Mathematical equations can be quite intimidating if you don’t know how to how to read them,
but they don’t need to be.
It is possible to learn how to make sense of them even if you don’t know much algebra.
So if when you see and equation it looks like a strange alien language, this video is for
you.
The first rule is you need to find out where these things called variables are.
A mathematical equation describes a relationship between things.
The most common form is something equals something else.
These letters are the variables and are stand-ins for numbers.
You can put any number into them but the equation fixes what the other numbers can be.
For example, y=x means that the numbers in y and x have to be the same.
But in y=2x, the number in y has to be double whatever the number in x is.
The best way to visualise this is with a graph, and when you do this each variable in your
equation gets an axis.
And the line on your graph shows the allowed pairs of values for your equation.
Now you can also have equations where the variables appear in multiple different places,
but you still only have two axes.
Equations with two variables are the simplest you can get, but many equations have multiple
variables.
So if you wanted to draw a graph of an equation with three variables you would need to have
one axis for each of the variables.
But often to make it easier to work with we just concentrate on two of the variables and
keep the other variables fixed.
But you can try different values to see what happens.
The other thing you get in equations are constants.
You have to keep an eye out for constants because they look like variables, they are
written with a letter, but actually they are just a single number.
A famous one is pi, but in science you get many others.
So how do you know which letters or symbols are constants or variables?
Well you don't.
You have to rely on the person writing the equation to tell you what all of the bits
mean.
Practically when you use equations in science, you have the numbers to put in to all the
variables apart from one, and that's the one you are trying to work out.
So you plug in all the numbers and find out what the last variable should be.
Lets look at an example of an equation and how I would go about reading it.
This is Newton’s law of Universal gravitation which looks at the force of gravity between
two masses.
First thing you do is work out what all the letters mean.
F is the gravitational force that you are working out.
m1 and m2 are the masses of the two bodies.
G is the gravitational constant, and r is the distance between the masses.
Now you work out which letters are variables and which ones are constants.
This formula just has got one constant: G which is a tiny little number.
Now you basically know how to use this formula.
If you have the masses of any two objects and the distance between them, you can plug
in the numbers and calculate the force of gravity between them.
So the force of gravity between an apple and an orange is about the weight of a grain of
pollen.
Very very small.
When you plug numbers in and solve the equation you have to know what order to do things in.
And this is the next thing you need to work out after you have identified the variables
and constants.
Knowing what order you would do the mathematical operations in an equation helps you get your
head around them, and there are some rules about how it is done.
Any variables that are just next to each other are multiplied with each other, and you do
these first.
At the same time you do any divisions - but only if it is a single number divided by another
number.
And then you do the additions and subtractions.
If you've got a division, but there is an addition or subtraction at the top or bottom,
you need to make sure these are done first before you can do the division.
And finally, anything in brackets goes before anything outside of the brackets.
There are more rules but this covers you in most situations.
When you come across an equation in a book or video, you are probably not going to start
putting actual numbers into it.
But running through what you would do if you had the numbers is a really useful way to
get your head around the equation.
In these examples I’ve mostly used normal letters but many equations also use greek
letters.
I think this is why equations look so weird to people because they are unfamilliar with
all these strange symbols.
But you should think of them just the same as normal letters, they can be used to represent
constants or variables so they are just the same.
You also get other notations like subscripts and these are all basically used as labels
to identify different constants or variables.
Other notation has specific mathematical meanings, and I can’t cover everything in this video,
but if you are ever confused about what something means I encourage you to look it up as they
normally end up being simpler than you think.
But also I've made a handy cheat sheet which I've put in the descripion below so you can
also check that out.
Now here are some of the other more common weird things that you’ll see.
You're all familiar with multiplication, division, adding and subtracting.
These are all things call mathematical operations.
But they are not the only ones, and here are some of the more common ones that you'll see.
This big greek epsilon is a sum operation, and what it means is that you take this thing
and repeatedly add it to itself, but put in different numbers each time.
This is the number that you start at, and this is the number you end at.
It also means that this variable has to be an integer variable, which means that it can
only take on whole numbers, zero, one, two, three, four.
No numbers in between.
So whenever you see a sum, just imagine this thing as a whole series of things being added
together, but each having a different value.
Similar to a sum is an integral, which really needs a graph to explain it.
It is basically a way of finding the area underneath a line that is defined here.
Like a sum it's got a beginning and an end, although these can go from minus infinity
to infinity, so you might see that written sometimes too.
And finally, related to integration is differentiation which looks like this and is an operation
that looks at how the steepness of a line changes, called the gradient of a line.
So when you have things like dy/dx, they are looking at the gradients of lines.
That's just a quick look at integration and differentiation these make up calculus but
that needs a whole video in itself to eqplain properly.
I put the here so that you don't freak out when you see them.
So those are the basics of how to read mathematical equations.
Step one find the variables and constants and what each one represents.
Step two work out what all the weird mathematical operations are.
And step three work out what order you would solve the equation in if you put in the numbers.
If you want more info check out this cheat sheet I have put together with all of the
greek letters and most of the more common mathematical operations, check it out in the
link in the description below.
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It is a lot of much fun, I really reccommend you giving it a try, just go to brilliant.org/dos
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