Ladies and gentlemen, surely no questions, eh? Everybody's ready, we're all fine.
Good. So what we will start this module is a recap of algebra.
I will say a recap because many, all of you have seen algebra before and you have been
doing these things before in your A-levels or in your high school.
But as I said, we want everybody who is coming into this module to get to the same level.
So even if you think like, oh, these things are easy, don't worry, they will get harder.
I still want you to practice those things.
So we're dealing with the real numbers. There are other than real numbers.
So we will start off with the real numbers. Then on the top of the real numbers is something
called imaginary numbers, which we will be talking about a little bit later in the course.
And these imaginary numbers are opening the dimension of dealing with the problems where
a square root of a negative quantity comes into the place.
As I said, it will be a later. So what we are looking at now is real numbers, which you
consider as the kind of normal numbers. The subsets, subsets of these real numbers are
the natural numbers, the integers, and the rational numbers.
I mean, I am unlikely to deal with any of those, but I will often probably mention that
I'm dealing with the integer or with the natural numbers.
Rational, I don't think I will speak about that.
For completeness, to understand, natural numbers are 1, 2, 3, 4, 5, and so on.
Integers are whole numbers, sometimes referred to, but they can be also a negative.
And zero counts as an integer. So you have minus 2, minus 3, minus 5, and 20, and 27.
And then you have a rational numbers, which are numbers kind of cool in the form of a
fraction. Everybody knows what fraction is.
Yeah, hands up if you don't. That's another thing very important.
I should mention that at the very beginning.
One of those things which you need to learn very quickly on top of the time management
and the right balance between fun and hard work is be able to say, I don't know.
We're coming from a background where in your class before you were the best, or the second
best, and it was usually the case, you know everything, and suddenly there may be times
and moments where when you don't know, don't be shy, it's okay.
It's okay. One of those things, you ask when you don't know, you will get the answer.
If you will sit down and think to yourself, well, I will work it out, it's not going to
happen. And I don't do telepathically understanding
the face that you don't get my message.
So if you don't know, you say don't know.
If you shy to say it in front of the class, come and see me or drop me an email.
So learn it. Faster you learn it, better for you.
Especially in those labs, and you're looking at these equipment and there's a bunch of
guys around you and they're talking about something and there is something you think,
oh, I don't know what that is. Ask them.
The stuff in the mechanical engineering, these are really, really awesome people.
Very, very supportive.
You will find out more you ask, more you're going to get.
So this is how it works.
The real numbers, the subset of the reals are the rational numbers, subset of those are
the integers and subset of those are the natural numbers.
I am not going to ask you any assessment questions on that.
You see, those are the information which are not going to be written there.
But those are little information which all of you should be writing like, not in XM,
but little information like that.
But useful.
If you want to represent these things, you can stick it in the number line.
So it's a straight line.
We will make a straight line.
There is an infinity that way, minus infinity that way.
And I put zero somewhere here.
So one will be here, two will be there.
I will be somewhere in here.
And minus two will be there.
So you can demonstrate it graphically about these numbers and how are they laid out on
the number line.
So these are the numbers.
We need to introduce those numbers because we are going to do math.
So if you get to the higher level math, there are no numbers, just the letters.
But it takes some time to get there.
So first with the numbers.
OK?
Everybody OK with numbers?
Good.