Math Nodes
OK this is the one you've been waiting for, right? Note that most math functions will operate on both scalars and vectors (and colors, which are treated as vectors). It even works for some strange things (e.g. division) which aren't well-defined for vectors.
abs returns the "absolute value" (i.e. positive size), so abs(-2) = 2.
add adds two values
cosine and sine and tangent are your usual trig functions (they work in radians). To get an intuitive grasp of trigonometry for 3d, the cosine of an angle is a measure of how parallel the lines forming that angle are to each other: 1 means exactly parallel (the angle is 0), -1 means exactly opposite (the angle is π radians -- 180°), and 0 means perpendicular. Sine is the other way around -- perpendicular = -1 or 1, and parallel or opposite = 0.
dotprod is a scalar value telling you how parallel two vectors are. For unit vectors, the dot produce is the same as the cosine of the angle they form; for non-unit vectors multiply the cosine by the product of the vectors' magnitudes. crossproduct is the dual of dotprod, returning a vector perpendicular to the plane containing the two vectors whose magnitude is the sine of the angle they form multiplied by the product of their magnitudes.
divide divides one value by another.
float2vec and vec2float let you pull vectors apart and put them back together again.
mix blends two colors using a third value. Actually it should be in the Filter menu. Or it should be changed to accept vectors.
modulo turns an open-ended value t into a repeating value by "wrapping" it into the interval [0 .. denominator]
multiply multiplies two values
multiplyadd multiplies two values and then adds a third value
norm returns the magnitude of a vector (this is a correction). To unitize a vector scale it by the inverse of its norm.
power raises a number to a power.
pulse takes an input value and maps everything below the lower threshold or above the upper threshold and maps it to 0 (black), and maps the rest to 1 (white). Smooth makes the transition smooth rather than sudden.
pulsetrain is like pulse but it performs the mapping 1/period times across the [0,1] interval. Um, that's not very user-friendly. It's like pulse but you it scales the input by 1/period and then wraps it back to [0,1] and it only has a lower threshold value. Play with it it's trippy.
squareroot calculates square roots. Same as using power and 0.5.
step is like pulsetrain but upside down and with only one threshold value.
subtract subtracts one thing from another.