So I understand that data and the manipulation of the data comes from the math of working with vectors and functions, but it also seems that computers do their calculations based off of points/pixels. I guess what I'm trying to ask is the fundamental question: what are computers "really" manipulating (i.e. vectors, functions, pixels, matrices using vector manipulation techniques, or some combination of this)?
@dvanmali Depending on who you ask, computers are really manipulating binary values in registers, which can represent all kinds of data; different semantics will be associated with this data based on context. One possible hierarchy of abstraction is that computers manipulate binary data, which in turn represent numbers, which in turn represent objects from linear algebra (such as vectors and matrices), which in turn represent objects like vectors and linear maps, which in turn may represent... all sorts of stuff. Our class on computer graphics focuses on this final layer of abstraction: how can we encode geometric and graphical objects as objects from linear algebra and vector calculus---so that these objects can be encoded as numbers, which can be encoded as binary data, which can be manipulated by digital computers. :-)