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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...

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...

Hi! My name is Vaibhav, and today we will learn about functions. Functions are very important concept, both for your engineering entrance exams and also to understand various concepts in mathematics. It's a very fundamental concept, and is used to describe a lot of phenomenon, including physical and chemical phenomena. And, also a lot of chapters we will learn further on such as limits, derivatives, continuity or be it any other chapter in mathematics, knowing functions is very important. It is a very fundamental chapter. It has various definitions, and so a lot of use for the next topics that you will learn. So, we will start with an intuitive definition of functions. Something that we will try to understand using examples, and then we will try to go into a more mathematically precise definition. Functions are used to describe, a special relation between two variables. So, here the word "relation" is a mathematical concept that we will understand later; but...

GUOLONG: That is Friday in one of the classrooms of Building 26, 11:00 AM. MARZIEH: So I was quite nervous. SHAWN: The first day is a little bit nervous for me. CARLA: I was nervous. I'm not going to deny it. NARRATOR: Facing your students for the first time can be a little scary, but it's also an opportunity to establish that your class will be user-friendly. BILLY: I think the first day of class really sets the tone for the rest of the semester. NARRATOR: How can you set the right tone? As they make their way to your classroom on the first day, what qualities are your students hoping for? BILLY: Being knowledgeable and understanding the concept. ADRIAN: And you need to feel that you can approach them. CHANDLER: Have just an air of confidence. ADRIAN: Being easy to understand. BILLY: And being enthusiastic. CHANDLER: Being there, having a presence, having a lesson plan ready. CAROL: They're well-organized. NARRATOR: That may sound like a lot. Let's start ...

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. PROFESSOR: Hi. Today we begin our final block of material in this particular course, and it's the segment entitled Infinite Series. And perhaps the best way to motivate this rather difficult block of material is in terms of the concept of many versus infinite. In many respects, this particular block could've been given much earlier in the course. But somehow or other, until we have some sort of a feeling as to what infinity really means, we have a maturity problem in trying to really grasp the significance of what's going on. In fact, in a manner of speaking, with all of this experience, there may be a maturity problem in trying to grasp the fundamental ideas. What I sha...