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the following content is provided under a Creative Commons license your support will help MIT open courseware continue to offer highquality educational resources for free to make a donation or view additional materials from hundreds of MIT courses visit mitop courseware at ocw.mit.edu so what is an 18821 p um well it's no more and no less than uh a presentation of the project that you've been working on as you've defined it and an account of the results that you've obtained in uh in studying that Pro problem and so these findings can come in many different forms um uh theoretical mathematics uh um you know the the gold standard is a proof a rigorous proof uh that's great if you can do it um that's great if the problem admits that kind of thing um but there are many other kinds of uh findings that you may want to report on in this report as well you may very well come up with things that you are damn sure are true but you can't figure out aof of...

One of the central tasks of this course has been to unpack the ways in which work in today's economy has changed over time. Often, when we talk about this topic, one of the first things that comes to mind is the role of technology in transforming work. Over the past few years, we have seen an explosion in what's known as the on-demand economy. It's visible everywhere. We as consumers are able to have our food delivered, grab a ride home, or even have someone run their errands, all purchased and arranged in a matter of minutes from our smartphones. Our colleague John McCarthy talks in more detail about these new ways of organizing work in a different video lecture in this course. What we're going to talk about now is how these employment arrangements are connected to two issues-- one, how we think about workers' rights in the on-demand economy, and two, how technology can promote new forms of worker advocacy in settings where gigs, not full-time jobs fo...

The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. MICHAEL: We're going to talk about the Wigner distribution function and integrate imaging. AUDIENCE: [INAUDIBLE]. MICHAEL: Yeah. So I'm going to start with a description of what a conventional camera does. A conventional camera produces one view of something. It does a pretty good job of imaging within a small range of distance from the camera depending on how you focus it. And what we can do is create optical systems which allow image sensor to capture multiple views. So basically, let's say, you have an array of tiny cameras that share one image sensor in the back, And one way of doing this is to use a pinhole or microlens array. So think of the pinhole cameras of yore...

PROFESSOR: Today's lecture continues the thing we're doing with scattering states. We send in a scattering state. That is an energy eigenstate that cannot be normalized into a step barrier. And we looked at what could happen. And we saw all kinds of interesting things happening. There was reflection and transmission when the energy was higher than the barrier. And there was just reflection and a little exponential decay in the forbidden region if the energy was lower than the energy of the barrier. We also observed when we did the packet analysis that a wave packet sent in would have a delay in coming back out. It doesn't come out immediately. And that's the property of those complex numbers that entered into the reflection coefficient. Those complex numbers were a phase that had an energy dependence. And by the time you're done with analyzing how the wave packet is moving, there was a delay. So today we're going to see another effect that is somet...

The question of how far we can go when we enhance, or adjust, or touch up an image in science is a critical one. You are all familiar, I'm sure, with the stunningly beautiful Hubble images published all over the world. But most of the world is not familiar with the fact that the colors we're seeing were artificially created, decided and implemented by humans. You can read a conversation I had with some of these researchers in American Scientist, in the resource section, look for this thumbnail. I think you'll find the article interesting, about the decisions the researchers made about coloring the detail of nebula. So in essence, the coloring, or enhancement, was mostly done for the purpose of communicating structure, and I would say also for helping bring attention to these amazing images. Now remember, these pictures of the universe, are representations, that is re- presentations, they are photographs of that universe, they are not the universe. All the phot...