Open course ware

PROFESSOR: Continue today. We're still in the spirit of origami. And we're going to do some origami design and foldability again. There are two main topics here on the design side we're going to talk about-- universal hinge patterns, which are the things that make underlying this robot, which I showed in lecture one. You may recall. So it's called a box pleat pattern. It's a square grid with alternating diagonal creases. And the idea with the robot is you're constrained to only-- you have to build the creases ahead of time. You can't say, you can't build one sheet that can fold anywhere at anytime. You want to build a sheet that can fold at any of the crease lines, at the built crease lines whenever you want. And so whereas with something like Origamizer, every design has a completely different crease pattern and it's difficult to control that, here we wanted to make one. It's not exactly a crease pattern, because you're not usi...

CASEY RODRIGUEZ: We'll continue our discussion of the Riemann integral. So let me just recall a few bits of notation from last time and then also, the main result that we proved at the end of last class. So we had partitions, which are just finite sets. So here, a is less than b, and we're looking at an interval ab. Partitions, they're just finite sets of ab. And then we also had tags, which were finite sets as well with c one between x0 and x1, which is less than or equal to xi 2, which is less than or equal to x2 and so on. And we call these tag partitions. And we also had the norm of a partition. This is the max of-- so we think of partitions as being-- as breaking up the interval ab up into smaller subintervals, x0 up to x1. I got to get a different piece of chalk. This one is going psychedelic on me. And then the xi ones are just points chosen in these smaller subintervals. The norm of a partition is the length of the largest subinterval. And then we had ...

PROFESSOR: We're going to continue with some neuroanatomy today. Leading up to the next anatomy unit, we've been talking about what happens when you remove large parts of the brain, like the [INAUDIBLE] brain, the chronic decerebrate animals. I talked a little bit about corpus striatum, what about the limbic system? If-- let me get my pen up here. This shows the Shmoo Brain. I put the outline there of the neocortex, which is what we're adding now. But here, I've put the limbic system structures in red so you know what we're talking about. You'll see the close connection to the olfactory system. This is representing olfactory cortex and cortex closely connected with it. Behind the basal forebrain there is the hypothalamus. And we define the limbic system as structures that are-- we closely connected with the hypothalamus, which is really the highest part of the brain, our ancestral brain here, the Shmoo one. Limbic systems generally concerned with m...