Shadowing and Lighting

I am currently reading the OpenGL Superbible, and I am on chapter 6, where the book discusses shadows. The book does a good job describing shadows conceptually, but it does a terrible job explaining mathmatically. Can anyone here give me a good mathematical explanation of shadows?

Dunno if this is a proper way of it but here goes.
you have an object above a floor, say. you have a light source
Get a vector from the light source to every vertex of the object and project it to the floor below. This way, the points of intersection between these vectors and the floor form the outline of the shadow. There is alot of other things to consider such as not considering the vectors which actually pass through the object, you only have to consider the vectors which pass thru the verteces but not through any of the faces. At least that is how i imagine shadows.