WEBVTT 1 00:00:00.000 --> 00:00:05.580 Ladies and gentlemen, surely no questions, eh? Everybody's ready, we're all fine. 2 00:00:05.580 --> 00:00:12.780 Good. So what we will start this module is a recap of algebra. 3 00:00:12.780 --> 00:00:17.480 I will say a recap because many, all of you have seen algebra before and you have been 4 00:00:17.480 --> 00:00:22.840 doing these things before in your A-levels or in your high school. 5 00:00:22.840 --> 00:00:29.520 But as I said, we want everybody who is coming into this module to get to the same level. 6 00:00:29.520 --> 00:00:35.760 So even if you think like, oh, these things are easy, don't worry, they will get harder. 7 00:00:35.760 --> 00:00:40.440 I still want you to practice those things. 8 00:00:40.440 --> 00:00:45.800 So we're dealing with the real numbers. There are other than real numbers. 9 00:00:45.800 --> 00:00:50.120 So we will start off with the real numbers. Then on the top of the real numbers is something 10 00:00:50.120 --> 00:00:55.920 called imaginary numbers, which we will be talking about a little bit later in the course. 11 00:00:55.920 --> 00:01:03.720 And these imaginary numbers are opening the dimension of dealing with the problems where 12 00:01:03.720 --> 00:01:07.400 a square root of a negative quantity comes into the place. 13 00:01:07.400 --> 00:01:13.080 As I said, it will be a later. So what we are looking at now is real numbers, which you 14 00:01:13.080 --> 00:01:22.240 consider as the kind of normal numbers. The subsets, subsets of these real numbers are 15 00:01:22.240 --> 00:01:29.920 the natural numbers, the integers, and the rational numbers. 16 00:01:29.920 --> 00:01:38.080 I mean, I am unlikely to deal with any of those, but I will often probably mention that 17 00:01:38.080 --> 00:01:42.000 I'm dealing with the integer or with the natural numbers. 18 00:01:42.000 --> 00:01:45.960 Rational, I don't think I will speak about that. 19 00:01:46.080 --> 00:01:53.560 For completeness, to understand, natural numbers are 1, 2, 3, 4, 5, and so on. 20 00:01:53.560 --> 00:01:58.280 Integers are whole numbers, sometimes referred to, but they can be also a negative. 21 00:01:58.280 --> 00:02:05.840 And zero counts as an integer. So you have minus 2, minus 3, minus 5, and 20, and 27. 22 00:02:05.840 --> 00:02:11.360 And then you have a rational numbers, which are numbers kind of cool in the form of a 23 00:02:11.360 --> 00:02:14.200 fraction. Everybody knows what fraction is. 24 00:02:14.920 --> 00:02:20.520 Yeah, hands up if you don't. That's another thing very important. 25 00:02:20.520 --> 00:02:23.640 I should mention that at the very beginning. 26 00:02:23.640 --> 00:02:29.200 One of those things which you need to learn very quickly on top of the time management 27 00:02:29.200 --> 00:02:37.400 and the right balance between fun and hard work is be able to say, I don't know. 28 00:02:37.400 --> 00:02:42.520 We're coming from a background where in your class before you were the best, or the second 29 00:02:42.520 --> 00:02:48.040 best, and it was usually the case, you know everything, and suddenly there may be times 30 00:02:48.040 --> 00:02:52.400 and moments where when you don't know, don't be shy, it's okay. 31 00:02:52.400 --> 00:02:59.080 It's okay. One of those things, you ask when you don't know, you will get the answer. 32 00:02:59.080 --> 00:03:03.240 If you will sit down and think to yourself, well, I will work it out, it's not going to 33 00:03:03.240 --> 00:03:07.720 happen. And I don't do telepathically understanding 34 00:03:07.800 --> 00:03:10.040 the face that you don't get my message. 35 00:03:10.040 --> 00:03:12.080 So if you don't know, you say don't know. 36 00:03:12.080 --> 00:03:17.480 If you shy to say it in front of the class, come and see me or drop me an email. 37 00:03:17.480 --> 00:03:20.160 So learn it. Faster you learn it, better for you. 38 00:03:20.160 --> 00:03:25.360 Especially in those labs, and you're looking at these equipment and there's a bunch of 39 00:03:25.360 --> 00:03:30.560 guys around you and they're talking about something and there is something you think, 40 00:03:30.560 --> 00:03:33.200 oh, I don't know what that is. Ask them. 41 00:03:33.200 --> 00:03:38.720 The stuff in the mechanical engineering, these are really, really awesome people. 42 00:03:38.720 --> 00:03:40.480 Very, very supportive. 43 00:03:40.480 --> 00:03:46.160 You will find out more you ask, more you're going to get. 44 00:03:46.160 --> 00:03:48.240 So this is how it works. 45 00:03:48.240 --> 00:03:54.240 The real numbers, the subset of the reals are the rational numbers, subset of those are 46 00:03:54.240 --> 00:03:58.280 the integers and subset of those are the natural numbers. 47 00:03:58.320 --> 00:04:03.800 I am not going to ask you any assessment questions on that. 48 00:04:03.800 --> 00:04:10.200 You see, those are the information which are not going to be written there. 49 00:04:10.200 --> 00:04:15.880 But those are little information which all of you should be writing like, not in XM, 50 00:04:15.880 --> 00:04:19.240 but little information like that. 51 00:04:19.240 --> 00:04:21.000 But useful. 52 00:04:21.000 --> 00:04:24.440 If you want to represent these things, you can stick it in the number line. 53 00:04:24.440 --> 00:04:25.440 So it's a straight line. 54 00:04:26.080 --> 00:04:27.280 We will make a straight line. 55 00:04:27.280 --> 00:04:31.040 There is an infinity that way, minus infinity that way. 56 00:04:31.040 --> 00:04:33.640 And I put zero somewhere here. 57 00:04:33.640 --> 00:04:36.840 So one will be here, two will be there. 58 00:04:36.840 --> 00:04:40.920 I will be somewhere in here. 59 00:04:40.920 --> 00:04:43.880 And minus two will be there. 60 00:04:43.880 --> 00:04:51.600 So you can demonstrate it graphically about these numbers and how are they laid out on 61 00:04:51.600 --> 00:04:52.960 the number line. 62 00:04:52.960 --> 00:04:55.360 So these are the numbers. 63 00:04:55.360 --> 00:04:58.960 We need to introduce those numbers because we are going to do math. 64 00:04:58.960 --> 00:05:03.960 So if you get to the higher level math, there are no numbers, just the letters. 65 00:05:03.960 --> 00:05:05.520 But it takes some time to get there. 66 00:05:05.520 --> 00:05:07.680 So first with the numbers. 67 00:05:07.680 --> 00:05:08.680 OK? 68 00:05:08.680 --> 00:05:11.840 Everybody OK with numbers? 69 00:05:11.840 --> 00:05:13.200 Good.