GILBERT STRANG: Hi, I'm
Gilbert Strang, and professor
of mathematics at MIT.
And I get a chance
to say a few words
about 18.06, Linear Algebra.
It's one of the
basic math courses.
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.
Data is coming in all the time.
We're in the century
of data, and data
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
in economics, everywhere.
So the subject had to
change to bring out
this important aspect, that
it's terrifically useful.
Often networks
are a great model,
where you have like--
like the internet.
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.
And a matrix describes
all those links.
Like when Google produces a
PageRank, you enter-- well,
you could enter linear
algebra, and see what happens.
I don't know.
I hope something good.
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
describes the internet.
OK, so a word about the course
itself-- the MIT course.
First of all, there
will be students coming
from all the departments.
That includes management.
Business data comes
in matrix form
just the way
engineering data comes.
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,
or multiplied two matrices.
So they've at least
seen matrices before.
But anybody could catch
up on that quickly.
And then, the course
just takes off.
Actually, we go back to ask, how
do you understand multiplying
a matrix by a vector?
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,
those column vectors
in the 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
a week.
And I use the chalkboard.
I hope you feel, in watching
them, that that's OK.
The nice thing
about a chalkboard
is you get to see-- what's
written doesn't disappear.
So your eye can
continually check back
and see how does it connect with
what's happening at the moment.
And then, there is one
hour a week of recitation.
Because that's a
smaller class, it just
means there's a
teaching assistant
there, who can help with
problems, suggest new problems.
It can be a problem-based
hour, where my lectures are
more explanation hours.
So about the textbook.
The homeworks come
from the book mostly.
Sometimes we add
MATLAB problems, sort
of specially constructed ones.
But the central
ideas of the subject
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 they are neat.
The TAs are good.
And that's something that
can happen in the recitation
with a smaller group.
There's chance for a discussion,
whereas in the lecture-- well,
I still ask questions
in the lecture,
as you'll probably see.
But it's a little
harder for students
to shout out an answer,
so they can shout all
they want in their recitations.
With each lecture, we
produce a written summary
of what it's about.
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,
do I know what the
question is here?
Do I know how to do it?
I think, as a result, you're
learning linear algebra.
A thought or two
about linear algebra
worldwide, because it
really is worldwide.
The feedback comes from
all over the world.
It's really nice to get.
Also, I enjoy going.
So if somebody invites me to
Egypt or Australia or China,
I tend to go if I can.
Because that's a lovely
part about mathematics.
It's really universal.
It's a language
almost of its own
that everybody can
learn to speak.
And I hope these lectures help.
