the Pigeonhole Principle, and sticks firmly to defined, finite ‘pigeons’ and ‘pigeonholes’, focusing on trivial applications and examples)

About:

The Pigeonhole Principle is an example of a counting argument, a way of counting something in two different ways to form two equal expressions, e.g. even numbers can be counted in ones and twos, 1+1+1+1=2+2 etc.

Also known as Dirichlet’s Drawer Principle, the basic principle is that if there are a number of objects, and one less container than objects, if you put the objects in the containers then one of the containers has at least two objects in it – or more mathematically:

“Let n be a natural number. If n+1 pigeons are placed in n pigeonholes, then some pigeonhole contains at least 2 pigeons.”*

The pigeons, obviously, aren’t the maths-y bit.

For examples, applications, and a generalised principle, check out our lesson resources below!

Lesson resources:

Presentation

Task sheets: 1, 2, 3

*To be rigorous, a proof should really be included. However, WHATMaths aims to introduce new concepts to those at GCSE level and above, so the proof has been omitted from this post. A separate post detailing the proof can be found here.