Name: 課程介紹｜MIT 18.06SC 線性代數 (Course Introduction | MIT 18.06SC Linear Algebra)
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GILBERT STRANG: Hi, I'm Gilbert Strang, and professor

Can I say a little about linear algebra itself?

Classes in linear algebra earlier years tended

to be pretty much for pure math majors, and a lot of proofs,

and usefulness of the subject kind of wasn't so clear.

Whereas, it's an incredibly useful subject.

tends to come in a matrix, in a rectangular array of numbers.

And how to understand that data is a giant, giant problem.

And people use matrices in solving differential equations

So the subject had to change to bring out

this important aspect, that it's terrifically useful.

Every website would be like a node in the network.

And if one website is linked to another one,

there would maybe be an edge in that network.

So that's a network with a billion nodes.

Like when Google produces a PageRank, you enter-- well,

you could enter linear algebra, and see what happens.

Well, anyway, thousands and millions of stuff

would come up ranked in order, and that order

comes from operating-- Google's very fast at it,

very good at it-- operating on that giant matrix that

OK, so a word about the course itself-- the MIT course.

First of all, there will be students coming

So there is hardly a prerequisite for the course.

There's no big reason why calculus has to come first.

Probably most MIT students will know before the course starts--

they will have multiplied a matrix by a vector,

So they've at least seen matrices before.

But anybody could catch up on that quickly.

Actually, we go back to ask, how do you understand multiplying

A key-- yeah, you guys will probably know how to do it,

but let me say it another way-- A matrix times a vector

produces a combination of the columns in that matrix,

So that's like the key step in linear algebra.

What you can do with vectors is take linear combinations.

Well, at MIT, the course is organized with three lectures

I hope you feel, in watching them, that that's OK.

is you get to see-- what's written doesn't disappear.

and see how does it connect with what's happening at the moment.

And then, there is one hour a week of recitation.

there, who can help with problems, suggest new problems.

It can be a problem-based hour, where my lectures are

are described in each section of the book,

and then, naturally, exercises to practice with those ideas.

And then, the neat thing about 18.06 Scholar

is you get short lectures, short videos, from six different TAs,

did about six problem-solving videos each.

And that's something that can happen in the recitation

There's chance for a discussion, whereas in the lecture-- well,

to shout out an answer, so they can shout all

With each lecture, we produce a written summary

So after you watch the lecture, you could look at that summary

and it reinforces, remembering the key points of the lecture.

And then we also added in some problems, four or five

problems from the book that you can just look at and see, OK,

I think, as a result, you're learning linear algebra.