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GILBERT STRANG: Hi, I'm
Gilbert Strang, and professor

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of mathematics at MIT.

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And I get a chance
to say a few words

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about 18.06, Linear Algebra.

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It's one of the
basic math courses.

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Can I say a little about
linear algebra itself?

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Classes in linear algebra
earlier years tended

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

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

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Whereas, it's an
incredibly useful subject.

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Data is coming in all the time.

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We're in the century
of data, and data

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

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

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And people use matrices in
solving differential equations

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in economics, everywhere.

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So the subject had to
change to bring out

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this important aspect, that
it's terrifically useful.

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Often networks
are a great model,

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where you have like--
like the internet.

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Every website would be
like a node in the network.

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And if one website is
linked to another one,

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there would maybe be an
edge in that network.

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So that's a network
with a billion nodes.

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And a matrix describes
all those links.

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

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you could enter linear
algebra, and see what happens.

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I don't know.

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I hope something good.

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Well, anyway, thousands
and millions of stuff

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would come up ranked in
order, and that order

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

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

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describes the internet.

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

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First of all, there
will be students coming

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from all the departments.

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That includes management.

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Business data comes
in matrix form

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just the way
engineering data comes.

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So there is hardly a
prerequisite for the course.

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

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

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they will have multiplied
a matrix by a vector,

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or multiplied two matrices.

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So they've at least
seen matrices before.

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But anybody could catch
up on that quickly.

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And then, the course
just takes off.

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

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a matrix by a vector?

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

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

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produces a combination of
the columns in that matrix,

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those column vectors
in the matrix.

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

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What you can do with vectors
is take linear combinations.

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

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a week.

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And I use the chalkboard.

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

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The nice thing
about a chalkboard

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

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So your eye can
continually check back

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

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

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Because that's a
smaller class, it just

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means there's a
teaching assistant

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

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

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more explanation hours.

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So about the textbook.

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The homeworks come
from the book mostly.

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Sometimes we add
MATLAB problems, sort

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of specially constructed ones.

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But the central
ideas of the subject

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are described in each
section of the book,

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

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And then, the neat thing
about 18.06 Scholar

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

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did about six
problem-solving videos each.

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And they are neat.

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The TAs are good.

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And that's something that
can happen in the recitation

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with a smaller group.

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

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I still ask questions
in the lecture,

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as you'll probably see.

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But it's a little
harder for students

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to shout out an answer,
so they can shout all

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they want in their recitations.

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With each lecture, we
produce a written summary

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of what it's about.

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

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

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

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

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do I know what the
question is here?

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Do I know how to do it?

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

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A thought or two
about linear algebra

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worldwide, because it
really is worldwide.

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The feedback comes from
all over the world.

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It's really nice to get.

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Also, I enjoy going.

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So if somebody invites me to
Egypt or Australia or China,

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I tend to go if I can.

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Because that's a lovely
part about mathematics.

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It's really universal.

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It's a language
almost of its own

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that everybody can
learn to speak.

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And I hope these lectures help.