WEBVTT 00:00:06.220 --> 00:00:09.770 GILBERT STRANG: Hi, I'm Gilbert Strang, and professor 00:00:09.770 --> 00:00:11.200 of mathematics at MIT. 00:00:11.200 --> 00:00:16.309 And I get a chance to say a few words 00:00:16.309 --> 00:00:18.970 about 18.06, Linear Algebra. 00:00:18.970 --> 00:00:21.100 It's one of the basic math courses. 00:00:24.590 --> 00:00:26.780 Can I say a little about linear algebra itself? 00:00:29.840 --> 00:00:34.650 Classes in linear algebra earlier years tended 00:00:34.650 --> 00:00:40.130 to be pretty much for pure math majors, and a lot of proofs, 00:00:40.130 --> 00:00:46.390 and usefulness of the subject kind of wasn't so clear. 00:00:46.390 --> 00:00:50.110 Whereas, it's an incredibly useful subject. 00:00:50.110 --> 00:00:52.010 Data is coming in all the time. 00:00:52.010 --> 00:00:55.360 We're in the century of data, and data 00:00:55.360 --> 00:01:01.930 tends to come in a matrix, in a rectangular array of numbers. 00:01:01.930 --> 00:01:07.370 And how to understand that data is a giant, giant problem. 00:01:07.370 --> 00:01:12.460 And people use matrices in solving differential equations 00:01:12.460 --> 00:01:14.760 in economics, everywhere. 00:01:14.760 --> 00:01:19.330 So the subject had to change to bring out 00:01:19.330 --> 00:01:24.910 this important aspect, that it's terrifically useful. 00:01:24.910 --> 00:01:27.560 Often networks are a great model, 00:01:27.560 --> 00:01:31.550 where you have like-- like the internet. 00:01:31.550 --> 00:01:36.600 Every website would be like a node in the network. 00:01:36.600 --> 00:01:41.570 And if one website is linked to another one, 00:01:41.570 --> 00:01:45.530 there would maybe be an edge in that network. 00:01:45.530 --> 00:01:48.190 So that's a network with a billion nodes. 00:01:48.190 --> 00:01:54.720 And a matrix describes all those links. 00:01:54.720 --> 00:02:00.710 Like when Google produces a PageRank, you enter-- well, 00:02:00.710 --> 00:02:04.070 you could enter linear algebra, and see what happens. 00:02:04.070 --> 00:02:05.150 I don't know. 00:02:05.150 --> 00:02:07.450 I hope something good. 00:02:07.450 --> 00:02:10.139 Well, anyway, thousands and millions of stuff 00:02:10.139 --> 00:02:14.230 would come up ranked in order, and that order 00:02:14.230 --> 00:02:18.050 comes from operating-- Google's very fast at it, 00:02:18.050 --> 00:02:23.350 very good at it-- operating on that giant matrix that 00:02:23.350 --> 00:02:25.520 describes the internet. 00:02:25.520 --> 00:02:29.820 OK, so a word about the course itself-- the MIT course. 00:02:29.820 --> 00:02:34.160 First of all, there will be students coming 00:02:34.160 --> 00:02:37.090 from all the departments. 00:02:37.090 --> 00:02:38.970 That includes management. 00:02:38.970 --> 00:02:42.400 Business data comes in matrix form 00:02:42.400 --> 00:02:44.390 just the way engineering data comes. 00:02:47.910 --> 00:02:52.930 So there is hardly a prerequisite for the course. 00:02:52.930 --> 00:02:56.552 There's no big reason why calculus has to come first. 00:03:00.540 --> 00:03:04.980 Probably most MIT students will know before the course starts-- 00:03:04.980 --> 00:03:07.760 they will have multiplied a matrix by a vector, 00:03:07.760 --> 00:03:09.820 or multiplied two matrices. 00:03:09.820 --> 00:03:13.020 So they've at least seen matrices before. 00:03:13.020 --> 00:03:17.310 But anybody could catch up on that quickly. 00:03:17.310 --> 00:03:20.080 And then, the course just takes off. 00:03:20.080 --> 00:03:24.960 Actually, we go back to ask, how do you understand multiplying 00:03:24.960 --> 00:03:26.540 a matrix by a vector? 00:03:26.540 --> 00:03:30.340 A key-- yeah, you guys will probably know how to do it, 00:03:30.340 --> 00:03:34.970 but let me say it another way-- A matrix times a vector 00:03:34.970 --> 00:03:39.930 produces a combination of the columns in that matrix, 00:03:39.930 --> 00:03:43.040 those column vectors in the matrix. 00:03:43.040 --> 00:03:46.970 So that's like the key step in linear algebra. 00:03:46.970 --> 00:03:51.460 What you can do with vectors is take linear combinations. 00:03:51.460 --> 00:03:56.040 Well, at MIT, the course is organized with three lectures 00:03:56.040 --> 00:03:58.670 a week. 00:03:58.670 --> 00:04:02.540 And I use the chalkboard. 00:04:02.540 --> 00:04:06.756 I hope you feel, in watching them, that that's OK. 00:04:06.756 --> 00:04:08.130 The nice thing about a chalkboard 00:04:08.130 --> 00:04:14.150 is you get to see-- what's written doesn't disappear. 00:04:14.150 --> 00:04:17.630 So your eye can continually check back 00:04:17.630 --> 00:04:24.970 and see how does it connect with what's happening at the moment. 00:04:24.970 --> 00:04:28.630 And then, there is one hour a week of recitation. 00:04:28.630 --> 00:04:31.430 Because that's a smaller class, it just 00:04:31.430 --> 00:04:34.050 means there's a teaching assistant 00:04:34.050 --> 00:04:39.710 there, who can help with problems, suggest new problems. 00:04:39.710 --> 00:04:45.020 It can be a problem-based hour, where my lectures are 00:04:45.020 --> 00:04:47.550 more explanation hours. 00:04:47.550 --> 00:04:49.770 So about the textbook. 00:04:49.770 --> 00:04:53.180 The homeworks come from the book mostly. 00:04:53.180 --> 00:04:56.590 Sometimes we add MATLAB problems, sort 00:04:56.590 --> 00:04:58.940 of specially constructed ones. 00:04:58.940 --> 00:05:02.720 But the central ideas of the subject 00:05:02.720 --> 00:05:05.870 are described in each section of the book, 00:05:05.870 --> 00:05:10.880 and then, naturally, exercises to practice with those ideas. 00:05:10.880 --> 00:05:13.720 And then, the neat thing about 18.06 Scholar 00:05:13.720 --> 00:05:20.220 is you get short lectures, short videos, from six different TAs, 00:05:20.220 --> 00:05:23.420 did about six problem-solving videos each. 00:05:23.420 --> 00:05:24.693 And they are neat. 00:05:24.693 --> 00:05:27.530 The TAs are good. 00:05:27.530 --> 00:05:31.780 And that's something that can happen in the recitation 00:05:31.780 --> 00:05:33.101 with a smaller group. 00:05:35.810 --> 00:05:39.370 There's chance for a discussion, whereas in the lecture-- well, 00:05:39.370 --> 00:05:41.610 I still ask questions in the lecture, 00:05:41.610 --> 00:05:43.970 as you'll probably see. 00:05:43.970 --> 00:05:48.110 But it's a little harder for students 00:05:48.110 --> 00:05:52.210 to shout out an answer, so they can shout all 00:05:52.210 --> 00:05:54.410 they want in their recitations. 00:05:54.410 --> 00:05:57.690 With each lecture, we produce a written summary 00:05:57.690 --> 00:05:59.780 of what it's about. 00:05:59.780 --> 00:06:02.950 So after you watch the lecture, you could look at that summary 00:06:02.950 --> 00:06:08.700 and it reinforces, remembering the key points of the lecture. 00:06:08.700 --> 00:06:13.170 And then we also added in some problems, four or five 00:06:13.170 --> 00:06:18.410 problems from the book that you can just look at and see, OK, 00:06:18.410 --> 00:06:20.570 do I know what the question is here? 00:06:20.570 --> 00:06:23.310 Do I know how to do it? 00:06:23.310 --> 00:06:27.740 I think, as a result, you're learning linear algebra. 00:06:27.740 --> 00:06:29.790 A thought or two about linear algebra 00:06:29.790 --> 00:06:33.950 worldwide, because it really is worldwide. 00:06:33.950 --> 00:06:36.930 The feedback comes from all over the world. 00:06:36.930 --> 00:06:40.380 It's really nice to get. 00:06:40.380 --> 00:06:42.550 Also, I enjoy going. 00:06:42.550 --> 00:06:48.170 So if somebody invites me to Egypt or Australia or China, 00:06:48.170 --> 00:06:51.850 I tend to go if I can. 00:06:51.850 --> 00:06:54.820 Because that's a lovely part about mathematics. 00:06:54.820 --> 00:06:57.580 It's really universal. 00:06:57.580 --> 00:07:01.110 It's a language almost of its own 00:07:01.110 --> 00:07:07.250 that everybody can learn to speak. 00:07:07.250 --> 00:07:11.160 And I hope these lectures help.