This is CS50, and this is Yale University.

Welcome to the grand finale.

Really, this is the last lecture of the course.

And I hope to interpret most of you when I say, wow, already?

And indeed, just think where we started off two, three months ago.

What we have achieved is simply unbelievable.

And typically, it's a good sign.

When time flies by, it means that we have been engaged a lot.

We have been learning a lot.

This is precisely the type of experience that we want to give as part of CS50.

So now today's is the last lecture, but the course

does not end here, as David will remind all of us in a bit.

In particular, the hackathon is coming up.

It's a great opportunity to meet friends in Cambridge, I thought,

but while potentially working on your final project.

And then while you're here in New Haven, the final

CS50 [? for ?] a great occasion to showcase

what you have achieved in these two, three months, and to present

this type of output not just to a friend of yours,

but really to the entire Yale community and beyond.

So this is CS50.

Indeed, today does not end year, but in a way,

we should start thinking about life beyond CS50.

And well, let me tell you, it does exist.

And so we decided to take the opportunity of the last lecture

to invite a few friends-- faculty from Yale College--

to present some of the great resources that Yale can offer to those of you who

want to dive more deeply into the realm and the wonder of CS

as a discipline and related fields.

So I'm going to introduce to you a few friends, faculty.

I would like to welcome all of them with a big round of applause.

So please join me in this.

[APPLAUSE]

And I have the pleasure to introduce Holly Rushmeier from the computer

science department.

Thank you, Holly.

HOLLY RUSHMEIER: So, yes, I'm Professor Rushmeier.

I am on the computer science faculty.

I teach a variety of courses.

Right now I'm teaching CPSC 201, Introduction

to Computer Science-- a course that I really love,

because it has the core ideas of computer science in it.

But another area that I really love, and what I do my research in,

is computer graphics.

And that's what I'll spend my few minutes here on.

And basically, what is computer graphics?

It's using computers to make and use images for exploration, communication,

and expression.

So exploration-- how do we understand things?

One of the things that we can do is read and write about things

to improve our understanding.

We also can explore things by drawing, gathering pictures, and manipulating

images.

We use graphics a lot for communicating ideas.

Creating a feature film-- that's communicating ideas.

That's telling a story.

Advertisements, documentaries-- all these things are using images.

And we have a part to play in creating those images.

And then some of it is just purely creative expression.

These images here are from some of our research work

here at Yale, including things like-- we're

interested in designing what makes things look like what they look like.

And that's a combination of their small-scale geometry-- whether they've

got little rings or bumps, or how they're woven--

and their large-scale geometry.

We're also interested in abstract visualizations to make things clearer.

So these strange little spheres floating and inside the matrix

are an illustration of a kind of calculation.

And we're interested in systems that help people.

So these images are showing a sculpture of the Madonna

from the Yale art gallery.

This is part of a system that we've created for art conservators

to study works of art using data from different imaging modalities.

And then on the bottom is another visualization.

It's visualizing the results of a perceptual experiment

that we did about how things look when they move.

So just a little bit of the span of things

we consider in computer graphics.

A little bit about-- another way of looking at graphics

is that we observe problems in the real world.

People want to design something new.

They want to tell something new.

They want to understand something new.

And we're going to produce something in the real world.

We're going to make pictures.

We're going to make objects.

But what we do in computer graphics is we get those physical things

we observe into the computer, and then we

create the data, data structures, algorithms, to work with those objects,

to create the solutions that then allows us

to make those things in the real world.

So in the physical world, we may be simply observing

shapes and forms and colors and lights and how people perceive things.

Or we may be using instruments to measure shapes and colors.

We may be designing new instruments or conceiving

of new ways of putting existing instruments together.

And we may just be observing how people perceive things,

or we may be doing psycho-physical experiments to figure out

how people perceive things.

So then we bring them into the computer.

We think of new ways to represent objects, shapes, colors,

their interaction.

We've-- how people can interact with those shapes to create new things.

What are good interfaces for people to create new things,

to express themselves, or to explore an idea?

And then we put things out into the physical world.

I had sort of a-- images from my oldest work and some of my newest.

My oldest work-- that's from like 30 years ago--

was when we were first trying to make images that would

be indistinguishable from real scenes.

So we were building a real scene-- a real simple scene--

and trying to make a physical image that looked exactly like it

and then set up an experiment where the challenge is, well, gee,

that's a real physical box.

That's a picture of a box.

We had to come up with the solution to overcome that.

So here at Yale, you have graphics courses.

You can take straight-up the standard computer graphics,

some special topics-- including a new one

that we have in computational issues in design and fabrication.

And we have a wide range of projects that people can work on,

including-- in particular, in my work-- I'm

very interested in digital humanities and analyzing

the shape and form, materiality, of things like manuscripts.

Cultural heritage-- maybe you want to get out in the cemetery at night

and take data and start examining old stones.

Or we have more hardcore computer graphics--

new methods for sketching, extracting, and reusing textures and building

new scanning systems.

So those are some ideas.

So thank you very much.

PATRICK REBESCHINI: Wonderful.

Our second guest today is Amin Karbasi, from the computer science and the EE

department.

So Amin, all yours.

AMIN KARBASI: Hello.

So I thought today that I'm going to talk about sensing data.

So basically, my work is about, in the realm

of big data, how we can actually reason about-- how

we can pick and reason about very uncertain data

and get useful information.

And in particular, I'm going to talk about three very specific applications.

The first one is the video summarization.

So what it means is that it would be really cool if instead of listening

to the whole CS50 lectures, there would be an algorithm that tells us

these parts are the most important part to look at.

The second application is going to be about automated teaching.

So instead of Patrick and David teaching you,

it would be really cool if a machine can teach you new concepts.

And the third one is about whether a robot can actually learn and reason

about the environment.

OK.

So the first application that I'm going to talk about

is the video summarization.

I'm going to show you a very short clip, and the idea here

is that we have an algorithm that picks frames of this short clip such

that if you look at these frames-- here are four-- you can basically

understand what is happening.

OK, so we can put these frames together and it tells a story.

OK, so that is one application, and we had worked on this one.

The second application that I'm going to talk to is about automated teaching.

So here the idea is that instead of-- so I

want to teach you a new concept without telling you

how to learn this new concept.

I am just going to show you some examples.

And so in particular, I made some imaginary insects.

I even called them vespula and weevils.

You have not seen them before.

And I'm going to show you examples.

I need you to cooperate.

And then you have to tell me whether this is a vespula or weevil.

In the beginning, you may not have any idea.

But you're smart-- I hope that after a few examples you can actually tell OK.

Ready?

Good.

OK.

So that is the first example.

Who thinks that's a weevil?

Raise your hand.

Who thinks that's a vespula?

OK.

So that is a vespula.

OK.

Good.

Now, how about the second one?

Who thinks that's a weevil?

Who think that's a vespula?

OK, that's a weevil.

OK.

How about the third one?

Weevil?

Vespula?

Very good.

OK.

And the last one.

Weevil?

Vespula?

Excellent.

I didn't tell you how to distinguish between them.

Somehow, you actually figured it out, right?

So that is the main idea of automated teaching through examples.

And then we also-- the question is, among all possible examples

that I could show you, I chose them very specifically such

that you basically get the concept and then generalize it in your head.

And the last example that I'm going to show you is about the work

that we did on a real robot.

So here the idea is that there is a robot that

has to open the door of a microwave.

It has a visual sensor, but the sensor is not actually very good.

So the robot doesn't know exactly where the door is.

It might be a little bit high, low, it might be tilted,

rotated-- so the robot has to make sense of the environment.

How does it do it?

Well, by basically touching different points and reducing the uncertainty.

The question is, among all possible positions that the robot can touch,

which ones are going to give the robot the most amount of information?

So let's look at how a robot does that and how we actually

taught the robot to do it.

So this is the uncertainty that the robot has.

In the beginning, it is very uncertain.

It touches one point.

Some of the uncertainty collapses.

Some remains, so the robot has to make more interactions with the environment.

It touches another point.

Now there are less uncertainty, more information,

but it doesn't exactly know where the button is.

And then finally, it's going to touch another point.

And now it is very certain where the button of the microwave door is.

And now it's going to open it.

Good.

So basically, I talked about three different problems,

and in all these problems, the question was,

which frame we should pick, which example we should show,

which position we have to touch.

These are very different applications, but it turns out

that they have exactly the same framework.

And this is what they work on.