Course overview
The following are the objectives:

understand the 3D rendering pipeline

gain a good understanding of what
RenderMan is  how it works, what it can do for you

learn to write basic & intermediate
level shaders

use MTOR to translate Maya scenes
suitable for rendering with RenderMan

understand some basic mathematics
useful in shaderwriting

learn what RenderManrelated resources
are available
Math concepts
Although it is possible to use
RenderMan without any knowledge of math, your experience with it would
be much more rewarding if you have an understanding of some fairly straightforward
concepts. These will be especially handy when you need to write your own
shaders.
The following are topics that
you need to be familiar with:

Coordinate systems
 Location, distance
 Reference frame
 Cartesian axes
 Polar coords

Points
 2D, 3D
 line segments
 distance between 2 points

Vectors
 scalar vs. vector
 magnitude, direction
 negation
 addition, subtraction
 multiplication with a scalar
 normalization
 dot product
 cross product
 tangent, normal, binormal
 matrices

Transformations
 RST [Rotate/Scale Translate]

Trigonometry
 right triangle, Pythagoras
Theorem
 sin(), cos() and tan()
 rotation about an axis

Color spaces
 RGB vs. HSV

Image representation
 RGB, Alpha channels
 Mipmap

Polygons
 convex vs. concave
 general polygons

Curves
 polylines
 splines

Surfaces
 primitives
 polymeshes
 patches

Interpolation
 linear interpolation
 step
 smoothstep
 spline

Math functions
 sin(), asin()...
 sqrt(), pow(), exp(), log()
 mod(), abs(), sign()
 min(), max(), clamp()
 ceil(), floor(), round()
 noise(), turbulence..
Rendering basics
A standard 3d rendering pipeline
aims to convert a 3D 'scene' (with objects and materials, lights and a
viewing camera) to an image, i.e. to a 2D representation.
Viewing transformation
 Object space
 World space
 Camera/eye space
 Camera projection
 Clipping against view volume
 Backface culling
Rasterization
 Screen space
 Image space
 Shading and illumination
[materials, lights]
Misc. topics
 Flat vs. interpolated shading
 Bump vs. displacement mapping
 Texture mapping
 Shadows
 Environment, reflections
Raytracing
Radiosity
Imagebased rendering