I've written some articles that might be useful to you. Have fun.
Derivation of Phong and Blinn-Phong BRDF normalization factors (PDF) - for two typical formulations, anyway.
I wrote this in the early 2009, when the question came up in a blog post I came across. Useful to know if you're interested in
physically correct (or at least plausible) rendering.
DCT-II vs. KLT/PCA (PDF) - short derivation of the relation between DCT-II and the KLT for stationary
Markov-1 signals. This is basically the derivation from
“Discrete Cosine Transform:
Algorithms, Advantages, Applications” by Rao and Yip, but condensed and with less sign errors, and with plotted basis
functions that actually match the equations :). I derived this for a presentation at University, but it's good to know no matter what.
The ubiquitious SSE vector class - pretty old opinion piece, seriously outdated
by now (compilers got a lot better at intrinsics). I mainly keep this here in case someone linked to it.