How is math used in computer graphics? I'm doing a research paper on the mathematics of computer graphics and animation (3D) and I do not know where to start. What mathematical equations and concepts are used for computer graphics and animation (3D)?

Two main results that tend to form the core of 3D graphics:
(1) 3D coordinates are represented by matrices:
$$\begin{bmatrix} x \\ y \\ z \end{bmatrix}$$
Transforms (like rotations) are represented by matrix multiplication: 
$$\begin{bmatrix} \text{new-x} \\ \text{new-x} \\ \text{new-x} \end{bmatrix}
 = \begin{bmatrix} m_{1,1} & m_{1,2} & m_{1,3} \\ m_{2,1} & m_{2,2} & m_{2,3} \\ m_{3,1} & m_{3,2} & m_{3,3} \end{bmatrix}\begin{bmatrix} x \\ y \\ z \end{bmatrix}$$
Transforms like moving a point a given distance are represented by adding:
$$\begin{bmatrix} \text{new-x} \\ \text{new-x} \\ \text{new-x} \end{bmatrix}
 = \begin{bmatrix} \Delta x \\ \Delta y \\ \Delta z \end{bmatrix} + \begin{bmatrix} x \\ y \\ z \end{bmatrix}$$
A move and a transform can be combined into 1 operation, which is how your video card does it:
$$\begin{bmatrix} \text{new-x} \\ \text{new-x} \\ \text{new-x} \\ 1\end{bmatrix}
 = \begin{bmatrix} m_{1,1} & m_{1,2} & m_{1,3} & \Delta x \\ m_{2,1} & m_{2,2} & m_{2,3} & \Delta y \\ m_{3,1} & m_{3,2} & m_{3,3} & \Delta z \\ 0 & 0 & 0 & 1 \end{bmatrix}\begin{bmatrix} x \\ y \\ z \\ 1 \end{bmatrix}$$
So to begin with, your computer does most of it's coordinate representations and transforms with $4$ by $4$ matrices.
(2) 3D has to become 2D to appear on your screen
Converting the 3D coordinate of a shape into the 2D point on your screen is called projection, usually perspective projection but sometimes orthographic projection or something else.  
Here is a start of learning about 3D projections.
